TAXATION AND RISK-TAKING

TAXATION AND RISK-TAKING

RISK TAKING AND PORTFOLIO ALLOCATION

Uncertainty is a feature of any economy , and attitudes towards risk taking are likely to play an important role in determining economic performance. Even in advance economies , where large corporations seek to reduce uncertainty , the rate at which new products and new techniques are developed still depends crucially on the taking of risks and the availability of finance for risky ventures. This has led in turn to concern that the tax system may discourage risk-taking and the supply of funds to finance it.

Taxation may influence risk-taking at two levels.It may affect portfolio decision by household (or institutions) and hence the availability of funds ; or it may affects the real investment decisions made by businesses and individuals . From the standpoint of the growth of the economy , it is the latter that are directly relevant ; however , the influence on financial markets is an important intermediate stage in the process. Most of the (substantial) literature on this subject deals with financial or portfolio decision , and the analysis here is (with one exception ) couched in these terms . At the same time , the real investment side is clearly important . In some cases the results for household portfolio behaviour can readily be translated to the investment policy of firms , and we return to this subject at the end of the lectured.

The principal issue is the effect of taxation on “ risk-taking”. The interpretation of this concept is not entirely straightforward. And we base much of the analysis on a case where it is clear-cut – where there are only two assets , a simple assumption about the individual’s objective function , which is taken to be the maximization of the expected utility from terminal wealth.In section 4-4 we discuss the relationship between this and the savings decisions examined in the previous lecture.

The basic portfolio model is described below . section 4-2 then present an analysis of the impact of income and wealth taxation in the two-asset model. Section 4-3 considers the effect of a number of special provisions of the tax code and their economic rationale . Section 4-4 extends the treatment in several directions , including the interaction with savings decisions , and a simple general equilibrium version of the model . The relationship between the theoretical result and observed behaviour is discussed briefly in the concluding section 4-5.

The taxes considered in this Lecture are principally those on income and wealth , with somne references to capital gains taxation. It is these that have attracted most attention in discussions of risk-taking , and there is a widespread popular feeling – not shared by many economist – that the substitutions of a wealth tax for income taxation would encourage risk-taking.

Our concern in this Lecture is with the positive question as to whether or not taxes discourage risk-taking ; we do not examine the presumption , implicit in much public discussion , that a discouragement would be socially undesirable . The welfare economics of a change in in risk- taking raises a number of difficult issues , including the criteria for optimality under uncertainty (e.g ,. Ex ante versus ex post welfare) . At the same time , we need to make the distinction between risk-taking by individuals and firms, or private risk-taking and, the total risk-taking in the economy , which we refer to as social risk-taking . It is quite possible that a tax may lead to individuals reducing their risk-taking but to the government’s assuming a greater degree of risk . Via uncertain tax receipts . Private and social risk-taking may move in opposite directions.

This may be illustrated by a simple case, which also serves as an introduction to the portfolio model with two assets . Suppose that the safe asset yields zero return and that a fraction a of the person’s intial wealth Ao is invested in the risky asset . The individual maximizes the expected utility of terminal wealth ,. A which depends on the uncertain return , x, per dollar of the risky asset invested . A is in fact equal to Ao (1+ax) . Denote the value chosen by a*. Suppose now that the government introduces a proportional income tax, at rate ti, so that x becomes x (1-ti ,) and that this applies for all values , including those where he makes a loss (x<0).If the individual can increase a to a*/ (1-ti), then he can secure for himself just the same level of before . in such a situation , private risk - taking measured by the net of larger fraction of the portfolio is invested in risky assets. this example brings out one further factor - that government revenue is uncertain . This introduces the question of the basis for comparison of taxes. It may not be feasible , for example , to secure equal revenue with all possible outcomes. one obvious posibility is ti compare taxes with the same expected revenue , and this is particulary appealing where the individual risks are not independent distributed. On the other hand , where individual risk are not independent , the government may have preferences concerning the distribution of revenue over diffrent outcomes. among other things , this draws attention to the need to consider the kind risky event that we have in mind - whether it is competitive risk, uncertainty surrounding technology , due to cyclical variations, etc, or whether indeed it is " political " risk concerning future changes in tax rates (Ekern, 1971)

PORTFOLIO MODEL

The basic portfolio model is that sketched above , except that we allow more generally for a non - negative rate of return , r , per dollar of safe asset invested , and that we explore more fully the way in which portfolio decisions depend on the utility function . It is assumed that neither x not r depends on the amount invested . As described , the individual maximizes expected utility from wealth at the end of the period, where this depends solely on the intial purchase of asset . it is assumed that the utility function is strictly concave , which implies that he is risk-averse ,i,e,. he prefers a safe wealth of A to a random distribution with mean equal to A (see the note at the end of the lecture ) . If we denote by E the expectations operator , then he chooses the proportion a invested in the risky asset to maximize

E[ U(A)] ≡ ∫{ Aₒ [ 1 + ax + ( 1 – a )r ]} Df

where U ' . 0 , U" , 0 and F (x) denotes the cumulative probability distribution of x with x > -1.

The first order conditions depend on the constraints on a . Here we assume that he can borrow as well as lend at the sure rate of return but that a is constrained to be non-negative . In other words, he cannot issue risky securities (the extension can readily be made). The first-order conditions for expected utility maximization are then

∂ E (U)= E [U’. (x-r)] = 0……………….4-1a

∂a

Or, E [U’. (x-r)] < 0 and a= 0 …………..4.2a

The assumption that the individual is risk averse (U” < 0) is sufficient ensure that the second –order conditions are satisfied. Since U” independent of x for a = 0 , we can see from (4-2b) that a corner condition (a=0) occurs if the safe . In what follows we concentrate on the interior solution , assuming x > r , and a finite degree of risk aversion.

In order to illustrate the working of the model , let us take the quadratic utility function

U (A) = Ba – Ab- A ²/ 2

Where b > 0 and A < b . This function received considerable attention in the early literature (Tobin, 1958; Markowitz , 1959 ; and Hicks , 1962). The first – order condition for an interior solution is (from (4-2a))

E[(b – A )- (x-r)] =0

E {[ b- Aₒ (1+ r) – aAₒ (x-r) ] }= 0

aAₒE[(x-r)²] = [ b - Aₒ(1+r)] (x-r)

We can deduce that the demand for risky assets (aAₒ) is a linear function of wealth (Aₒ) and that is decreasing , since x> r . The fact that the risky asset is an inferior good is an unattractive and implausible feature of the quadratic utility function (Arrow, 1965)

Utility functions that may be more plausible , but that also yield linear demand functions for assets , are as follows.

^{wealth
state in (2)}

A₀(1+ r)

P Indifference curve

A₀(1+ x₂) T

45⁰ A₀(1+ r) A₀(1+ x₁)

Wealth in state (1)

Figure 4.1 portfolio possibilities where two outcomes to investment (two state of nature)

For much of the analysis we focus on a special case of the model which allows a convienent graphical representation. There are two “ states of the world” ( outcomes of the invesment decision)

State (1) . Risky asset yields more than the safe asset : (x₁> r)

State (2) . Risky asset yield less than the safe asset : (x₂ < r)

The individual’s opportunity locus is depicted in Fig 4-1 . , Where is wealth in state (1) is measured along the horizontal axis and his wealth in state (2) on the vertical axis. If all wealth is used to buy the safe asset , he is at the point S on the 45 ⁰ line ,i.e. he obtains the same income in bith states of the world. If all wealth is invested in the risky asset , he is at the point T , representing a wealth of A₀(1+ x₁) in state (1) and A₀(1+ x₂) in state (2) , By mixing his portfolio , he can attain any point on the line ST. (i.e., 0 ≤ a ≤ 1) or its extension beyond T (a > 1) where he is borrowing . His expected utility is

E(U) = p₁U {([1+ r ) + a( x₁- r) A₀ } + p₂U {([1+ r ) + a( x₂- r) A₀ } (4.5)

Where p₁ is the probability of state (i) (p₁ + p₂ = 1) . The resulting indifferent curves (i.e., giving constant expected utility , E(U) = constant ) are illustrated in fig . 4.1 , In the case shown , the portfolio choise is P , and a is equal to the ratio of the distance SP to ST.

WEALTH AND PORTFOLIO ALLOCATION

In the subsequent discussion , certain properties of the portfolio allocation are crucial , particularly the response to an increase in the level of wealth . This moves the budget constraint in a parallel manner -- see Fig 4-2a - and the new point correspodensing to a given value of a is found by moving along a ray through the origin . Thus , the new point T, where a = 1 , lies on the ray through T . The locus of point chosen as wealth changes is called here the wealth – portfolio locus, analogous to the income –consumption curve. If it is a ray through the origin as in Fig 4.2a , this mean that as wealth increases the proportion of total asset allocated to the risky asset remains unchanged . This is the case corresponding to a exercise 4.2 ,. If on the order hand, the wealth – portfolio locus bends down , the proportion allocated to the risky asset increases with wealth (as in Fig 4-2b) . If all of an increase in wealth goes into the safe asset, there is an equal increment in terminal wealth in the two states of the world . Diagrammatically , this case , which corresponds to Exercise 4-1 , gives a wealth – portfolio locus with a slope of 45⁰ (Fig 4-2d) . Thus, the wealth – portfolio locus has a slope less than 45 ⁰ if the wealth elasticity of demand for the risky asset is greater than zero.

The wealth – portfolio locus is empirically observable (for example , from cross- section data) , and this raises the question of the precise identification of the safe and risky assets. In much of the literature (e,g,. Tobin , 1958). They are identified as money and bonds , respectively , in which case the return to the safe asset is zero in cash terms. On the other hand , this does not allow for uncertainty concerning the price level . As long as good prices are uncertain, all financial assets have some risk, in terms of the the consumption which they can generate . Financial asetts have in certain periods appeared to be more risky than equities that were thought to provider better “hedges” against inflation.

Even in the absence of inflation , it is not always obvious what is to be treated as the safe asset. For an individual who consumes no housing , the purchase of a house is risky , if the price of houses varies relative to the prices of the commodities he does purchase . For an individual who is planning to consume his wealth one period from now, a one-period bond is safe and a two-period bond (with variability in its capital value) is risky . For an individual planning to consume his wealth two-period from now.

Wealth in state (2) S’ Wealth in state (2)

P’ S’

S T’ P’

P T S P T’

45⁰45⁰

Wealth in state (1) Wealth in state (1)

(a)

(b)

Wealth in state (2) S’ Wealth in state (2)S’

P’ P’

S T’ S P T’

P T

45⁰45⁰

Figure 4-2 . Wealth portfolio loci- different case : (a) wealth elasticity of demand for risky asset = 1 (same portfolio composition at all wealth levels) ; (b) wealth elasticity of demand for risky asset greater than unity (increasing proportion of wealth allocated to risky assets as wealth rises) : (c) wealth elasticity of demand for risky asset greater than zero but less than unity ; (d) wealth elasticity of demand for risky asset equals zero.

Investing in a one – period bond and then reinvesting is a risky investment strategy ; purchasing a two –period bond is safe (stiglitz , 1970b) . Whether a particulary asset is risky or not depends not only on the individual’s consumption plan, but also on what other assets are available to him. For instance , if the individual hold a large portfolio of equities , and if long-term bonds are negatively correlated with equities , then the bond provide a kind of insurance ; he may be wiling to hold long-term bonds even if the expected return were lower than the safe rate of interest . Thus, the application of the model requires a good deal of caution.

4-2 EFFECTS OF TAXATION

Taxation affects both the returns to different assets and the degree of risk. The latter is clearly very important . When losses can be fully offset and taxes are propotional , the government becomes in effect a non- voting partner in the enterprise.

We consider here proportional taxes on wealth (at rate t_w) and income (at rate t_i) with the revenue used to finance government spending , which enters U in an additively separable fashion . The terminal wealth depends on the assumptions made about (1) the extent to which losses may be set against taxation and (2) the tax deductibility of interest paid on borrowing (where a > 1) . It is assumed initially that there are full loss offsets and full deductibility . The equation for terminal wealth becomes therefore.

A = (1-t_w) {1 + [ r + a(x-r )] (1-t_i)} A₀ (4.6)

And the first –order condition for an interior solution for expected utility maximization :

(1-t_w) (1-t_i) E[U’.(x-r)] = 0 (4.7)

Since the term (1-t_w) (1-t_i) may be cancelled , this has the same form as (4-2a) , and this applies also to (4-2b) . On the other hand , this does not imply that a is unaffected by taxation. Since the argument of U’ is terminal wealth , which depends on t_it_{w .}

In particular we can see at once that (1-t_w) operates just like a reduction in initial wealth . It is equivalen to shifting the budget constraint inwards. Thus, a proportional wealth tax increases , leaves unchaged or decreases the proportion of the portfolio allocated to the risky asset as the wealth elasticity of the demand for the risky asset is less than , equal to, or greater than unity.

EFFECT OF INCOME TAXATION

The income tax is less straightforward , so that we begin with the special case where the return on the safe asset is zero (r= 0) . It is then immediate that, if a * is the solution with t_i = 0 , then a= a*/(1-t_i) satisfies the first-order condition. The investment possibilities open to the individual , and expected utility , are unchanged by the tax (moreover, this applies where there are more than two assets) . This case is illustrated in Fig 4-3., If the person holds only the safe assets (a= 0) , then he is at the same point (S) as before the tax was introduced . The opportunity locus starts therefore from S.A dollar invested in the risky asset rather than the safe asset yields an extra (x₁) (1-t_i) in the good state and an extra (x₂) (1-t_i) in the bad , so that the slope of the locus (ratio of the returns ) is unchanged , but the point corresponding to a given value of a is nearer S .Thus the point a =1 moves from T to T’. Since the choice remains . P , the propotion invested in the risky asset must rise to a (1-t_i) as a measure of private risk-taking . this is unaltered. Where the return to the safe asset is strictly positive, the analysis is

Wealth in state (1)

P Indif

45⁰ T

Wealth in state (1)

Figure 4-3 Income tax : zero return on safe asset

COMPARISON OF WEALTH AND INCOME TAXATION

From the results obtained so far, we can examine the conclusions thet can be drawn about the relative effects of the two taxes. As already noted, there is the difficulty of choosing the basis fo comparison. One comparison of interest is that of taxes that lead to an equal reduction in expected utility (i.e. to the person being on the same indeference curve), and this is shown in Fig. 4-5. Since both income and wealth taxes shift the budget constraint parallel to the no-tax constraint, the person chooses P’ in both cases. However, the portfolio allocation is different. The point on the no-tax budget line ST with the same value of a as at P’ in the wealth tax case is given by Q (the ray through P’), whereas the point on ST corresponding to the income tax case is R (extension of the line joining

to P’). Since Q is clearly above R, the income tax leads to more (social) risk-taking for a given reduction in utility. What in effect happens is that private risk-taking is the same in both situations, but the government is taking more risk in the income tax case so that social risk-taking is higher.

If the government is concerned with the expected revenue, then this may be compared by drawing lines with the slope of the relative probabilities. From the earlier analysis, it may be seen that this equals the downward slope of the indiference curve where wealth in the two states is equal (the 45

line), so that it is greater than that of the budget line where there is an interior solution. Let us assume that the wealth tax is paid on terminal wealth, so that the revenue in the equal expected utility case is represented

by the vector P’Q. The revenue from the income tax is given by the vector P’R. The expected revenue would therefore be equal if the relative probabilities were equal to the slope of the budget line.We have seen however that the relative probabilities are greater , the slope of the equal expected revenue lines being steeper than the budget constraint , so it follows (see dashed lines Fig 4-5) that an income tax yields a higher expected revenue than an equal utility wealth tax . The case r = 0 is especially straightforward, since the income tax leads to no reduction in expected utility. The expected revenue, however , is positive . For a wealth tax to raise the same expected revenue , the tax rate must be strictly positive , and a necessary and sufficient condition for social risk-taking to be lower (at equal expected revenue ) is that the wealth elasticity of demand for the risky asset be greater than unity (from our earlier analyses, it should be clear than this result is general for the case r = 0) . The case where r > 0 is left as an exercise to the reader.

COMPENSATED VARIATIONS

Readers may have noted a difference in our treatment of risk-taking in this Lectures , and that of Labour supply and saving decisions in the preceding Lectures. There, we decomposed the effect of taxation into a subtitusion and an income effect . The ambiguity in the effect of taxation was due to the fact that the two effects worked in the opposite direction.

The same principle applies in the case of risk-taking . The analysis of the compensated changes is, however , almost trivial in this case. We can show that, if . t_i, is the tax rate on income and Z (=aA₀) is the demand for the risky asset , then

∂((1-t_i)Z = - Z + (1-t_i) ∂Z = 0

∂ t_{i 0} ∂ t_i o (4.12)

Rise in the price of all assets, compensated for by an increase in wealth which leaves all individuals indifferent , leads all individuals to change their portfolio in such a way as to leave private risk-taking unchanged.. To see this , let A₀₀( t_i) be the demand in the absence of taxation . Then, if we try.

A_{00 =}A₀ 1+ r and Z =Z * / (1-t_i) (4-13) 1+ r (1-t_i )

The terminal wealth in state j after the tax and compensating wealth adjustment is

A₀₀[ 1+ r (1-t_i )] + (1-t_i )Z(x_j-r) = A₀(1+ r ) + Z * x_j-r) (4-14)

So that the after – tax wealth in every state of nature is identical to that before the introduction of the tax, with the asset choice Z* . Using this result , it is easy to show that the portfolio allocation Z is optimal given wealth A₀₀ . The effect of the tax with this compensated adjustment in wealth is therefore to keep Z (1-t_i) constant. The same argument applies in the many asset case.

INTERPRETATION OF DEMAND ELASTICITIES

In the preceding chapters we related properties of the utility functions to those of the demand functions . This can be done in the case of risk- taking as well . Two properties of the utility function turn out to be critical. :

1. The logarithmic derivative of marginal utility

R_A ≡ - U”/U’ (4-15a)

Often referred to as the measure of absolute risk aversion.

2. The elasticity of marginalutility

R_R ≡ - U” A/U’

Reffered to as the measure of relative risk aversion.

SUMMARY

In this section we have examined the effects of wealth and income taxation . The former has a pure wealth effect , reducing the investment in the risky asset in the “normal” case where the wealth elasticity is greater than zero . The income tax has a substitusion effect such that the holding of the risky asset is increased so as to keep constant the “ private risk” (Z(1-t_i.)) . On the other hand , social risk taking measured by the amount invested in the risky asset, is increased. It is therefore quite possible that an income tax may increase the overall level of risk-taking , and in this respect the analysis of this section may be seen as generating counter-examples to the populary held opinion on this subject . It may however be objected that such counter-examples depend critically on the assumption of full loss offsets and other provisisons of the tax system , to which we now turn.

4-3 NO LOSS OFFSETS

So far it has been assumed that losses may be set fully against tax; this may not however be the case. To see whether the results depend crucially on the assumption. We now consider the extreme case of no loss offsets: where the return to the risky asset equais

and x otherwise. Initially, we can contrast the tax and no-tax situations. Later we compare taxes with different degrees of loss offset.

To see the effect of the tax (without loss offset), let us take the special two-state case with the return in the second state negative. A dollar invested in the risky asset now yields an extra in state (1) and in state (2), so that the downward slope of the budget line is

This is steeper; i.e., the absence of teh loss offset provision makes the risky asset less attractive at the margin, relative to the no-tax situation. It does not however follow that this kind of income tax will necessarily discourage risk-taking, since there is in addition the wealth effect. This is illustrated by Fig. 4-6 for the case where r=0. The no-tax budget line is ST, the with-tax line is ST’. The move from p to p’ may be decomposed into a wealth effect PQ and the movement round the indifference curve QP’.

Q T

T’

Wealth in state 1

Figure, income tax with no loss offset ( and zero return on safe asset)

The net result may be seen from the fact that the vertikal distance from S to P’ in Fig. 4-6 is equal to

; in other words, it is an index of the amount invested in the risky asset. Depending of the wealth elasticity of demand, this may decrease or increase, the latter being shown in Fig. 4-6. Even therefore without loss offsets it is possible that social risk-taking may be increased by income taxation.

On the other hand, with sufficiently large tax rates, the demand for risky asset is reduced where there are no loss offsets. To see this, all we have to observe is taht for tax rates near 100 per cent, almost the entire portfolio is allocated to the safe asset. This follows because, as the tax rate approaches 100 per cent, the maximum return on the risky asset approaches zero and the expected return becomes negative. Since the indifference curves are convex, the demand curves for the different assets are continuous functions of the tax rate.

We turn now to the comparison of taxes with and without loos affsets. It seems likely taht a reduction in the extent to which losses can be set against tax will reduce risk-taking. The effect does however depend on the basis for comparison. To examine this, let us assume that α of losses can be offset

. Then, if the tax rate is held constant, so that expected revenue falls (and expected utility rises) as α is increased, we can show that

denote the affter-tax return to the risky asset with loss offsets provosion, α, and r^ the after-tax return to the safe asset, so taht terminal wealth is

And the first-order condition

Differentiating with respect to α, and re-arranging

Now on the right-hand side c^x^/

is strictly positive where x < 0 and zero otherwise. It follows that the second term is evaluated only at positive values (where

then x^<r^ and U”<0), and that the whole right-hand side is positive. Since the coefficient of

is positive, it follows that α is increased.

This conclusion does not however necessarily hold where the tax without loss offsets has a lower tax rate. Suppose, for example, that we compare taxes with equal expected utility. Since the removal of the loss offset provosion unambiguously makes individuals worse off in all states in which losses are incrurred, it is clear that to compensate the tax rate must be lower. Thus, for any particular portfolio allocation, the pattern of returns is such that there is a larger probability of very small and very large incomes. The new distribution. To analyse the consequences for portfolio allocation, we use general result of Diamond and Stiglitz (1974). To do this, we note that, since U is by assumption a strictly increasing function of A, and hence of x, we may therefore invert this relationship and write the first-order condition (4-17) as

The basic result which can now be used is that an increase in the dispersion of a random variable, keeping the mean constant, increase the expected value of a convex function and decreases that of a concave function. Applying this to left-hand side of the first order condition (4-18), the removal of loss offsets leads to an increase in the dispersion of U, and hence to a fall in the expected value where the function

is concave. It is left as an exercise to the reader to explore the relationship between this condition and the properties of absolute and relative risk aversion (and whether they are increasing or decreasing). It can be shown that it is by no means guaranteed that social risk-taking is lower as a result of the (expected utility-preserving) reduction in the loss offset provision (see Diamond and Stiglitz, 1974).

The empirical relevance of the no-loss offset case depends of the form of a country’s income tax law, and on the range of an individual’s economic activities. Where losses may be set against other forms of income, where losses may be carried forward, and where capital losses may be set against investment income, the full loss offset case may be a reasonable approximation. On the other hand, there are typica;;y restrictions on the transfer of losses (e.g., capital losses not being eligible for relief on income tax) or where no carry-over is allowed. The no-loss offset case may therefore be more applicable.

A natural question to ask is why tax authorities so commonly impose limitations on the extent to which losses are to be offset. After all, it is exactly in those situations where individuals incur losses that risk-sharing with the goverment ought to be important. The answer is that it is extremely difficult for the goverment to distinguish, in many cases, between production and comsuption activities. An individual coul raise horses because he enjoys raising horses, or he could raise horse as a meaningful economic activity, i.e., for profit. The goverment would not like to subsidize the former, but might not want to discriminate against the lateer as an econimic activity. They only way it can distinguish is to require the individual who claims that he is raising the horses for profit to make a profit. If he return out to be unsuccessful, then he is classified as having embarked on the activity for enjoyment, even if that were not his motive (and even if he hates horses).

LIMITED DEDUCTIBILITY OF INTEREST

If interest expenses are not deductible, there is a kink in the budget constraint at the point where all of the individual’s wealth is invested in the risky asset, i.e., below and to the right of the point T in Fig. 4-1. The effect depends on the balance of the substitution effect, which discourages risk-taking by individuals who previously borrowed, and the wealth effect.

Exercise 4-4 examine the effect of not allowing interest deductibility (but with full loss offsets) and how it depends on the properties of the wealth-portfolio locus.

Again, we can enquire into the reason for this limitation which some (but not all) countries impose ; again, we find the answer in limitations on the government’s ability to identify the objective of borrowing. For example, a parent could, in principle, give a dollar to his child, and have the child lend the dollar back to parent ; the parent then could pay an arbitrary amount of interest to the child. This is a mechanism by which income from the parent could be transferred to the child ; so long as the two have different marginal rates, it is desirable for them to do this. In fact, of course, restrictions are imposed on the rates of interest that could “quality” ; but there is clearly room for considerable discretion in transferring income from one taxpayer to another.

Similarly, the ability to deduct interest enable individuals to take advantage of special provisions of the tax code. For instance, in the united states interest on municipal bonds is tax-exempt. Consider an individual with a 70 per cent marginal tax rate. Assume the borrowing rate is 10 per cent, but the interest rate on municipal bonds is at 7 per cent. He borrows $100. He pays @10 in interest every year, which is tax-deductible, so his “net cost” is $3. He receives $7 in tax-free interest. Thus, for a zero investment, he receives annually $4. Obviously, if he could do this he would demand bonds up to the point where his marginal tax rate falls to 30 per cent. In fact, there are restrictions in that one cannot borrow to buy tax-free bonds, but since funds are fungible, he may be able to borrow to current consumption, and use what he would have spent on current consumption to purchase bonds.

EXEMPTION OF CAPITAL GAINS

Most countries provide special treatment of capital gains. Levying lower rate of tax than on other forms of investment income. In this section we examine the extreme case where there is no tax on capital gains : the extension to the case of partial exemption should be apparent to the reader. The implication depend on the characterization of the two assets. For purpose of illustration we assume that the safe asset yields a return solely in the form of taxable interest, and that the return to the risky asset is entirely capital gains (again the extension to the partial case is immediate). Although this is a caricature, it allows us to examine the frequently made assertion that the special provisions for capital gains encourage investment in risky assets.

Terminal wealth now becomes, with a tax at rate

on the safe asset only

S’

.Q P

.P’

. 45

T. Wealth in state (1)

Figure 4-7 taxe on safe only (exemption of capital gains)

Again, the slope of the budget constraint is altered by the tax, but in contrast to the no-loss offset case it now slopes less steeply. Moreover, it continues to pass through T (since at this point individual is neither holding the safe asset not borrowing)-see Fig. 4-7. Suppose now that we consider the indifference curve passing through the new equilibrium P’. Q is the point on this curve with the same slope as the original budget line, and it is clear that we can again distinguish a “wealth” effect (P to Q) and subtitution effect (Q to P’). The latter is in the direction of increased risk-taking. The former depends on the wealth elasticity of demand for the risky asset, but where this is greater than it operates to reduce risk-taking. This is illustrated by Fig. 4-7. From (4-19) we can see that tax, for a given value of a, reduces the wealth in each state nature by the same absolute amount. The locus of points of constant values of a has therefore a slope of 45

--see the dashed kine through P in Fig. 4-7. If the wealth elasticity of demand for the risky asset is positive, then the slope of the wealth-portfolio locus is less than 45

(refer back to Fig. 4-2), and Q involves a lower value of α, and hance lower social risk-taking, than at P. As shown, the net effect is for risk-taking to increase (P’ is below the dashed line). However, it is quite possible for the tax on the safe asset to reduce risk-taking, counter-intuitive though that may seen. As in other situations. The substituation effect operating in the expected direction may be more than offset by the wealth effect.

The justification sometimes given for the exemtion of capital gains, or for their being taxed at a lower rate, is that this provision encourages risk-taking. In this section we have seen that this is not necessarily the case : the outcome depends on the properties of the asset demand functions.

4-4 Generalization Of Results

Some of the simplifying assumption made in the preceding two sections were crucial : some were not. The object of this secrtion in to see how robust some of our main result are and how far the can be extented.

RISK AND REDISTRIBUTION

The analysis of the preceding two sections assumed that the proceeds of the tax are spent on a public good, which enters the utility function in a saparable way. Thus, the variability in the supply of public goods consequent on the variability of goverment tax revenue has no effect on risk-taking. In this section we consider the other polar case, to show how our results are dependent on that assumption. We assume that the proceeds of the tax are redistributed to individuals in the form of uniform lump-sum payments. There is in effect a progressive linear tax schedule. Moreover, we assume initially that there is a common risky asset which is purchased by all individuals, i.e., all risky are perfectly correlated. Thus, if all individuals are identical, with identical initial wealth, and if α* denotes the aggregate portfolio choice, the the per capital lump-sum redistribution is (with an income tax at rate

)

And this random variable, depending on x. The individual chooses his portfolio the maximize expected utility, derived from terminal wealth. Which can now be written;

For a given α*. This implies a first-order condition

GENERAL EQUILIBRIUM

The effects of taxation depend critically on the institutions available within the society for adjusting to risk, and this raises the question of general equilibrium incidence. This subject as a whole is discussed in later lectures, but since we do not explicitly treat uncertainty we present here a simple case where there is an efficient risk market, the terms of contracts being chosen to provide individuals with the correct incentives.

The model is of “capitalists” who are risk-neutral, and “managers” who are risk-averse. Capitalists provide to managers, who employ it in a rsky production activity and distribute part of the return to the capitalists. The capitalists cannot monitor the actions of the managers directly ; hence, they rely on incentives to ensure that the managers take the actions that maximize return. We assume that the return per dollar (x) is a function of the effortof managers (L) and risk (0) in a multiplicative way

and

The manager α receives of the return. His expected utility is

4-5 MULTIPERIOD SAVINGS PORTFOLIO ALLOCATION MODEL

In the model analysed to this point, it is terminal wealth, not income or consumption, that enters the utility function. This can be relationalized as viewing the object of savings to be future consumption, if we “idealize” the individual as living for two periods, a work period during which he saves, and a retirement period during which he consumes the proceeds of his saving. On other hand, we might think of the individual as living for a long time and being therefore concerned primarily with the income that he gets from his investment ; in that case, one might think that the appropriate formulation was that where income or return entered directly into the utility function (for instance, Feldstein, 1969). This is not, however, necessarily the case, as the following simple genaralization of our earlier model illustrates.

We assume that the individual lives for ever. Again, this is an extreme case ; it ic chosen for its mathematical simplicity ; more realistis cases of indivisual living for a large but finite number of periods may be analysed in a similar way. He maximizes the sum of the utility derived from cunsumption discounted at rate

we assume that the utility function has constant elasticity.

Let

denote maximum value of discounted expected utility that the individual can obtain from wealth

at time u. Since the individual lives for ever, the discounted value of a given capital at u+1 is simply 1/1(1+

time its value at time u. This simplifies the analysis considerably and means that in writing, the objective function we can drop the time subscript from x and incorporate the discount factor.

The solution to the optimization problem may be seen by applying the principle of optimality, according to which the maximum value x(

) is given by

Where

is given by (4-34). The level of utility is equal to the utility we get immediately from consumption plus the utility from the future consumption ; but the letter is just a function of the amount of wealth at the beginning of next period, discounted by (1

if we know the function Z, we could immediately infer the optimal value of a and thus the effect of taxation on risk-taking. We need therefore to find a function Z that satisfies (4-36). (formally, it is functional equation). Fortunately for the case of constant elasticity utility functions, Z take on a very simple form. Let us postulate that

We shall show that there exists a value of the constant k for which (4-36) is identically satisfied. By direct subtitution, using the particular form of the utility function (4-33).

_where

From this we can see that if this applies, then the portfolio decision is separable from that about savings, and that α is chosen to maximize the rate of return raised to the power (1-

to take account of risk aversion. The earlier analysis for the one-period model is directly applicable. In particular, wealth taxation leaves the portfolio unchanged (with the isoelastic utility function, the wealth elasticity of demand for the risky asset is unity), and income taxation leads to a rise in social risk-taking.

The value of k, and the optimal savings policy, may be derived from (4-37). Dividing by A1-1 and writing T=(1-tm)1-t

The first-order condition for the choice of

_is(dividing by T)

Hence, using (4-39)

and

This gives a value of k satisfying the equation, and shows that the savoings policy depends on the degree of risk aversion (

, the return on the portfolio (y), the wealth tax (T), and the discount rate.

MORE THAN ONE RISKY ASSET

The basic model used in this Lecture is that of a safe asset and a single risky asset. There are a number of questions that can be raised about this formulation. First, what happens idf there is no safe asset? As we have earlier noted, where there is uncertainty surrounding infllation no monetary asset is without ris. However, efen if the safe asset is risky, the result obtain so long as the two assets are positively correlated and one is unambiguously more varibale than the other (in the sense of Rothschild and Stiglitz, 1970). For example, if the only source of risk is the macroeconomic behaviour of the economy, and both returns react in the same way but one is more sensitive, then the results apply.

Second, if there exists more than one risky asset, we can, under certain circumstances, divide the problem of portfolio allocation into a two-stage process, as originally suggested by Tobin (1958). The investor decides first on the proportions in which to purchase the risky assets and then on how to divide his total wealth between the safe asset and the “mutual fund” or “unit trust” made up from the risky assets. The conditions under which this “separation” property holds have been investigated by Cass and Stiglitz (1970). They conclude that these conditions are very restrictive. The separation property holds for special distributions of returns (where all jointly normally distributions).

This means that where there are several risky assets the applicability of the earlier model is rather limited. We have noted some results that carry over (for example, that concerning the substitution effects) and others are discussed by Cass and Stiglitz (1972). However, important features of the analysis do not apply. In particular, there are no result paralled to those betseen the measures of risk aversion ang the wealth elasticities of demand.

The conclusion that should be drawn is that the two-asset model is valuable as a source of insights and counter-examples, but that not all of the results can be expected to generalize to the many-asset case.

4-6 CONCLUDING COMMENTS

The effect of the tax system on risk-taking has long been the subject of controversy. As was demonstrated in the classic paper of Domar and Musgrave (1944), it iss possible that taxation may actually encourage risk-taking. Since the government is sharing the risk. Further developments in the theory of portfolio allocation showed how the outcome depends on the properties of the utility function and on the particular features of the tax (e.g., the extent of loss offsets and preferential treatment of capital gains). As in the preceding Lectures, there are both income and substitution effects, although the letter has a particularly straightforward form in the present case (being proportional to the quantity of risky assets purchased).

In further analysis of the portfolio decision, empirical evidence is clearly important, and it has been used to draw inferences about the effects of taxation. Thus, arrow (1965) concluded from time series evidence on the demand of money in the United States that the wealth elasticity of demand for the risky asset is positive but less than unity (because the elasticity of demand for money is greater than unity). This implies in the two-assets moddel that both wealth taxation and income taxation increase social risk-taking. In contrast, the cross-section evidence (e.g., Projector and Weiss,(1966) gives a rather different impression, suggesting that the elasticity of demand for the risky asset is greater than unity. There are however considerable difficulties in drawing conclusions from observed portfolios about the risk attitudes of individuals. The identification of “safe” and “risky” assets is far from straightforward, and, as we havw seen, the resluts from the two-asset model do not carry over to the general many-asset case.

The study of the effects of taxation on portfolio behaviour is in some respects at a less advenced stage than the areas of household behaviour discussed in Lectures 2 and 3. On the other hand, the analysis has served to bring out several key features. Of particular importance is the role of the goverment in risk-sharing. If, for example, the privat market provides complete risk-sharing for all but “social risks” (like the business cycle), then argument that the government can increase risk-sharing through the tax system is less convincing. Indeed, in one extreme case analysed, we showed that there would be no effect at all on risk-taking. Noreover, the risk-sharing arrangements available in the economy may themselves be affected by the tax system. We considered a simple example of the general equilibrium determination of risk-sharing contracts.

In this Lecture we have focused on the case where individuals act to maximiza expected utility, and certain limitations ought to be noted. First, individual motivations for undertaking risk may not be described adequately by such a model. This is a subject of longstanding controversy. Second, individual behaviour may be determined more by rules of thumb (perhaps used because of limitations on information-“bounded ration-ality”). There is considerable evidence of irrationality in portfolio allocation (e.g., individuals at low marginal rates purchasing tax-exempt bonds). In that case, the effect of taxation may be quite different from that analysed in this Lecture ; unfortunately, rule of thumb models do not typically give clear predictions abaout what the effect of taxation would be.

Finally, we should return to teh connection between portfolio choice and the real investment decisions of the economy ; that if individuals demand for the risky asstes, then risky project will find it easier/cheaper to find finance. The lingkages are however complex, and several factors need to be taken into account. In several places we have referred to limitations imposed by the capital market, e.g.. restrictions on borrowing. Relatively little investment is financed through the issue of new equities. This may be for tax reasons, as we discuss in the next Lecture, or because of imperfections in information or in the capital market. Moreover, the behaviour of the firm under uncertainty is problematic. If there are incomplete markets for risk, there wiil not in general be unanimity among shareholders ; and even if they were to agree on objectives, imperfect information on the part of shareholders may gives managers a degree of discretion.

NOTE ON RISK AVERSION

The purpose of this note is to collect together some of tha main propertaies used in the text.

The individual is assumed to maximize expected (the discussion of the axiomatic basis for expected utility may be found in, among other places, Arrow. 1965, and Malinvaud. 1972 Ch.11). The utility of wealth is assumed to be strictly increasing (U’>0), and he is assumed to be risk-averse (U”<0). The meaning of the letter may be seen if we consider the choice beetween a certain prospect A0 and a 50 per cent chance of gaining h or losing h. If he prefers the certain outcome, then

In the contrast, if U”=0 he is indifferent between the certain and risky outcomes and is said to be risk-neutral. In this latter case he maximizes expected wealth.

Intuitively, the more concave the utility function. The more risk-averse the individual. This may be formalized in terms of thr risk premium that the individual is willing to pay to avoid the uncertain prospect. Let us define Π as the premium he is just willing to pay to avoid the risk associated with an investment that yields

where z has mean zero and variance σ².

CHAPTER V

TAX AND CORPORATE

5-1 TAX AND CORPORATE

In this matter, we see the impact of taxation on corporate decision making. Where in this case, our focus is on the stage of partial equilibrium effects. It was assumed that the price paid by the company are not affected by the tax. Thus, in considering the imposition of, for example, income tax, it can be assumed that it increases labor costs for the company. In fact, it can lower the wages received by workers.

This material describes several types of tax imposed on the company. The main part of this material concentrates on corporate profits tax, which has been a lot of controversy. The material begins at the 5-2 with the analysis of the impact on the cost of capital to firms, and financial policy determination. What is the impact of a tax depends on the provision for interest deduction? How is it related to the preferential treatment given to increasing the value of assets under the personal tax system? Implications for decisions on real variables, especially investment and capital costs under different assumptions about depreciation, with the financial means in a manner in which capital is considered independent variables. On the 5-4 expanding the scope to allow for imperfect competition. Alternative goal of the company is the cost of the adjustment and the role of expectations. In the final section, described the reviews with some empirical evidence on taxation and investment.

TYPE OF TAX

There are different types of taxes that have been imposed on the company or.
(1) Taxes on individual factors

Kind of tax is a tax on labor income, are usually charged as a fixed percentage of income. In the United States, social security taxes are income tax, and other taxes and apply the same in many countries. The opposite of income tax which the government provides wage subsidies. Subsidies can also be paid at the margin, which is due to increased employment. Corporate profits tax is sometimes seen as a tax on the return on capital in the corporate sector. If there are constant returns to scale, and hence there is no "pure profit", and if the interest is not deductible, then it seems clear that the corporate profits tax should be viewed in this way. On the other hand, the rate reduction provisions generally apply and may mean that the tax falls mainly on pure profit, not return on capital. And because of the wage subsidy is a subsidy for investment: investment tax credits or grants. Taxes on individual factors, may be a general tax or taxes are limited to certain forms from certain activities. Thus, payments to bondholders are generally exempt from corporate profit tax, and return in the form of an increase in the value of assets (capital gains) are treated differently from other returns. Tax factors can be limited to a single sector of the economy, such as the Selective Employment Tax in the UK. The tax levied on the services sector (with subsidies for manufacturing). Corporate profits tax payback treated differently in the corporate and non-corporate. This has clear implications on the general equilibrium.

(2) Tax on total output or total input

One tax is widely discussed in recent years is the value added tax (VAT), which is proportional to the value-added tax by the company. The consequences depend on the definition of the tax base. On the basis of income, value added is defined as the payment of wages plus a return on capital (net of depreciation), so it is equivalent to the same payroll tax rate coupled with the same tax advantages (depreciation provisions but with no reduction in interest). Another variant of the VAT is the base product, where no depreciation provision and consumption base, where all purchases of capital goods is reduced. The latter is equivalent to the same income tax plus a tax rate equal to the depreciation benefits free. In considering the effects of different tax, the impact on the level of integration in the economy should be considered. Thus, the gross turnover tax can provide an incentive for vertical integration. The same applies where there is a difference in the discounted value of current tax payments depending on the time of the transaction.

TAX EFFECT

Suppose a firm maximize profits and competitive in the face of fixed factor prices (W) for the vector of labor input (L) and r for capital input (K), and p fixed output prices. If the company is the production function F (K, L), then choose K and L to maximize profits, which on a certain date,

Π = pF (K, L) - w.L-r.K

Where we assume F to be twice differentiable and concave.
Tax consequences can be separated into the effects of output and factor substitution effect. The first depends on whether universal or partial tax and the competitive nature of the market. If we treat capital and labor as an aggregate, then from the first order condition for profit-maximization
P ∂ f / ∂ K = r

P ∂ F / ∂ L = w

For a given output, an increase in r relative to w leads to less capital-intensive techniques (moving round isoquant). By taking labor and capital as the aggregate, we certainly overlook some important effects. A regressive income tax, such as social security tax, have the same effect. In the case of capital, taxation can influence the choice of resistance. Analysis of the effect is left to the reader.
This analysis concentrates on the corporate profits tax. In general, that this increases the relative cost of capital, w the deductible but not the cost of capital. To the extent that this is true, it leads to a lack of capital that is used to give the output. The main problem is that what happens to the cost of capital as a corporate tax increase. This in turn depends on the financial policy of the company that is a mix between debt and equity.

The above formulation assumes that firms can vary capital and labor inputs. In practice, there are limitations on the flexibility of input options. Thus, many models have been treated as a variable capital stock, the rate of change in this stock (through investment) into the decision variables. (The same applies for the job). We might ask how the level of investment is affected by the tax. Is it advisable to tax corporate profits? How far offset by the effect of investment grants or tax credits? It is important to observe that not only the current tax rates but also the expectations of the relevant tax rate. Anticipated increase in tax credits may lead firms to delay investment until the tax increases on companies to invest sooner rather than vice versa. So not only is the level of investment that may be affected, but also time.

REASONS FOR CORPORATE TAX

Before analyzing the effect of taxation of corporate profits, it is reasonable to ask why the tax is imposed. If a person starts from the position that the company is nothing more than the way in which individuals have assets, then the tax on the income of the corporation is simply a tax on the income of the people who own the company. In other words, a tax on certain classes of assets and / or factors. If the asset (factor) can shift the cost of the removal company to non-sector, the consequences of this tax will be felt throughout the economy. After-tax return will be the same in the corporate and non-corporate.

If this view is correct, it is difficult to see the justification for a separate tax corporate profits. It is possible that it is an efficient method in gathering form of tax cuts. An alternative view see the activities of different companies with several important ways, so there is no reason why a priority corporate income should be taxed at the same rate as other income. One argument is that the status of the companies deliver certain privileges, particularly limited and tax is a levy on the resulting benefits. Another thing, if the tax falls mainly on pure profit and therefore less distortion than taxes on other types of income.

5-2 CORPORATION TAX AND COST OF CAPITAL

The important role of monetary policy when considering the effects of the corporate profits tax is well illustrated by the view "Marshallian" of the tax falls on pure profit. The views Marshallian, as represented for example by the arguments made before the Colwyn Committee in England in 1920, is that the tax advantage does not affect output in both the short and long term. The reason is that the tax was imposed (at rate t_c) at a profit, so that the company received net:

Π = (1 - t_c) [Pf (K, L) - wL - rK]

The first order condition for the choice of K is pF_k = r, and is not affected by the tax. In the short term, profit-maximizing behavior of firms in the industry are not affected. In the long entry and exit is determined by the marginal firm, which by definition is to make pure profit to zero, so that the long-term output unchanged. Tax falls on pure profit, or return to entrepreneurship.
This analysis depends on the assumption that the tax base does not include the cost of capital (rK), so it falls only on pure profits, a point that was brought by Robertson (1927). The definition of the tax base is a key issue. As in the case of personal income tax, from theoretical concepts to gain fiscal legislation is far from simple. There is a difficulty about such items as depreciation, depletion, inventory accumulation, increasing the value of assets and losses, and intercorporate dividends. However, there are certain key features Taht deeply affect the nature of corporate tax

FINANCIAL STRUCTURE

This analysis focuses on the financial fundamentals of the company identity. We can identify the following admission:

Gross profit, which is the value of output minus the cost of the variable input (labor),
π_u = p_u F_u - w_u L_u.

New bond issue (where B_u shows bond at the beginning of the period).B_ (u +1) - B_u.New equity issues (where θ_u shows equity at the beginning of the period), θ_ (u +1) - θ_u and we can identify the following payments:

1. Dividends, D_ (u,)

2. Interest payments to bond-holders, B_ (u,)

3. Investment, I_u, Fundamental relationship is that the same income in the u disbursement period: π_u B_ + (u +1) - B_u θ_ + (u +1) - θ_ (u) = D_u I_u + + rB_u

We can determine the retained earnings. RE_u = π_u - rB_u - D_u. That profit is not distributed as interest or dividends. Therefore, the
I_u = RE_u + (B_ (u +1) - B_u) + (θ_ (u +1) - θ_u)

That investment is financed by retained earnings, loans or new problems.
For now, we take π_u and I_u as fixed and consider variations in financial decisions. It should be noted that the basic accounting identity implies that at least two of the financial variables should be changed at a time. In addition, they are linked from time to time: for example, this implies an increase in the current bond interest payments increase in the future.
In the absence of taxes, net financial flows from the corporate to the private sector are:
Y_u ≡ D_u rB_u + - (B_ (u +1) - B_u) - (θ_ (u +1) - θ_u) and from the above formula can be seen that it is similar to π_u - I_u. In other words, the net flow is determined by real variables and does not depend at all on the financial structure. This is the basis for the Modigliani-Miller theorem: in the absence of taxes (and bankruptcy). Corporate financial policy is irrelevant and has no effect on firm value. It was originally shown, under the assumption that specific enough by Modigliani and Miller (1958), but extended to more general models Stightz (1969a - 1974a).

The tax system with a particular provision is as follows:

1. Corporate profits are taxed at a rate t_c,

2. Interest payments are deductible by the company,

3. Interest payments are deductible by individuals with personal tax rates, t_p,

4. Dividends and interest received are taxed at t_p,

5. Capital gains are taxed at an effective rate t_g <t_ (p ^ 1)

Corporation tax is often referred to as "classic", and involve a simple tax on corporate profits, with no "credit" is given to the shareholders for corporate tax paid. It can be seen as a tax on the merger, the shareholders personally liable for the taxes on dividends and capital gains. Many variations are possible. In some countries made efforts to integrate personal and corporate tax structure, the individual receives credit for imputation corporate tax paid on his behalf. In some countries the interest payments are not deductible by the individual, in others there has been a proposal to tax capital gains at the same rate as dividends.
With the tax system, corporate tax liability is t_c (π_u - rB_u), and financial identity becomes
π_u (1 - t_c) + (B_ (u +1) - B_u) + (θ_ (u +1) - θ_u) = D_u I_u + r + (1 - t_c) B_u
For the private sector, no income tax liability and capital gains tax, so the after-tax net financial flows

Y_u = (+ D_u rB_u) (1 - t_p) - (B_ (u +1) - B_u) - (θ_ (u +1) - θ_u)

TAXATION AND FINANCIAL POLICY.

The way we analyze the effect of taxation on the financial structure of the company is to use what is sometimes called a perturbation argument. We assume that the economy is in equilibrium, and then consider interference feasible for the company's financial policies, examine their effect on individual consumption possibilities have company. For most analyzes, we aggregate and consider "representative" members of the private sector who own shares of the company. We also assume that the tax rate is constant over time, and completely expected. Implications of expectations regarding changes in tax rates will be discussed in the next section.

The first thing we think of is setting back in ways that reduce both the transmitted funds to the private sector. Suppose the company was reducing both D_u and (θ_ (u +1) - θ_u) for $ 1. Former "cost" private sector $ (1 - t_p), the effect of the latter depends on the capital gains tax, and can be seen as a benefit of $ (1 - t_g). Since t_g <t_p, this is a net benefit to shareholders and bondholders not worse. This is one of the key puzzles of corporate financial policy. With tax system explained, if the company pays dividends? Where is the tax rate on capital gains is less than that on dividends, it is clearly better to buy back stock (capital gain yield) than to pay dividends. Several explanations have been given to the fact that the company regularly pays dividends. The first is that the dividend serves as a signal about the "real" value of the company. So if the dividend is reduced, potential stock buyers believe that it may be because the company is in bad financial trouble, that is, unable to pay dividends. It is not yet very persuasive, because buying back stock can serve as a signal equally effective. Even more important is the legal restrictions on share repurchases. Even some of the tax code treats such repurchase is equivalent to paying dividends. Thus, companies in the UK to buy back its own shares by obtaining a special court order. In the United States the redemption of shares may be considered by the Internal Revenue as dividends.

For the reasons just described, a company may not seek to buy back shares, but there are a number of actions the company can do that. At least in a perfect capital market, basically the same. The assumption, for example, that the company plans to issue a dividend of $ X. Instead, the company acquired a company with a value of $ X. This is the real deal-not purely financial involved. Private sector receives from the corporate sector will be $ X received dividends. "Original" the company is now worth $ X more than it would have had a dividend that has been distributed, and there is thus contingent capital gains liability, but at tg than the dividend. That two actions have the company pay dividends and buy another company, entirely equivalent clear if the same individual had two companies. Even if different individuals have different companies with two similar actions, as long as there exists another company with the same risk characteristics as the company making the acquisition. The fact that most of the profits of the corporate sector can not be distributed as dividends because it can be easily explained within this framework. In the following, we simply assume θ_ (u +1) - θ_u ≥ 0, so that any payments to shareholders should take the form of dividends. The company is also prohibited from being under-capitalized, there are cases where the tax authority has a limited tax deduction of interest payments, but it has a particularly firm, which is being led. Due consideration of bankruptcy, most of the companies owned by many parties did not attempt to raise the debt equity ratio to the point where the tax authorities may impose constraints.

We assume that the perturbation is a financial policy that the company increased the dividend of $ 1 in period 1, financed by a loan, with interest and principal repayment are met in the second period by a decrease in dividends. Of finance for the company's identity, (5-5), we can see that the decline in dividends in period 2 is 1 + r (1 - t_c). Implications for the net flow into the private sector depends on the capital gains tax liability. If, at first, we assume that t_g is zero, then the change

Pemegang Saham Pemegang Obligasi

Period 1 - 1 + 1

Isu-isu baru pengurangan pinjaman

Period 2 (1 -

)[1 + r(1 -

)] - 1 - r(1 -

)

peningkatan dividend pengurangan penerimaan

This would be beneficial for shareholders if:

(1 -

)[1 + r(1 -

)] > 1 + r(1 –

)

and with

this is clearly not satisfied. In contrast to reducing

borrowing

0 Q χ

Effects on the individual depends on his level of discount, or the opportunity cost of funds,
Which we rate as r (1 - τ) if it reduced its debt to receive (1 - t_p) dividends, or if it increases the loan, then τ = t_p, if it increases the tax free savings in the medium (eg, pension funds), then τ = 0. In order to increase shareholder loan where desired
(1 - t_p) [1 + r (1 - τ)] ≥ (1 - t_p) [1 + r (1 - t_c)]
This condition simply because it t_c ≥ τ. Basically, people who replaced loan companies for personal loans: since interest deductible, is this what you want depends on where the greatest tax savings. Where τ = 0, clearly dominate the corporate lending, but where τ = 0, is more problematic, and with a typical rate of corporation tax (about 50 percent) is very likely that this is less than the marginal tax rates of the "representative" of shareholders.
Let us suppose that for now t_c <τ = t_p. Shareholders as favors corporate debt reduction and dividend payments. How far this process should be done? It may be noted that the conditions for the optimal monetary policy is independent of the number: if t_c ≠ τ, then (5-9) can never hold with equality. This is in contrast with previous models in which there is usually Lecture interior solutions. In this case the possibility to get a corner solution. To see this, let us return to financial identity (5-5 '), and write the net financial transfers to the shareholders as
χ_u = D_u - (θ_ (u +1) - θ_u)

Assuming, D_u θ_ ≥ 0 and (u +1) - θ_u ≥ 0, and it is clear that at least one is zero (if not, the company can reduce both dividends and new issues ang reduce taxes paid). If we consider the variation in B_ (u +1), holding debt constant in all other periods, then this yield locus (obtained by taking the company's financial identity fot two consecutive periods and eliminate B_ (u +1)):

χ_ (u +1) + [1 + r (1 - t_c)] χ_u = (1 - t_c) {π_ (u +1) + [1 + r (1 - t_c)] π_u}

B_ + (u +2) - [1 + r (1 - t_c)] ^ 2 B_u - I_ (u +1) - [1 + r (1 - t_c)] I_u

Shown in Fig. 5-1 (which deals with the case where the right side is positive). By successively reducing the loan, the company can reach a point where χ_ (u) = 0.
Does the company want to go further and create new problems, thus making χ_u negative? The effects of this can be seen as:

Shareholders Bondholders

Period 1 - 1 + 1New issues debt reduction

Period 2 (1 - t_p) [1 + r (1 - t_c)] - 1 - r (1 - t_p) dividend increase revenue reduction. This would be beneficial for shareholders if: (1 - t_p) [1 + r (1 - t_c)]> 1 + r (1 - τ) and with τ = t_p Clearly this is not satisfied. In contrast to reducing

Χ 〖〗 _ (u +1)

Figure 5-1 choice of financial policy dividends, no tax savings will increase in new issues. Where t_c <t_p we get a corner solution in P, with dividends suspended as far as possible.
Where t_c> τ, the desired increase in lending policies and this can be continued to the point Q, where χ_ (u +1) = 0. Going further would mean that new issues should be made to finance debt payments. In this case, the condition (5-9) will be (1 - t_p) [1 + r (1-τ)] ≥ 1 + r (1 - t_c) because new issues are not interesting as a reduction in dividend tax relief. It is possible that for a fairly low rate of personal tax is satisfied, and we will have an "all-debt" company.

A fuller treatment of the financial policy, and it is an extension for various periods, provided by Stiglitz (1973), but it seems likely the assumption is made that the company will be in a corner solution. Most reasonable assumption might t_c <τ = t_p, and this is a case that we are focusing later. In this situation, the company reduced the dividend to zero or, more plausible, an "acceptable" minimal. Where investment exceeds retained earnings, any increases financed by borrowing. (As can be seen from (5-10 '), an increase I_u shifting locus in Fig. 5-1 in toward the origin and P moves down the vertical axis). Where an investment is less than retained earnings, any increase I_u reduce the rate at which debt is being paid off (hence have the same opportunity cost). Conversely, an increase in Q causes a decrease D_u I_u: investments financed by retained earnings. This description of the company's financial policy does not seem completely consistent with the observed behavior. For Estabilished companies, new issues are relatively unimportant, the company does not typically attempt to recapitalize because of all the problems of equity, on the other hand, they do not appear to move in the direction of reducing the element of equity by borrowing more than what is required for investment. At the same time, there are a number of features of the model warrants comment.

CAPITAL GAINS AND MARKET VALUE

An important role is played in the previous argument on the assumption that capital gains are taxed at a lower rate than dividends, indeed we set t_g = 0. To test this, we need a model of the determination of the market value of shares of the company-and it also provides an alternative way of lowering the results given above without any uncertainty. The model used here ranging from capital market conditions that equilibrium in u period dividends received plus capital appreciation should be equal to the opportunity cost to have a company, where the latter is r (1 - τ). Treat the company as a single holding, the condition on the internet tax refund is:

(1 - t_p) D_u + (1 - t_g) (Ѱ_ (u +1) - Ѱ_u) = r (1 - τ) Ψ_u

Ѱ_u Where is the stock market value of the company. This can be rearranged:

Ѱ_ (u +1) - [1 + (r (1 - τ)) / (1 - t_g)] Ѱ_u = (- (1 - t_p)) / (1 - t_g) D_u

Solve the difference equation

Ѱ_0 = ((1 - t_p) / (1 - t_g)) Σ_ (i = 0) ^ α ▒ D_i / [1 + (r (1 - τ)) / (1 - t_g)] ^ (i +1 )

The market value of the stock is the same as that for the present value of dividends discounted at a rate that depends on the opportunity cost of capital and the tax treatment of capital gains. If capital gains are taxed at the same rate as other income (t_g = t_p), and if τ = t_p, the stock market value is equal to a certain flow-dividend-as in the case of no taxes.
Effect of switching from retained earnings to the loan (dividends + $ 1 in period 1), - $ [1 + r (1 - t_c)] in period 2) can now be examined. From (5-14) increases the value of the company in which

1 + (r (1 - τ)) / (1 - t_g)> 1 + r (1 - t_c)

which can be rewritten as

(1 - t_g) (1 - t_c) <(1 - τ)

Or
τ <t_c + (1 - t_c) t_g

The right side is the total tax burden of equity returns is taken as capital gains (profits tax plus capital gains tax on the rest). This raises the important role played by the tax treatment of capital gains. If profits are taxed at the same rate as other income (t_g = t_p), then this inequality will obviously continue, if τ = t_p, and the loan would be desirable. At the other extreme, with t_g = 0, the condition τ <t_c, as before. In general, the situation in between, although the effective rate on gains rather low, so we are in practice close to the case analyzed previously. Provision for capital gains tax liability may not change the qualitative conclusions drawn.

QUALIFICATIONS FOR ANALYSIS

The analysis so far has assumed that the corporate tax is a type of "classic" version, however there are alternatives, or has been, in effect. For example, the UK has hired "imputation" system, in which shareholders receive some credit for the tax paid by the company: profits distributed regarded as having paid taxes at a rate t_m. This means that the total D payments are treated as equivalent to the amount earned up D / (1 - t_m) the taxpayer is then taxed at the rate of (t_p - t_m). Treatment of these cases is left as an exercise for the reader.

In the absence of integration, optimal monetary policy depends on the relative levels of personal and corporate taxation. This brings us to the question of differences in the position of individual shareholders. What

NI < B

(includes RE < B B < RE

classical RE < NI NI < RE

system)

optimal Borrowing Borrowing Retained earnings

B < NI

RE < NI NI < RE

RE < B B < RE

Optimal New issues New issues Retained earnings

Figure 5-2 Corporate financial policy and the tax regime "<" indicates "lower". NI, new issues, RE, maintain: B, loans. The diagram was constructed using the inequality (5-15), (5-16) and (5-17) and assuming τ = t_p happens if we leave the fiction of "shareholder representative"? in which all individuals are in a tax bracket that certain policies are optimal, then the analysis continues to apply. On the other hand, where there are critical differences across boundaries, such t_c = t_p, then we must consider the possibility of "tax arbitrage". We can in fact show that, if there is an all-equity firm, there will never be an all-debt company. to see this, consider a company that produces return (safely) from r *, which is owned by an individual in a low tax bracket, so the company pursues a policy-all debt. Assume the company costs $ 1. Suppose now that a wealthy individual not borrow offering $ 1 back (safely) (maybe a little more) of r *, and use the $ 1 to make the exact same investment. He then sold the company to another wealthy individuals (the next generation) to the value of assets, which have grown 1 + r * (1 - t_c). The return net to the rich (without investing itself) is

r * [(1 - t_g) (1 - t_c) - (1 - t_p)]

It is positive (and hence profitable for him) precisely in conditions (eg, (5-15a)) we see above will cause the company to pursue a policy of all-equity. Therefore, there is the possibility of tax arbitrage between low and high individual marginal tax rates, and there can not exist all corporate debt in an economy where there is an all-equity firm.

5.3 TAX AND INVESTMENT

We turn now to the real, as opposed to financial, decisions made by the company. In the context of a competitive company, maximizing the market value of the stock at a given price for output and input, we examine the impact of taxation on the supply of output, and in particular on capital employed. Wich tax mechanisms affecting the cost of capital investments is discussed in the previous section, and this is because it depends on the financial policies. However, first we need to discuss the provision for depreciation.
Shrinkage

Assets will generate gross flows back, from which depreciation should be deducted to calculate net returns. The tax system to make some provision for depreciation when calculating the profit tax. Generosity in assessing their relative, a useful benchmark is the "true economic depreciation" (Samuelson 1964a), which is the replacement cost of physical wear and tear. (At this point we assume that all prices are constant over time, the effect of inflation is discussed later in this section.) This provision is neutral deciosions depreciation of investment, as illustrated by the following simple model. Suppose assets generate flows back Πu, corporate income tax rate is t, and the discount rate is r (lt). With the depreciation allowance on δu time u, the value of the asset at the time * u: 7

Ψ = ∫ _ (u *) ^ ∞ ▒ 〖[Π_u〗 (lt) + tδ_u] e ^ (-r (lt) (uu *)) du (5-18)

Differentiating with respect to u * to give the time derivative,

Ψ = r (l-t) Ψ-(l-t) Π_u tδ_u (5-19)

This is a change in the value of assets, and the true economic depreciation is by definition equal to (-ψ). Re-set, with the level of economic δ_u correct,

δ_u = Π_u-Rψ and Ψ = rΨ-Π_u (5-20)

Differential equation because it is not affected by the tax. Since the boundary conditions, in which the point of scrapping, were also affected, then that is a tax - the true economic depreciation neutral. (The role of the assumption that the discount rate is discussed below.)
If there is a perfect market for all assets used, there will be no difficulty in calcuting true economic depreciation, but the used capital goods market is not perfectly known. As a result, the government usually uses practical formula depreciation rules, for example:
1. a fraction of the expenditure allowed each period (straight line);
2. fraction of the value of the written (declining balance) are allowed;
3. fraction of expenditures decreased lineary over a lifetime (number of digits) are allowed;
4. the whole or part of the value may be eliminated altogether (free depreciation or investment tax credits.)

Formula does not usually warrant a true economic depreciation. Wheter they are more or less care in general depends on the relationship between "real life" and is used for tax purposes. (Depreciation free is an exception, because white is always more generous for durable assets.) Consider the case of straight-line depreciation in asset cost C r which produces an infinite stream of returns Π_o e ^ (-7m) from zero time. Let us assume that in the absence of taxation on the margin of this project is receiving, i, e ..,
C = Ψ_0 = ∫ _0 ^ ∞ ▒ Π_0 e ^ (- (r + y) u) du = Π_0 / (r + y) (5-21)

The introduction of a tax on the level of t, with a discount rate, and the true economic depreciation, leaving the value unchanged. Unlike the straight-line depreciation,
Ψ_0 ^ * = (lt) ∫ _0 ^ ∞ ▒ Π_0 e ^ (- [r (lt) + y] u) du + t ∫ _o ^ Γ ▒ 〖(∁〗 / Γ) e ^ (-r (lt ) u) du
= (Π_0 (lt)) / (r (lt) + γ) + t ∁ (DA) (5-22)

DA which shows the value of depreciation allowances per dollar. Rearranging,

Ψ_ο ^ * = Π_ο / (r + γ) + t ∁ [DA-γ / (γ + r (lt))] (5-23)

where we have substituted from (5-21). Straight-line depreciation because it is bigger or smaller than the true economic depreciation, in accordance with the
DA = l / Γ ∫ Γ ▒ _0 ^ e ^ (-r (lt) u) du ≷ γ / (γ + r (lt)) (5-24)

There were no significant Γ so that it applies to equity, because shorter "life tax" straight-line depreciation provides more generous benefits. Case declining balance is more straightforward. Suppose no allowance at δ ∁ e ^ (-δu) at the date u. This gives (again using (5-21))

Ψ_0 ^ (**) = Π_0 / (r + γ) + tC {∫ _0 ^ ∞ ▒ 〖〗 δe ^ (- [δ + r (l)] u) du-γ / (γ + r (lt) )} (5-

25)

It is clear that the term in brackets is zero if δ = γ and this is in accordance with the true economic depreciation. It is positive (negative) if δ> γ (δ <γ). In what follows we concentrate particularly on a relatively simple form of shrinkage and shrinkage free.
Bond Investments financed

In the previous section we identified as the central case in which the investment is financed by borrowing on margin. Where investment exceeds retained earnings, additional loan capital, where investment exceeds retained earnings, surplus used to reduce debt. Therefore we start with the case, in which the cost of capital at the margin is r (l-t_c), interest is assumed throughout this section that the tax is expected to remain at their current levels of important assumptions, as we show in Section 5-4.

We assume that the firm chooses capital input (K) and employment (L) to maximize profits, and that there is no charge for the cost of the adjustment range of input factors are discussed in the next section. Suppose we consider variations in the company's policy to K, so the company has a unit of capital in period l, but no change in the next period. In other words, investment increased by one unit and then reduced by one unit in the next period. If we assume that the price of capital goods is unity, this involves borrowing an additional S1 for one period. In the absence of taxation, change in profit is positive if
p ∂ F / ∂ K> r + γ where γ is the true economic rate of depreciation. Let us now introduce taxation, with the true economic depreciation (we discuss alternatives below). Changes in profit is positive if (L-t_c) p ∂ F / ∂ K> r (l-t_c) + γ-γ t_c. Maximization of profit because it requires (as the term in (l-t_c) cancel) the
p ∂ F / ∂ K = r + γ (5-26). There is an appropriate first order conditions for L are not discussed). If the tax system allows the true economic depreciation, interest and taxation was full (possible general equilibrium effects through r not considered in this lecture). In this sense, the tax system can be said to be "neutral", in other words, for a constant value of r, the first order conditions are not changed by the tax.
These findings need to be changed when there is shrinkage free. Suppose a company can write off the entire investment as well. This effectively reduces the price of capital goods from l (l-t_c), because there is a direct tax savings〗〖t _c. On the other hand, suppose that only a fraction of the interest ς deductible. The first order condition becomes

(L-t_c) p ∂ F / ∂ K = r (l-〖〗 ςt _c) (l-t_c) + γ (l-t_c) (5-27)

p ∂ F / ∂ K = r (l-〖〗 ςt _c) + γ (5-28)

From here we can see that the free shrinkage, coupled with no interest deduction, also left the first condition-oreder affected. In the usual case where the interest deductible, the free shrinkage reducing the lower right side of the existing tax
value. In this sense, the tax actually "encourage" investment. In addition, the effect can be very marked. Let r = 16 percent and 15 percent γ = ς = 1, t_c = 50 percent. Then the reduction of the cost of capital (right-hand side of (5-28)) is 31-23 per cent. Plug the other hand, if the interest is not deductible, then the true economic depreciation is not neutral and free depreciation is needed to secure the neutrality (it is not a "bribe"). Finally, we may note that the effect of the depreciation tax free is to turn into one in pure profit, then the time, intra marginal effects differ from the tax rate reduction and true economic depreciation.
Depreciation free economy is an extreme form of accelerated depreciation, and no case among many. It is possible for example that companies are allowed to write off δ fraction of the capital that is greater than the true economic depreciation. In allowing for this, need to take into account the fact that the depreciated value decreases faster than physical capital (Boadway and Bruce 1979). Thus, the benefits of early highere allowances to be set against the benefits of lower shrinkage later. Depreciation is free is an extreme case, where no subsequent depreciation is possible.

FINANCE BY RETAINED EARNINGS

We now examine the implications of taxation for investments in which it is financed by retained earnings. It is assumed that a small investment can be depreciated φ free (i, e .., abolished at once), and that (l-φ) remains true economic depreciation interesting.
We again consider a variation of one unit of capital stock in period l. The shareholders have therefore to finance (l-〖〗 φt _c) of investments financed by the government as a partner to sleep). Financing by retained earnings for the period to mean that shareholders are forgoing dividend for the period. In exchange for an increase in the second period. As in the previous section, we treat cost as an oppurtunity r (l-τ), where τ = t_p if alternative uses of funds are taxed at the personal level (or investments financed by borrowing in the form of a tax deduction). The first order condition then

p ∂ F / ∂ K = (r (l-τ) (l-φt_c)) / (l-t_c) + γ (5-29)

(The reader should check that this can be achieved by a perturbation argument used previously.)
Tax effects depending on whether

(L-τ) (〖(l-φt〗 _c)) / 〖〗 lt _c ≷ 1 (5-30)

Accordingly, the equity financing, changes in the conditions of free depreciation rate and the opportunity cost. If τ = 0 then the cost of capital is raised if φ <1, but the tax is fully offset where φ = 1 It can contrased the case of financial debt with interest deduction, where depreciation is free to go "too far". Or, we can see the relationship between τ and t_c. If φ = 0, then this condition t_c ≷ τ. Of this analysis is obviously good Taht taxation may increase or decrease the cost of capital. This is illustrated by the special cases shown in Table 5.1. Thus, with t_c = 50 percent, the net capital cost may be doubled or halved. As a result, the effect on the capital that could be used either. Table 5-1 Financial Policy and the cost of capital (net of depreciation) true economic. Depreciation Depreciation Guide

(Φ = 0, δ = γ) (φ = 1)

Financial debt: interest deductible rr (l-t_c) interest is not r / (l-t_c) r

deductible
Retained earnings r / (l-t_c) (l-τ) r (l-τ)

INFLATION IMPLICATIONS

In the analysis to this point we have not considered explicit inflation. We now assume that there is a level of (anticipated) inflation constant ρ so that all the prices went up by a factor of (1 + ρ) for each period. Suppose, as before, the company increased investment in period l by one unit, with the offsetting reduction of one unit of physical investment in the afterlife. The reduction in investment spending in the current period 2 (1 + ρ) for capital goods become more expensive, on the other hand, the cost of replacement investment has increased. The effect on profitability conditions for investment financed by borrowing, in the absence of taxes, is (King, 1977, ch.8)

p ∂ F / ∂ K ≷ (l + r) - (l + ρ) + γ (l + ρ) (5-31)

Hence the first order condition

p ∂ F / (∂ K = r-ρ + γ (l + ρ)) (5-32)

Inflation affects investment in two ways: first, the interest rate relevant now real rate (r-ρ) and secondly, the provision of depreciation must be done at the moment, cost is not historic.
Effects of taxation depends on the treatment of interest payments and depreciation. Usually (in late 1970), the tax system is not indexed with respect to the loan, so the nominal interest rate is tax deductible, on the other hand, there has been debate about changing the depreciation provision to allow for the effects of inflation. (For a discussion of inflation accounting and taxation, see, eg, Aaron, 1976, and kay, 1977.) If the depreciation allowance allowed full replacement cost (δ = γ (l + ρ)), then an additional unit of investment in period l, offset by corresponding reduction in, the next advantage incresase if

[P ∂ F / ∂ K-γ (l + p)] (l-t_c) - (r-ρ) + t_c i ^ *> 0 (5-33)

Where i ^ * shows that interest payments can be set against tax. Of these, the first order condition is

p ∂ F / ∂ K = (r-ρ) + γ (l + ρ) + t_c / (l-t_c) (r-ρ-i ^ *) (5-33a)

If all interest is tax deductible (i ^ * = r) then the right side is reduced by taxes. To achieve neutrality, only real interest payments should be deducted (King, 1077, p.242) - a factor that is often overlooked in the public debate.

ADD UP

In this section we have examined the impact of taxation on the effective cost of capital in a different financial regime. Where the investments financed at the margin (margianl very important trait) by financial bonds, providing a true economic depreciation means that the first order condition for investment is not affected by the tax (capital costs do not change). In this sense it is tax neutral. Neutrality can also be achieved by a reduction in depreciation free without interest. Other situations can cause the cost of capital to rise or fall as a result of taxation.

One feature that was brought by the analysis is the key role played by the detailed provisions of the tax law, in relation to aspects such as reduction in depreciation, interest and allowance for inflation. There is no such thing as corporate tax, and its effects may vary substantially across the country, or from year to year, depending on the terms of this. In addition, the impact depends on the interaction with the private taxatio, through funding decision. These features have important implications for empirical studies reviewed in section 5-5. Before coming to this, however, we need to take a broader view of the factors that affect investment.

5-4 A BROADER VIEW INVESTMENTS

The model described so far have assumed a competitive company, maximize profits or the value of the stock market, make decisions about the choice of capital-labor ration based on the current cost of capital. There is no room for market imperfections, for depatures of profit / value maximization, for the irreversibility of investment, to expectations about future tax rates or prices. In this section we describe some of the ways in which the analysis can be developed. This treatment is brief, not least because of progress in formulating a more relistic investment model is still limited.

MARKET IMPERFECTIONS

At one level of analysis extended to the case of a company that acted amperfectly competitive in product markets directly. If we assume that the company acts as trought that face downward-sloping demand curve, the value of the marginal product of capital is only replaced by marginal revenue product. Consideration of capital costs apply as before. Thus, we can handle groups or large monopoly pure competition monopolistic (discussed in more detail in lecture 7). Where but we are trying to expand the model to oligopolistic interdependence, there is no simple extension that can be made. In the absence of a widely accepted theory of corporate behavior, it is impossible to make definite predictions about the impact of taxation on investment. Thus it is possible that, in a small group compettion perfect, the capacity may be an important strategic decision, there may be a tacit collusion Liting capacity (it has the benefit that each n (see, for example, spence, 1997, and dixit, 1980) gives. diifferent view of the investment process.

Information Risk, and Imperfect Capital Markets Imperfect
We did not explicitly discuss the role of risk and uncertainty. Analysis of the financial structure of the company does not require thet there is no uncertaintly, and modiigliani-Miller theorem does not depend on it. Original demonstration (Modigliani and Miller, 1958) allowed for the class of risk, and this has been extended to much more general conditions (Stiglitz, 1969a). What is important however is that no bank ruptcy.
Assuming no bank ruptcy, and reasonable that individuals can issue a limited risk free interest rate of the bonds at a certain level, is not realistic. This means, for example, that someone with zero assets may invest an unlimited amount in a company that people trust with certainy will yield zero profits. When we allow for bank ruptcy, the bonds into riskier assets and risks depending on the loan amount. Capital market because it is inherently imperfect. If receips expected by the lender less than expected by the borrower, because the differential information or beliefs, and the difference increases when a company borrows more, it can cause in the absence of the tax-to-debt equity ratio of the optimal interior.

The effect of monetary policy has important implications for the determination of investment, and financial and real decisions are now even more closely linked than ever before. The capital cost may depend on the scale of the enterprise. The level of investment can be determined not only by the cost of capital but also by financial avaibility. (This provides a natural link to theoris who consider investment as a function of cash flow). Corporate profits tax may affect investment, even if it is neutral towards the cost of capital. In addition, there is likely a different effect: "old" companies, whose profits exceed desired investment, may be relatively little affected, but new companies with limited access to capital markets, and investment is constrained by cash flow desired, may have their investments reduced.

Uncertainty raises serious questions about the goals pursued by the company. Even in the world of course, shareholders may have different marginal tax rates and hence different policies favored. While there are differing views on the future of an attitude of risk, the problem of securing unanimity tends to be more severe. Recent literature suggests that it is difficult to formulate a satisfactory model of the behavior of companies where shareholders have different interests or beliefs. Except in rather special circumstances there is no unanimous agreement on the maximand companies, and conventional assumptions as maximizing the value of the stock market do not apply. Different flowers in turn explain some of the "puzzle" of corporate behavior, such as dividend policy.

MANAGERIAL MODEL OF THE FIRM

The problem of determining the company's goal has been disccused riting generally more widely in managerial model of corporate behavior. A simple illustration of this approach provived by Baumol sales maximization models. He assumes that managers running large companies have some latitude to pursue their own interests, and that the goal is to maximize the scale of the company: "all profits beyond some minimum level of vague, he was ready to scarifice further increase in profits if he can thus earn greater ". It was unveiled as the subject of maximizing revenue minimum profit constraint. If revenue can always spending extra promotion, the binding constraint on firms Optium, because if not "surplus" profits can be used for, say, advertising and therefore can increase revenue. Tax effect then depends on the form of profit constraints, and in this case it is unfortunate that the "vaguely defined". Either gross or net income can be postulated constraints, there may also be constraints on dividends or other financial flows that make a significant profit.

An alternative approach is that of Wlliamson, where managers aim to maximize utilitty function defined over staff expenses (power or status indicators), managerial emoluments and benefits that exceed the minimum requirements. Williamson will consider trade off can be seen, at least in part, such as the consumption of the company, through staff expenditures, and consumption outside the company (salary). In this respect there is a parallel with the discussion of labor supply in lectire 2. Implications for the desired level of capital depends more on the shape of profit constraints.
The idea of managerial discretion has been developed in a dynamic contextualization with Marris and others. In the complicated forms, it involves managers aim to maximize their own utility, mainly from the growth rate is achieved, the constraints imposed taking over. The latter requires that the market value of the stock does not fall below some specified fraction of the value of real assets. To the extent that it allows the latitude to managers, they choose a higher level of investment than would maximize the value of the stock market (for a given initial scale). The effect of the tax benefits in the model discussed by Solow.

In this model, the uncertainty is not addressed explicitly, but it is clear that a key role in explaining the existence of managerial discretion is played by differential information available to shareholders and managers. Thus, the simple model discussed in the previous lecture, the capitalist can not observe the effort put in by the manager, and had to resort to incentive schemes. (We discuss the cost of the same in the context of bureaucratic oversight in Lecture 10). We can actually see the relationship between managers and shareholders as a matter of indirect control in the precense of imperfect information. The shareholders are trying to design an incentive structure that leads managers to pursue their own interests to consider the concerns of the shareholders. But because of the direct control mechanism is not perfect, there will not be a complete coincidence. At the same time, there are alternative options open to shareholders from selling shares Taht, possibbly to take more bidders.

COST ADJUSTMENT

In the previous section have asssumed that the capital stock can be adjusted freely, but it is more realistic to allow constraints on the flexibility of the company. Opposite assumption that investment is really irreversible may be too extreme in that the second hand market for capital goods do come out, but it might be closer to reality than the assumption of complete reversibility.

It is equally possible that there is a cost of adjusting the capital, and there has been a substantial literature on optimal investment policy when there is an investment cost function C (I). Most of it has been assumed that the function of increasing and convex (C ^ '> 0, C "> 0 for I ≥ 0). Various reasons have been given for the cost of marginal increase in investment (C"> 0), including the increased cost of purchasing new equipment and internal cost of adjusting to a larger scale. This is not entirely convincing, since there are factors such as indivisibilities, which works in the opposite direction, and the case of a concave or a linear function (C '≤ 0) was examined by Rothschild. He suggests that this leads to a concentration of firms in one period response , the constraints to propagate the reaction over a period (such as a convex function).

Adjustment cost model focuses attention on the key issues of the investment and the role of expectations. What comes from this model not only the optimal level of capital, but also the time of adjustment. Thus, where prices are now expected to continue to rule, companies can choose the path of a solid investment, gradually approaching the goal so as to reduce the cost of adjustment (where C '> 0). On the other hand, if you expect the price of capital falls, it may will delay investment to take advantage of more favorable tax treatment, and then we turn now to this aspect.

EXPECTATIONS ABOUT POLICY

Expectations about price or tax policy change is important even without the assumption of adjustment costs. Thus, the preliminary analysis section 5-3 are based on companies that have static expectations, and needs to be changed where changes are anticipated. Suppose, for example, that there is a free depreciation on investments propotion φ, the true economic depreciation on the remainder, and that fraction ζ interest is tax deductible. The difference is confident the company expects that the depreciation rate will be changed to non-φ ^ * next period. The effect on profit is positive if (using the same arguments as before pertubation) with bond financing

p ∂ F / ∂ K (l-t_c)> (l-〖〗 φt _c) [l + r (l-〖〗 ζt _c)]-t_c γ (l-φ)

+ Γ (l-φ ^ * t_c) - (l-φ ^ * t_c) (5-34)

The last term is the savings on one unit of physical investment in the next period and then, such as depreciation, cost (l-φ ^ * t_c) per unit. Rearranging, the first order condition is
p ∂ F / ∂ K = (r (l-〖〗 ζt _c) (l-〖〗 φt _c)) / (l-t_c) + γ + ((l-γ) (φ ^ *-φ) t_c) / (l-t_c) (5-35)
The first conclusion to be drawn is that, where the tax parameters are expected to change, the results obtained previously neutrality no longer holds. Thus, the combination of free shrinkage (φ = 1) and no reduction in rate (ζ = 0) o ensure that the conditions of the first order is independent and if the company expects φ t_c change (φ ^ * ≠ φ) Hope decrease in investment allowance reduces costs capital, and the effect may be quite significant. Suppose the company expects φ fell 50-40 per cent, then 50 per cent t_c =, γ = 0:15 ni equivalent to lowering the cost of capital of 8.5 percentage points.

In general, the consequences of tax policy changes that are expected to be short-lived is that, before the introduction of, say, subsidies, investment will fall sharply, and shortly before removal would increase sharply, falling soon after to below the level that should be obtained. There may therefore be a significant effect of temporary tax policy beyond the period of operation (acting in the opposite direction intened). Anticipation of this policy may be particularly important where passing legislation is drwan out process. In the U.S., congressional approval of tax changes can be very delayed.
Governments therefore need to take into account the company's expectations when considering the impact of tax policy, a point emphasized by Lucas. Let us start with the situation described above, where φ is expected to decline. If we set r = 16 per cent, ζ = 1, then the cost of capital increased to (3/3 × 16 +15-8 half) per cent = 181/2 percent. If the government does φ cut to 40 percent, then the static expectations (φ * = φ) capital cost increased to (4/5 × 16 +15) = 27.8 percent percent. However, if the cut is expecteed temporary φ, so φ ^ * = 0.5, the increase was even more marked with more than 35 percent. Taking into account changes in expectations may therefore be an important, a very difficult interpretation of the impact of past policy. Center for each treatment hope is some understanding of how they are formed. Empirically, there has been considerable experimentation with different models of the formation of expectations for variables such as the inflation rate. The success to date is rather limited, and there is reason for hope about the modeling espect policy parameters become more complex. This obviously caused serious difficulties for the design of short-term policy issue which is of course much more tahn generally applicable only to corporation tax.

5-5 EMPIRICIAL EXAMINATION AND INVESTMENT TAX

Study empiricial tax effects on corporate behavior has become one of the most active areas of applied research in the field of public finance. In this section we focus however on the apparent decision of the company, and in particular the impact of taxation on investment. This not only serves to illustrate the problems that arise, but also the considerable intrinsic interest. On the other hand, one of the main conclusions of the previous section is that, in the presence of taxation, financial and real decisions can not be completely separated, indeed, one of the main problems with empirical work regarding the correct specification of the marginal cost of capital after tax.

The main evidence has been based on the investment behavior of the observed. This may relate to the company, where there have been numerous studies of time series of investment by individual companies, for industry, or economy-wide aggregates. There is a long tradition in econometric studies of investment, from the earliest attempts to estimate the accelerator models, but we concentrate here on the work of Jorgenson and colleagues. These studies, although controversial, particularly rrelevant because they provide an explicit treatment of the effects of taxation, and because they have become a reference point for many subsequent literature.

ECONOMETRIC STUDY OF INVESTMENT BEHAVIOR

The main feature of this approach is that Jorgenson desired capital that goes into estimating equations relate directly to the theory of optimal corporate behavior, in the absence of uncertainty and adjustment costs. The key element of this model is the cost of capital, c, which we have discussed in the previous section. Thus, we have the equation of the form
p ∂ F / ∂ K = ra_1 (t) + γa_2 (t) ≡ c (5-36)

Where a_1, 〖a〗 _2 is a function of the tax rate (t to be the vector representing the different dimensions of the tax system). Reffering back to the 5-3, we can see.to Jorgenson added this important assumptions about the technology that the elasticity of substitution and the degree of return to scale equal to unity:

F (K, L) = AK α ^ L ^ (1-α) (5-37)

Therefore, (where F indicates output):

∂ K / ∂ K = αF / K

And hence, from (5-36), capital desired output associated with the

K ^ * = αpF / c (5-38)

Having determined the optimal capital in this way, then Jorgenson arrivest the relationship can be estimated taking into account the backlog of projects unfinished retrieval and replacement investments.

Models have been estimated using a variety of data typesof the equation estimated total investment in manufacturing and non-manufacturing non-agriculture, distinguish between equipment and structures, using time series evidence for the period 1931-1963.
Tea effects of tax policy work trought c and hence K *. Of the estimated coefficients, Hall and Jorgenson calculate how effective the tax changes already in the United States.
This empirical work has been the subject of considerable debate, and we can distinguish several lines of criticism. The first concerns the treatment of output. A number of authors have taken issue with the fact that it is treated as an exogenous variable in the estimation of the investment equation. In part this is theoterical argument, based on the observation that adecision output variables for a competitive firm. It is objected that the model closer to accelator Jongerson than neoclassical theory, which generates the demand factor as a function of factor prices and output.

TREATMENT OF TAX POLICY

Final objection concerns the treatment of tax policy. As we have seen, taxation, depreciation allowances. This is the hypothesis that changes in taxation have the same effect as a change in another variable to include the cost of capital. There is a good reason to expect the fact that taxation to have different effects. It may for example take the time for new steps to taxes affect business decision-making.

The second objection to treatment Jongerson tax policy is that it is assumed that the company has static expectations with respect to tax policy. Planned investment is assumed on the basis that the applicable tax rates and depreciation provisions will rule forever. It is patently unrealistic. Investment tax credit benefits can be expected to be temporary, or higher can be expected in the future. As we have seen, this can lead to anticipatory investment behavior does not match the long-term desired stock of capital. Quantitative importance of these factors may be very large. It is therefore possible that the effective cost of capital has changed far more dramtically than assumed in the calculation Jongerson, and that the response to agiven percentage change is less than expected. In general, the effect of the policy can be estimated only with explicit treatment of expectations formation.
Thirdly, there is the proper form in which the parameters are introduced tax. As we have seen, the cost of capital depends on the financial means, and on the interplay between the personal and corporate tax systems. In addition, the cost of capital at the relevant margin, rather than the average cost of capital. There are difficulties in implementing it, and the comparison of the empirical formula commonly used in empirical work derived above shows that they coincide within the liver under certain assumptions. This examination allowed donkey exercise for the reader.

Add up we have discussed the analysis of investment Jongerson long as it is a pioneering effort to base empirical work on the theoretical framework ecplicit. Furthermore, it demonstrates the impact of tax Polivy has powerfu. But it seems premature to accept this dsebagai really set. As we have seen, there is considerable difficulty in making the transition from theoretical models to empirical work, including the specification of the production function and the lag structure, merging variable tax and econometric problems. The assumption that firms have static expectations with respect to tax policy simplifies the analysis but it can give a misleading impression in which the companies anticipate changes in tax rates and investment allowances. There is much less criticism that can be leveled against the risk of a theoretical framework that takes into account itself insufficient rigor in the share capital, imperfect competition, from the firm's decision-making process and behavior under uncertainty. Empirical analysis of the impact of tax policy on investment has made progress substaintial, but enhanced capabilities as in other areas to predict the impact of fiscal policy depends on improved understanding of key economic relationships.

5-6 CLOSING COMMENTS

We have seen in this lecture that the effect of taxation on the level and timing of investment may be much more complex than is often portrayed. Corporation tax itself can take many guises, depending critically on the provision for the reduction of interest and depreciation. Tax policy affects the capital structure of the company and hence the marginal cost of capital. In this case, depending on the tax rate on capital gains relative, interest and corporate profits.

Perhaps as important as the impact on the level of investment is that the pattern, which we have not discussed. Tax provisions may affect decisions about the durability of capital goods. Different companies may be affected differently. Where capital markets are not perfect, and the availability of financing to the investment constraints, firms in different stages of development or with different risk charateristic can respond in different awys not captured by the models that we have discussed. There are a number of ways in which the analysis needs to be expanded to consider the complexity. In a lecture that follows, we will, however, work with a simplified version of the effects of the corporate tax is a cost of moving to a general equilibrium framework.

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