PUBLIC SECTOR PRODUCTION AND PRICE

PUBLIC SECTOR PRODUCTION AND PRICE

A. Marginal Price Principles

The principles of public company pricing has long been a subject of discussion, and specific reference should be made to traditions in France, dating back the work of the Ecole des Ponts et Chaussées in the early nineteenth century (Ekelund, 1973). Much literature has argued in favor of marginal cost pricing, an thet case forcibly put in a paper Hotelling Hotelling klasikny found the price to be set at marginal cost, and that any resulting deficit in reducing the cost of the industry, will be financed by a lump-sum tax. This is to price the marginal cost must be seen as the first-best argument.

As we have emphasized in previous Lectures, there is a reason why there may be restrictions on the use of lump-sum taxes and why the government may have to rely on taxation distortion (indeed, actually called by Hotelling tax tends to finance the deficit has to be raised by way of distorting - so for them the price of economic activity is not the same marginal cost - there is no presumption that the optimal price in state enterprises will require marginal cost pricing if desired distribution can not be achieved by the bump.-sum means pieces may have used public sector as a tool for this purpose.

B.Control on Public Enterprises

Formal similarity between the issues of taxation and public enterprise prices provide considerable insight, but failed to do justice to the complexity of the questions that arise from the relationship between the company and the state government, and before presenting our analysis should comment briefly on some of the relevant issues.

On the central question is the nature of the "directives" from the government to the "state", and the degree of autonomy of the latter. There are different levels of autonomy. On the one hand, the company can be run like a government department (as sometimes happens with the Post Office), on the other hand, the company can become an autonomous corporation like IBM or ICI, with the country receiving benefits as the other shareholders (this true, for example, of certain joint ventures).

 More common is the intermediate case, in which public companies have independent management, but arranged by country of destination and are subject to certain restrictions. Formal organizational relationship may, however, are not perfectly reflect the level of autonomy. The civil servants running the Post Office may have the freedom of action that the head of satay steel companies, which may be directed to search for plans in certain areas, to build some kind of plant. Etc.In the design of administrative structures, the key role played by incentive information problems we have mentioned on several occasions.

An interesting question raised is not that we have room to explore here, and just assume that the structure is the nature of the two following steps. First, the government set corporate objectives and constraints. For example, he decided on the level of return on capital targets to be achieved by the industry and the amount of state subsidy (if any). Second, firms determine pricing policy so as to maximize the function of the subject is the goal constraints. For example, given that the National Electricity Corporation must make a profit of $ x, how should it determine the price relative to domestic and industrial users? The nature of the efficiency and equity of outcome depends on decisions made in the second stage.

With this kind of structure, there is no direct relationship between public companies. National Electric Corporation does not account for the impact of the policy on the National Coal Corporation. Such interaction - that affect such things as transfer pricing - need to be considered by the government lays down guidelines for each company, for example, to allow for the fact that they can produce closely competing products (eg, long-distance trains and air services).

Two-tier structure is one reason why it is parallel with the literature on optimal taxation incomplete.In this case, there is a problem one stage. If we apply the results of Ramsey directly at the individual company level, we ignore the fact that the problem itself is the subject of choice. Profit targets for different industries set by the government, and consider interdependence. On the other hand, if we collapse problems in one stage, and treat all public companies as a whole, we ignore the fact that the design guidelines are an important feature of the decentralization of public sector institutions.

C.MARGINAL COSTS

1. Profit

The simplest situation is that of a single public company, producing a quality product in the nal Z (in per capita terms), if it is not competitive in the economy (in which per capita private output vector is denoted by X). all individuals have identical utility function U (X, Z, L), where L is the amount of labor supplied per person. Labor is taken as numeraire. We are represented by a vector q of the product price by the private sector and the public output price p. Production constraints assumed form

Ω ≡ F (X) + C (Z) - L = 0 (15-1)

There are F (X) provides workforce needs in the private sector, and (Z) are in the public sector. It is assumed that the convex production sets, conditions for profit.

Π ≡ q. X - F (X) (15-2) (For example, the value of net output minus labor costs), maximized necessary condition for which is that qi = Fi, where the latter shows an instance of the Xi. assumed at this stage that there are constant returns to scale in the private sector. So Π ≡ 0. Implications of pure profit we will discuss later.

Public companies are assumed to determine the price, p, to maximize social welfare, as measured by the indirect utility function of the representative consumer, denoted by V (qp). companies limited by income (per person)

pz - C (Z) + T> Π0 (15-3)

where T indicates subsidized by the government and Π0 profit targets. Assumed subsidy financed by lump-sum taxation, so that T enters the indirect utility function. There are no other taxes are assumed at this stage. The solution to the price problem can be seen by forming the Lagrangian.

L = V (qpT) + λ [PZ - C (Z) + T-Π0 (15-4)

First condition with respect to p can be written using the properties of the indirect utility function (assuming constant returns to scale in the private sector means that the change is only in the V is that arising directly from p):

- ΑZ + λ [Z + (p-C1) ∂ Z / ∂ p] (15-5)

where α is the marginal utility of private pendapatan.Misalkan first that T is the independent variable, so that the lump-sum taxation can be used to finance any deficit. First condition with respect to T (using the fact that (provided ∂ V / ∂ T =-α) is that

- Α + λ = 0 (15-6)

From (15-5) it follows that (provided ∂ z / ∂ p ≠ 0) the conditions necessary for optimal is that

p = C1 (Z) (15-7)

            price equals marginal cost. This is an overview of the standard arguments for the price it costs marjinal.Dimana no constraints on the use of T, and the company has a profit target of effective, then the rule should be modified price. Let T ≤ 0, and the marginal cost price is not enough to allow the company to meet (15-3). This situation is illustrated in Fig. 15-1, which target the profits to be breaking even. At this level of output where price equals marginal cost, the deficit shown by the hatched area. In other to meet profit targets, the company had to reduce output to ZB, where price exceeds marginal cost. As illustrated in the diagram, the instructions to the company to break even fully determine its pricing policy. It sets a price above marginal cost to the extent necessary to avoid a deficit.

In practice, public companies produce more than one product, and it introduced a degree of That the mark-ups over marginal so must conform to "the market will bear", that is, inversely proportional to pasticity request. Against the position that the price should oportional marginal cost, advanced by, among others, Frisch (1939) and Allais (1948).

In other to consider the merits of the rival views, we can modify the initial analysis, so the maximization problem is now represented by the Lagrangian:

L = V (q, p1, p2, T) + λ [p1Z1 p2Z2 C + + (Z1, Z2) + T - Π0] (15-8)

The tax rate assumes that the lump-sum fixed. The first of these conditions with respect to p1, p2, and prices are:

-ΑZ_1 + λ [(p_1-C_1) (Z_1 ∂) / (∂ p_1) + (p_2-C_2) (Z_2 ∂) / (∂ p_1) + Z_1] = 0

(15-9)

-ΑZ_2 + λ [(p_1-C_1) (Z_1 ∂) / (∂ p_2) + (p_2-C_2) (Z_2 ∂) / (∂ p_2) + Z_2] = 0

There C1 denotes ∂ C / ∂ Z_1. Parallel to the Ramsey problem should be clear at this point, if we write C1 ≡ p1-t1.

If we consider the special case in which the demands are independent and there is no income effect, then, rearrange,

(P_1-C_1) / p_1 ((p_1-C_1) / p_1) = (λ-α) / λ

This results in Ramsey familiar, that "tax" should inversely proportional to the elasticity of demand, because it supports "what the market will bear" look rather than the rule of proportionality Frisch-Allais. This, and other implications, brought out by Boiteux (1956). Devinations level of marginal cost pricing depending on budget constraints. If this is not binding (eg, because the lump-sum tax can be used) λ = α and p1 = C1. At the other extreme, the approach takes advantage α, and the right side (15-10) tend to unity.  maximum, λ These results restrict price-discriminating monopoly case, because marginal revenue equals marginal cost implies

(P_1-C_1) / p_1 (ε_1 ^ d) = 1 (15-11)

D.Benefit  in the Private Sector

Assumptions made so far do not allow for pure profit in the private sector, which arise in the competitive case where there is a decline back to the scale. We now consider the implications of the profits for the price of a public company and its relation to the optimal tax formula.

There is no general loss in anger for untaxed (as in the analysis to this point). But this is no longer true in which consumers receive income benefits, because multiplying all producer prices by 5 implies that the income gains are also multiplied by 5. The effect can be offset simply by multiplying all consumer prices by 5. The assumption of good untaxed inocouos not in this case. We can normalize the price of ore a manufacturer of consumer prices.

Restrictions on commodity taxation is very important then to be considered in conjunction with restrictions on the rate of tax on pure profit. Suppose we set on the unity of the producer price (the work). The advantage of the private sector (per capita)

Π = s X - F (X) (15-2 ')

It is assumed to be taxed at the rate t, so that the lump-sum income received by a household is (1 - τ) Π (≡ I). Such taxes can be quivalent to all consumer prices rising by a factor of 1 / (1 - τ), since the demand function is homogeneous of degree zero in consumer prices and

The exhausting of pure profit that can be achieved by a uniform tax on all goods (and labor). In what follows we assume that τ is fixed, and that there is an untaxed goods, which is taken to be labor. Individual budget limit then, the Z output of the public sector.

q X + Z = L p + (1 - τ) Π (15-12)

Combined with production constraints and (15-2 '), this yields the budget constraint of the public sector (per capita):

p Z - C (Z) + (q-s) X + τ Π = 0 (15-13)

or

p Z - C (Z) + q X - F (X) - (1 - τ) Π = 0 (15-3 ')

Let us now consider the position of the public sector as a whole to determine the price to be charged is liable to tax all goods except labor (and no poll tax or subsidy). Maximization problem can then be formulated in terms of the Lagrangian:

L = V (q, p1, p2, I) + λ [p Z - C (Z) + q X - F (X) - (1 - τ) Π] (15-14)

Another condition for the first-choice adala pk ∂ V / (∂ p_k) + ∂ V / ∂ ∂ II / (∂ p_k) + λ [+ Σ_j Z_k ▒ 〖(q_j-F_j) (X_j ∂) / (∂ p_k)〗 - (1-τ) (∂ Π) / (∂ p_k)] (15-15)

Effect on profit given by (from (15-2 '))

(∂ Π) / (∂ p_k) = Σ_j ▒ 〖(Σ_m ▒ 〖X_m (S_m ∂) / (∂ X_j))〗〗 (S_j ∂) / (∂ p_k) (15-16)

All profits are returned to the government, so there is no supply of entry consideration. In the case of private goods, where the rate of tax on profits of less than 100 percent, the supply side must diperhitungkan.Sebuah natural question at this point is why the government does not impose a 100 percent tax profits. Previously, we provide some explanation as to why lump-sum tax should not be the sole source of income. However, if the tax advantages of non-distortionary, surely they should be set at 100 percent, and thus the question which we have been concerned ceased to be relevant?

 In practice, the government does not follow this policy Henry George-like. Although the war some countries have imposed additional 100 percent tax rate, they usually do not charge a regular 100 percent tax on profits and income from the fixed factor. The reason for this will come back to the lack of information at the disposal of the government. Most importantly, he found difficulty in distinguishing pure profit from the return to capital, or the return to entrepreneurship. This is seen most clearly in the case of unincorporated enterprises. If there is a 100 percent profit tax, no company would ever declare profits will always distribute "pure profit" as a reward to entrepreneurs.

SUPPLY OF GOODS GENERAL PUBLIC PRIVATE

At first we need to make an important distinction, between production and public provision. The two are often confused, even though logically and in practice they are different. The government provides for national defense, but a lot of the production of goods purchased for the national defense is in the private sector. The government has, in many countries, amonopoly mail service, but the cost for the use of the letter a little differently than a private company. In Lecture previeus we deal with public commodity produced, the following is related to the goods and services provided freely, perhaps rationed amount, to all members of society.

Free provision of goods can be seen as a limiting case of subsidies. namely, delivery of commodities to consumers at prices below the cost of production. In this sense, the analysis of this lecture, and that the price of the public sector, are aspects of the same subject. But there are distinct features of the provision of public services which approach does not capture and that is the focus of much of our discussion: the provision of public services there is no need for monitoring the use, while any price, positive or negative, the use must be recorded.

The issue of monitoring the use of the first to introduce the relevant aspects of the characteristics of the goods or the public should be given: it may be impossible, or very expensive, the cost for the use of a particular commodity. In other words, it is not possible to exclude non-contributors. This is basically a technical question, and depending on the technology available.

In this view, the personal is at one extreme of the spectrum, where one unit increase in consumption by Mr. X to reduce consumption available to others by one unit, and pure public goods at the other extreme, where the increase in consumption of Mr X cause no reduction for others. Polar cases sometimes characterized in the following way.

X_i ^ h a h household consumption of commodity i. Then for personal items,

Σ_h x_i ▒ 〖〗 ^ h = x_i (16-1)

Where Xi is aggregate supply. Conversely, for pure public goods,

X_i ^ h = x_i all h (16-2)

It may be noted that it is not responsible disposal free of charge. For public goods, such as defense, this is probably not unreasonable assumption, on the other hand, for items such as televisions, free disposal is possible, and (16-2) should be replaced by

^ X_i x_i all h ≤ h (16-2 ')

Case intermediated rather difficult to characterize, and various approaches have been proposed in the literature. One is to write the consumption possibility frontier for the economy as well:

ᵡ (x_i ^ 1, ..., ..., x_i ^ h, x_i) = 0 (16-2) with

(∂ ᵡ) / (∂ x_i ^ h) = 0 (for all h) for pure public goods,

(∂ ᵡ / ∂ x_i ^ h) / (∂ ᵡ / ∂ x_i ^ k) = 1 (for all h, k) for pure public goods

Table 16-2 Experimental evidence on willingness to pay

	Costly exclusion	Demand irresponsive	Low cost of individual supply	Distributional arguments
	?	?	?	?
National defence Roads and bridges TV and radio Education Water Police	Yes Yes Yes ? Yes	Yes Yes	Yes Yes ? Yes Yes	Yes Yes ? Yes
Medical care Fire protection Legal system – criminal case                       – civil cases Leverage and rubbish National park

2.OPTIMUM EFFICIENCY SUPPLY PURE PUBLIC GOODS

In this section we consider the optimal level of provision of good, pure single public, consumed in quantity G by everyone. There are aggregate production relationship:

F (X, G) = 0 (16-5)

Where X represents the vector production both personal number.

The government fully controlled economy is assumed to choose the level of G, and the allocation of private Xh for household h (h = 1 where ....... H) to maximize individualistic social welfare function. If the individual utility function Uh (Xh.G). then ma social welfare function is written as follows

Ψ U 1, ..., U h, ..., UH] (16-6) where Ψ is assumed to function, twice differentiable concave to be increased in all the arguments. If we form the Langrangean

= Ψ - λF (X, G) (16-7) the first order condition (∂) / (∂ x_i ^ h) (X, G) = 0 (16-8a)

F (X, G) = 0 (16-8b)

Conditions (16-8a) gives the condition first-best welfare standards (equation marginal rate of substitution and transformation). New conditions (16-8b).

Of (16-8a) we can see that (ie, the left side is the same for all h). we can then divide the hth term in the sum on the left side (16-8b) to give

This is a basic condition for the provision of public goods optimal: the number of the marginal rate of substitution between public goods (and some good private) should be equal to the marginal rate of transformation (MRT ΣMRS =). There is a clear intuitive interpretation of this condition for a full optimum. Marginal benefit of an additional unit of the public good is the benefit people get one, plus the benefit of the person to get, etc. Conversely, an additional unit of good given to the private sector or one given to people 2.

The solution can be illustrated diagram enemies cases where there are two people and two goods (X = private good, G = pure public good). Figure 16-2 shows at the top of the indifference curve for the citizens first and AB production constraints. Suppose we fix the UI of my constituents in the indifference curve. II residents likely will be displayed at the bottom of Fig. 16-2 by the CD (which differ between AB and UI). Clearly, Pareto efficiency requires the marginal rate of substitution equals the slope of the second individual CD curve (ie, at the point E). but this is only the difference between the marginal rate of transformation (the slope of the production possibilities schedule) and the individual's marginal rate of substitution of the first (the slope of his indifference curve). Thus, we have the MRT-MRS3.Pembiayaan Public Goods by Distortinary Taxation

If government spending is financed by taxes that result in overload, it seems most likely on the rules intuitively equate groundsthat ΣMRS the MRT will lead to too high a level of expenditure. As given by Pigou,

That raised an additional £ incomes cause direct harm to taxpayers as a body over and above the losses they suffered in the actual payment. Where there is indirect, it should be added to the direct loss of satisfaction involved in the withdrawal of the marginal unit of resources by taxation, before this is balanced versus satisfaction generated by the marginal expenditure.

3.OPTIMUM SUPPLY PURE PUBLIC GOODS DISTRIBUTION

In this section we examine how the conditions for the provision of public goods is influenced by considerations of optimal distribution, paying particular attention to the situation where there are restrictions on the set of feasible tax.

Redistribution and Non-distortion PerpajakanPada previous section we derived the best fir allocation rules ΣMRS = MRT, where b is the optimal use of lump-sum taxes and transfers. Normally, the government does not enjoy complete freedom in the choice of a lump-sum tax, and indeed we have previously found that this can be restricted uniform poll tax or subsidy. Where it is, the ΣMRS = MRT condition ia no longer necessarily apply. To see this, let us assume that the government can levy taxes Th household h, where Mh is income (fixed). There is a good oneprivate (quantity h = Mh-Th) and a public good (G). government chooses G and X to maximize.