Perman et al.: Ch. 4. Welfare economics and the environment

Transcription

1 Perman et al.: Ch. 4 Welfare economics and the environment

2 Objectives of lecture Derive the conditions for allocative efficiency of resources Show that a perfect market provides efficient allocation of resources The impact of public goods and externalities on the conditions for allocative efficiency

3 Welfare Economics (Environmental) economic analysis Positive Analysis Normative analysis Efficiency Pareto efficiency Welfare economics Optimality Social welfare function Intertemporal allocation Intratemporal allocation Intertemporal allocation Intratemporal allocation

4 First section Ch. 4 Pareto Efficiency

5 Pareto Efficiency Conditions About Pareto Efficiency Conditions Assumes only ordinal utility functions Interpersonal comparisons are not possible Two assumptions in first section of Ch. 4 No externalities in either consumption or production No public goods.

6 Assumptions We assume a simple world: Two products: X and Y Two consumers: A and B with utility functions U A (X A,Y A ) and U B (X B,Y B ) (4.1) Produced by two firms: 1 and 2 with production functions X X X X ( K, L ) Y Y Y Y( K, L ) (4.2) The amounts of resources are fixed: Capital: K T and Labour: L T

7 Marginal utility and marginal product The marginal utility that A derives from the consumption of good X is denoted U A X U A X = U A / X A. The marginal product of the input L in the production of good Y is denoted as MP Y L MP Y L = Y/ L Y Equivalent notation applies for the other marginal products.

8 Marginal rates of substitution The marginal rate of utility substitution for A (MRUS A ) rate at which X can be substituted for Y at the margin, or vice versa, while holding the level of A s utility constant. given by the slope of the indifference curve. The marginal rate of technical substitution between K and L in the production of X (MRTS X ) rate at which K can be substituted for L at the margin, or vice versa, while holding the level output of X constant given by the slope of the isoquant.

9 Marginal rates of transformation The marginal rates of transformation for the commodities X and Y MRT L is the increase in the output of Y obtained by shifting a small amount of labour from use in the production of X to use in the production of Y, or vice versa MRT K is the increase in the output of Y obtained by shifting a small amount of capital from use in the production of X to use in the production of Y, or vice versa.

10 Efficiency requirements Three conditions must hold to achieve allocative efficiency : 1. Efficiency in consumption 2. Efficiency in production 3. Product-mix efficiency

11 Efficiency in Consumption (Marginal rates of utility substitution) Consumption efficiency requires that the o marginal rates of utility substitution for the two individuals are equal: MRUS A = MRUS B (4.3) If this condition were not satisfied o it would be possible to rearrange the allocation as between A and B o so as to make one better off without making the other worse off. Figure 4.1

12 Fig. 4.1 Efficiency in consumption (commodity space) B Y A X A Xa I B1 A Xb A 0 I B0 a: MRUS A <MRUS B b: MRUS A =MRUS B B Ya I A. a A move from a to b along I A I A represent Pareto improvement A Ya B Yb. b A Yb B 0 B Xa B Xb I A I B0 I B1 B X A Y

13 Efficiency in Production Marginal rate of technical substitution Two inputs, L and K, which can be used to produce the goods X and Y. Efficiency in production requires that the marginal rate of technical substitution between L and K be the same in the production of both commodities MRTS X = MRTS Y (4.4) If this condition were not satisfied it would be possible to reallocate inputs to production so as to produce more of one of the commodities without producing less of the other. Figure 4.2

14 Fig. 4.2 Efficiency in production (commodity space) K Y L Xa L Xb X 0 L X I Y1 I Y0 a: MRTS L <MRTS K b: MRTS L =MRTS K K Ya I X. a A move from a to b along I x I x increases output of Y without reducing output of X K Xa K Yb. b K Xb I X I Y0 I Y1 L Y Y 0 L Ya L Yb K X

15 Product-mix efficiency (Marginal rate of transformation) Marginal rate of transformation (MRT) The rate at which one commodity can be transformed into another by means of marginal reallocations of one of the inputs to production Product-mix efficiency requires that MRT L = MRT K = MRUS A = MRUS B (4.5) Figure 4.3

16 Y Y M Fig. 4.3 Product-mix efficiency (commodity space) Production possibility frontier: Output combinations that can be produced with available resources. Slope = marginal rate of transformation (MRT). I For two individuals with equal marginal rates of utility substitution There is one indiff. curve with slope MRUS A = MRUS B Y a Y b a Moving from a to b means shifting to higher indiff. curve b Efficiency condition: MRT K =MRT L =MRUS A =MRUS B Y c c I 0 X a X b X C X M X

17 Summary Pareto efficiency conditions An economy attains a fully efficient static allocation of resources when simultaneously satisfying equations 4.3, 4.4 and 4.5: Efficiency in consumption MRUS A =MRUS B (4.3) Efficiency in production MRTS X =MRTS Y (4.4) Efficiency in production mix MRT K =MRT L =MRUS A =MRUS B (4.5)

18 A Pareto efficient allocation Not unique For an economy there will be many Pareto efficient allocations There will be a family of points where the slopes of the indifference curves for A and B are equal satisfying: MRUS A = MRUS B The utility possibility frontier is the locus of all efficient combinations of U A and U B Fig. 4.6

19 Figure 4.5 The utility possibility frontier U B Utility possibility frontier locus of all Pareto efficient combinations of U A and U B B U max T Moves from R to T, Z and S: Are all Pareto improvements B U R R Z S Not possible to say which of the points T, Z and S on the frontier is best from the point of view of society. Choosing a point along the utility possibility frontier will make one individual worse off to make the other better off Pareto efficiency criteria do not cover such choices. 0 A U R A U max U A

20 Optimality Social Welfare Function

21 Social welfare function and Optimality In order to choose between Pareto efficient allocations we need the concept of a social welfare function, SWF, A SWF can be used to rank alternative allocations. For the two-person economy, an SWF will be of the general form: W = W(U A, U B )

22 Social welfare indifference curves SWF is formally of the same nature as a utility function We can depict a SWF as social welfare indifference curves Fig. 4.6 shows a social welfare indifference curve WW that has the same slope as the utility possibility frontier at b which point identifies the combination of U A and U B that maximises the SWF. The fact that the optimum lies on the utility possibility frontier means that all of the necessary conditions for efficiency must hold at the optimum.

23 Figure 4.6 Maximised social welfare (utility space) U B Utility possibility frontier B U a W a At optimum all necessary conditions for efficiency must hold. Plus: equality of the slopes of a social indifference curve and the utility possibility frontier: W U U W U U B B A X Y A A B X Y Slope of social welfare indifference curve (4.7) Slope of utility possibility frontier B U b b Social welfare indifference curve B U c c W 0 A U a A U b A U c U A

24 Social welfare maximum At a social welfare maximum/optimality the slopes of the indifference curve and the frontier must be equal so that it is not possible to increase social welfare by transferring goods, and hence utility, between persons. Allocative efficiency is a necessary condition for optimality But moving from an allocation not efficient to one that is efficient Will not necessarily improve social welfare. But when there is an inefficient allocation there is always some other allocation which is both efficient and superior in welfare terms compare points C and E in Figure 4.7.

25 Utility possibility frontier At C the allocation is not Pareto efficient, At D the allocation is Pareto efficient Still, C gives a higher level of social welfare than D. But E is efficient and superior to C because move from C to E is a Pareto improvement. Social welfare indifference curves

26 Market allocation and SWF Given ideal institutional arrangements Markets can achieve allocative efficiency. It cannot be claimed that markets alone achieve fair allocations. If there were a generally agreed SWF there would be no problem in ranking alternative allocations. There is not an agreed SWF Defining relative weights for utilities of individuals are an ethical/political matter. Economists have devised criteria for evaluating alternative allocations that do not involve explicit reference to a social welfare function.

27 4.4 Compensation tests Attraction of Pareto improvement criterion is that it avoids the need to refer to the SWF to decide on whether or not to recommend that reallocation. Two problems with the Pareto improvement criterion does not fix a unique allocation Most projects involve winners and losers and Therefore outside of the terms of the Pareto improvement criterion. Welfare economists have tried to devise compensation tests comparing allocations where there are winners and losers which do not require the use of a SWF.

28 Kaldor compensation test Consider a two-person, two-commodity world. Moving from allocation 1 to allocation 2 involves one individual gaining and the other losing The Kaldor compensation test says that allocation 2 is superior to allocation 1 if winner could compensate loser and still be better off. Kaldor test may be inconsistent it may sanction a move from one allocation to another but it may also sanction a move back to the original allocation.

29 Hicks test Hicks test: Could the loser compensate the winner for forgoing the move and be no worse off than if the move took place If the answer is no the reallocation is sanctioned. Compensation tests treat winners and losers equally No account is taken of fairness of the distribution of well-being.

30 PART 2 ALLOCATION IN A MARKET ECONOMY

31 Efficiency given ideal conditions For a central planning agency to achieve allocative efficiency it is must know all of the economy s production and utility functions. This is infeasible and one of the reasons that attempts to run economies in this way have been unsuccessful. The attraction of free markets is that they do not require that any institution or agent have such knowledge markets are decentralised information-processing systems. Environmental and resource issues are studied as they arise in an economy where markets are the dominant social institution for organising production and consumption.

32 Efficient allocation In a market economy Requirements for efficient resource allocation in a market economy: 1. Markets exist for all goods and services produced and consumed. 2. All markets are perfectly competitive. 3. All transactors have perfect information. 4. Private property rights are fully assigned in all resources and commodities. 5. No externalities exist. 6. There are no public goods. 7. All utility and production functions are well behaved. Behavioural assumptions firms maximise profits and individuals maximise utility.

33 Utility maximization Figure 4.8 refers to an individual in a two-commodity economy. Utility maximisation requires that the budget line is tangential to an indifference curve This means the slope of the indifference curve is equal to the price ratio. Given that the slope of the indifference curve is the MRUS, we have: P MRUS= X PY Since all individuals face the same prices, we have: A B X MRUS MRUS I.e., the consumption efficiency condition is satisfied in this ideal market system. P P Y

34 The line Y max X max is the budget constraint. Y max is the amount of Y available if all income is spent on Y, X max is consumption if all income is spent on X. The slope of the budget constraint gives the price ratio P X /P Y. Utility maximisation requires consumption X* and Y* corresponding to point b on the indifference curve U*U*. Where he slope of the indifference curve is equal to the price ratio.

35 Profit maximization Profit maximization implies that firms minimise the costs We are focusing on cost minimisation for a given level of output. This question is examined in Figure 4.9 Cost-minimising firm will choose the input combination given by the point b The slope of an isoquant is the MRTS so that cost-minimising choices of input levels must be characterised by: P MRTS= K PL All firms face the same P K and P L, which means that MRTS X = MRTS Y I.e., production efficiency condition for allocative efficiency.

36 K Figure 4.9 Cost minimisation. K 3 K 2 X* X*X* is the isoquant corresponding to some given output level X*. K 1 L 1, K 2 L 2, and K 3 L 3 are isocost lines. a Isocost lines shows the combinations of K and L that can be purchased for a given total expenditure K 1 The slope of an isocost line is the ratio of input prices, P K /P L. b c X* 0 L 1 L 3 L 2 L Note: Error in Fig. 4.9 in the book Y on the vertical axis should be K.

37 Product mix condition The remaining condition for allocative efficiency is the product mix condition which involves both individuals and firms. We will look at the choice of input levels that gives maximum profit Consider the input of labour to the production of X, with marginal product X L Choosing the level of X L to maximise profit involves balancing the gain from using an extra unit of labour against the cost of so doing. The gain here is just the marginal product of labour multiplied by the price of output, i.e. P X X L. The cost is the price of labour, i.e. P L. Profit is maximised where P L = P X X L (the same for capital)

38 Product mix condition Profit maximization leads to: PX MRTL MRTK P The fact that all agents are confronted with the same prices means: P X A B MRTL MRTK MRUS MRUS PY Y This shows that the profit-maximising output levels in the ideal market economy satisfy the product mix condition for allocative efficiency.

39 4.6 Partial equilibrium analysis In the efficiency and optimality analyses above we have used a general equilibrium approach looking at all sectors of the economy simultaneously. Many applications use partial approach which is much easier to operationalise This involves looking at only the part of the economy e.g. the production and consumption of cola Also the partial equilibrium analysis demonstrates that an ideal market system secures allocative efficiency We will briefly summarize the results

40 Partial equilibrium analysis All consumers face a common market price P X, and each will adjust their consumption until their marginal utility (MB in money units) is equal to that price. Each firm faces that same fixed market price, and adjusts its output so that marginal cost (MC) of production equals that price. So we have: P X = MC X = MB X (4.13) The equality at the margin of costs and benefits shows that cola is being produced in the amount consistent with the requirements of allocative efficiency.

41 Consumers surplus and Producers surplus We can use Figure 4.11(d) to introduce the concepts of consumers surplus and producers surplus

42 Figure 4.11 A partial equilibrium interpretation of economic efficiency. B(X*) NB(X*) d B(X) C(X) B(X) = total benefits (B) to consumers from consumption of commodity X C(X) = total costs (C) of producing commodity X NB(X*)= max. attainable net benefits form producing and consuming X (a) C(X*) 0 e a X* X NB(X) NB(X*) NB X (b) 0 g X* MC X X f (c) (d) h 0 g / P x f / h / 0 MB X X* X S X =MC X D X =MB X X* X In (d) the area beneath the demand curve (D x =MB x ) between zero and X* units shows the total consumers willingness to pay, WTP. Consumers surplus is the difference between total WTP and actual expenditure at the price P x. Producers surplus is the area of the triangle h P X f. The supply curve (S x =MC x ) is the marginal cost curve. The surplus on production is given by the vertical distance from the price line to the supply curve. Source: Perman, R., Y. Ma, M. Common, D. Maddison & J. McGilvray: Natural Resource and Environmental Economics, Pearson Education Limited, 4th edition, 2011, Ch. 4.

43 4.7 Market allocations not necessarily equitable The attainment of efficiency is the exhaustion of the possibilities for mutually beneficial exchange. If one individual has a much larger initial endowment Voluntary trade based on self-interest is not going to equalise wealth.

44 Theorems of Welfare economics Welfare economics is based on two fundamental theorems: 1. A competitive market equilibrium is an efficient allocation. 2. To every efficient allocation there corresponds a competitive market equilibrium based on a particular distribution of initial endowments. The point of the second theorem is that the efficient allocation realised by a competitive equilibrium is conditioned on the distribution of initial endowments. If an efficient allocation is considered inequitable It can be altered by lump-sum taxes and transfers To another efficient allocation.

45 PART 3 MARKET FAILURE PUBLIC POLICY AND THE ENVIRONMENT

46 MARKET FAILURE To recapitulate, we have seen that for markets to produce efficient allocations, it is necessary that: 1. Markets exist for all goods and services produced and consumed. 2. All markets are perfectly competitive. 3. All transactors have perfect information. 4. Private property rights are fully assigned in all resources and commodities. 5. No externalities exist. 6. There are no public goods. 7. All utility and production functions are well behaved. 8. All agents are maximisers.

47 Table 4.4 Characteristics of private and public goods Public goods Some of the services that the natural environment provides have the characteristics of public goods, and cannot be handled properly by a pure market system. Table 4.4 Characteristics of private and public goods Rivalrous Excludable Pure private good Ice cream Non-excludable Open-access resource Ocean fishery (outside territorial waters) Non-rivalrous Congestible resource Wilderness area Pure public good Defence

48 Public goods and economic efficiency For a two persons economy and two private goods we found that the product-mix condition for allocative efficiency was MRUS A = MRUS B = MRT* (4.14) Where X is a public good and Y is a private good the corresponding condition is: MRUS A + MRUS B = MRT (4.15) 4.15 will not be satisfied in a pure market economy Markets cannot supply a public good at the level required * Marginal rate of transformation (MRT) The rate at which one commodity can be transformed into another by means of marginal reallocations of one of the inputs to production

49 4.9 Public goods In the case of a private good Each individual can consume a different amount Efficiency requires that all individuals must, at the margin, value the good equally It also requires that the common valuation, at the margin, is equal to the cost, at the margin, of the good. In the case of a public good each individual must, by virtue of non-rivalry consume the same amount of the good Efficiency does not require that they all value it equally at the margin. It does require that the sum of their marginal valuations be equal to the cost, at the margin, of the good. Markets cannot supply public goods a role for Government.

50 16 Fig [MWTP = marginal willingness to pay ] Efficient level of supply for the public good is the level at which the sum of two MRUSs is equal to the MRT between it and the private good. I.e., supply the public good at the level where aggregate marginal willingness to pay is equal to marginal cost..

51 Preference revelation and The free-rider problem Government intervention is the obvious way to bring about the required supply of a public good The costs of installing street lighting should be covered by taxing each individual according to their willingness to pay. However, in practice the free-rider problem comes up in trying to get the individuals to reveal their true preferences for the public good.

52 4.10 Externalities An externality is said to occur when the production or consumption decisions of one agent have an unintended impact on the utility or profit of another agent and when no compensation/payment is made by the generator of the impact to the affected party. Externalities are a source of market failure For a beneficial externality the market will produce too little For a harmful externality the market will produce more of it than efficiency requires.

53 Table 4.6 Externality classification Arising in Affecting Utility/production function Consumption Consumption U A (X A, Y A, X B ) Consumption Production X(KX, LX, YA) Consumption Consumption UA(XA, YA, XB) and and production Y(KY, LY, XB) Production Consumption UA(XA, YA, X) Production Production X(KX, LX, Y) Production Consumption UA(XA, YA, Y) and and production X(KX, LX, Y) Row 1: a consumption externality where agent B s consumption of commodity X is an argument in A s utility function. Row 5 has the production of Y determining, for given capital and labour inputs, the amount of X produced.

54 The Coase theorem The idea that given a suitable assignment of property rights private bargaining between individuals can correct externality problems and lead to efficient outcomes Political question how property right should be assigned To the polluter or the victim Both alternative will yield efficient allocations Transaction costs will prevent Coase solutions in most cases Other policy instruments required to internalise externalities.

55 Figure 4.13 The bargaining solution to an externality MB = marginal benefits to A from being allowed to emit pollution/noise - and the amount that A would pay for the right to a marginal increase in emissions MB MEC If A has right to pollute - B will buy pollution rights MEC = the marginal costs to B from the A s emissions - and the amount that B would pay for a marginal reduction in A s emissions. a Efficient outcome where MEC=MB c b d If A has right to pollute - A will sell pollution rights 0 M* M 0 Hours of music

56 Fig PMC stands for private marginal cost. Private costs are the input costs that the Y producer actually takes account of in determining its profitmaximising output level, i.e. C = P K KY + P L LY = C(Y) so that PMC = C/ Y MEC: marginal external cost Social marginal cost as: SMC = PMC + MEC To maximise profit, the Y firm will produce at Y 0 Efficiency requires the balancing at the margin of benefits and costs which include the external costs