Energy & Environmental Economics

Transcription

1 Energy & Environmental Economics Public Goods, Externalities and welfare Università degli Studi di Bergamo a.y (Institute) Energy & Environmental Economics a.y / 29

2 Public Goods What is a public good? Pure public goods: goods which are: - Non-rival: use of a unit of the good by consumer j does not reduce the possibility for another consumer i to derive utility from the same unit of that good. - Non-excludable: it is not possible or too expensive, to exclude anyone from the access to the good While non-rivalry is an intrinsic feature of the good under examination, excludability may depend on the institutional and technological setting. Non rivalry may exist up to a certain degree of utilization, beyond which congestion prevails. Club Goods non-rival, but excludable goods Commons: non excludable, but rival goods. (Institute) Energy & Environmental Economics a.y / 29

3 Examples Pure public goods: a lighthouse; a planet s temperature ranging between limits consistent with human life; clean air. Club Goods: ideas and blueprints; a swimmming pool, a landscape; Commons: timber, game, and other products from an uncontrolled forest; shing. (Institute) Energy & Environmental Economics a.y / 29

4 The optimal rule for private good provision Suppose there are two goods, both private. Assume a very simple technology: 1 unit of good 1 can be converted into 1 unit of good 2, and viceversa. So, the marginal cost of good 1 in terms of good 2 is equal to 1. We already know what is optimal in this case: each consumer equates its marginal rate of substitution to the relative price u x 1 = p 1 u p x 2 2 and under perfectly competitive conditions, p 1 p 2 = mc = 1 so that u x 1 u x 2 = mc (Institute) Energy & Environmental Economics a.y / 29

5 The intuition behind this rule is: the allocation is e cient when any individual is willing to give up, in exchange for one more unit of good 1, no more and no less of good 2 than it is strictly necessary to produce that additional unit of good 1 (Institute) Energy & Environmental Economics a.y / 29

6 . (Institute) Energy & Environmental Economics a.y / 29

7 The optimal rule for public good provision With public goods the situation changes. Suppose now that good 1 is pure public and good 2 is private, with the same production technology. Then if you increase production of good 1 by one unit, you still have to give up one unit of good 2, so that the marginal cost of good 1 in terms of good 2 is still one. The di erence lies in the e ects on utility. Since good 1 is non-rival, that single additional unit positively in uences the utility of all individuals, with the sacri ce of just one unit of good 2 overall. A theorem by Samuelson (1953) states that in this case, the optimal rule is n i=1 u i x 1 u i x 2 = mc = 1 The intuition behind this rule is now: the allocation is e cient when the individuals, taken together are willing to give up, in exchange for one more unit of good 1, no more and no less of good 2 than it is strictly necessary to produce that additional unit of good 1. (Institute) Energy & Environmental Economics a.y / 29

8 Contributing to a public good: the free riding problem Suppose that the public good is a lighthouse and the population consists of sailors who all bene t from the lighthouse. The taller is the lighthouse, the better is lighting and the higher is individual utility. Obviously, a taller lighthouse requires larger quantitites of bricks, and all sailors are required contribute by bringing as many bricks as they want. Besides bricks, the other good consumed by sailors is bread, and the relative price of bricks and bread is 1 (Institute) Energy & Environmental Economics a.y / 29

9 Then each sailor maximizes his utility function max u j! x j, G j + G i i6=j where x j is bread consumed by sailor j, G j is the number of bricks contributed by sailor j and i6=j G i is the sum of bricks contributed by the other individuals (the "quantity" of publc good is measured by the numer of bricks, i.e. by the height of the lighthouse) The budget constraint for the individual is: y j x j G j Since the individual is maximizing his own utility, he equates his marginal rate of substitution to the price ratio u j G u j x j = 1 (Institute) Energy & Environmental Economics a.y / 29

10 and since this is true of all individuals, we have u j G u j x j > 1 The provision of the public good is less than optimal (it would be possible to increase all the utilities by increasing further the height of the lighthouse). The reason for this is that each individual bene ts not only from the "bricks" he himself contributed, but also from those contributed by others, and he cares only about how his own contribution in uences his own utility, not the utility of the others. The outcome of this "sel sh" behaviour is that everyone is worse o than with a more "socially committed" pattern of choice. (Institute) Energy & Environmental Economics a.y / 29

11 Declaring your preferences Suppose now that lighthouses are of a xed height, so that, the only thing to do is to choose between having one lighthouse (1) or none (0). De ne w j as the j-th individual willingness to pay to have the lighthouse. It is determined as follows u j y j w j, 1 = u y j, 0 i.e. the maximum the individual is willing to pay is the amount which would make him indi erent between having the lighthouse or not. Suppose also that everyone is asked to state how much he would be willing to pay to have the lighthouse built. The lighthouse will be built if bw j + bw i c i6=j where c is the production cost of the xed-size lighthouse and bw j is the willingness to pay declared. by the individual. As we shall see, bw j does not necessarily coincide with w j. (Institute) Energy & Environmental Economics a.y / 29

12 Suppose that n w i c i=1 i.e., should individuals tell the truth about their preferences, and should each pay not more than his true willingness to pay, the lighthouse would be built and everyone would be indi erent (or better o ). with the lighthouse than not. (Institute) Energy & Environmental Economics a.y / 29

13 Shall individuals reveal their true preferences? Suppose rst that, should the lighthouse be built, each individual will be charged a uniform contribution t = c n. If for some individual j w j < t he then does not want the lighthouse to be built, and he is going to declare bw j = 0, hoping that the lighthouse project does not pass. If for some other individual w i t he will probably tell the truth (in this case.bw i = w i ) Then it might happen that n bw i = w i < c i=1 i2s n w i i=1 where S is the set of individuals who reveal their true preferences.in this case the lighthouse project will be stopped, even if it would be optimal when everyone pays no more than his true willingness to pay. (Institute) Energy & Environmental Economics a.y / 29

14 Suppose now that should the lighthouse be built, the j th individual will be charged a contribution t j = bw j. Then there is an incentive to declare less than one s own true willingness to pay, in the hope that the overall outcome is building the lighthouse anyway. Obviously the individual behaviour in this case depends to a large extent on what each one expects the others to declare. Suppose for instance that the j th individual thinks that bw i c i6=j Then under the rule t j = bw j, he will declare bw j = 0.If instead he thinks: bw i < c i6=j he will declare bw j = c i6=j if!! u j y j c bw i, 1 i6=j u y j, 0 (Institute) Energy & Environmental Economics a.y / 29

15 Social Choice In general, public goods are decided upon by means of social choice mechanisms. Social choice theory is a very sophisticated district of the land of economic theory, which we cannot cover in this course. Just to give an idea, think of one of the best known social choice mechanisms, i.e. voting over alternative projects under a majority rule. Here is an example of the so-called Condorcet paradox. (Institute) Energy & Environmental Economics a.y / 29

16 I choice II choice III choice Individual 1 Police station School Bridge Individual 2 School Bridge Police station Individual 3 Bridge Police station School Police st. vs School: Police st. wins Police st. vs Bridge: Bridge wins School st. vs Bridge: School wins Social preferences are not transitive!. (Institute) Energy & Environmental Economics a.y / 29

17 Externalities In general, externalities appear when 1 The behaviour of individuals and rms have a direct impact on other rms production functions and costs or on other individuals utility 2 Agents who su er (enjoy) the externality are not compensated (charged) for it, nor agents who cause the externality are charged (compensated), as it usually happens For this reason sometimes externalities are de ned as "absence of markets" (Institute) Energy & Environmental Economics a.y / 29

18 Classi cations Positive externalities: the behaviour of one subject has a favourable impact on the pro t/utility of another subject. Examples: the neighbour s owers, on-the-job training Negative externalities: the behaviour of one subject has a noxious impact on the pro t/utility of another subject. Examples: the neighbour s owers (if I m allergic), an ill-frequented pub, the greenhouse e ect Firm-to-Firm: chemical industry polluting the lake where a sher operates, on-the-job-training Firm-to-individual: Fumes, wastes, noises, again training Individual-to-individual: the neighbour s owers, the saxophone player Individual-to- rm? (Institute) Energy & Environmental Economics a.y / 29

19 An example of Firm-to-Firm externality Consider a chemical plant producing an output y K and, as a by-product, a polluting waste which is dispersed in a lake. Call Z the amount of pollution and assume with Z 0 (y K ) > 0. Instead Z = Z (y K ) C K (y K ) is the cost function of the chemical factory On the same lake operates a shery rm, whose cost is C F (y F, Z ) where y F is sh catch (the output of the shery), and C p y (y p, Z ), C p Z (y p, Z ) > 0 (the larger the pollution, the larger is time, e ort, fuel, etc. needed to catcha given quantity of sh) (Institute) Energy & Environmental Economics a.y / 29

20 The socially optimal solution Assume that the only magnitude of interest are pro ts, and that there are no other interested parties than the two rms. Which is the maximum pro t that the two rms together may generate? Assuming for simplicity prices equal to 1 both for sh and chemicals, joint pro t is y K + y F C K (y K ) C F (y F, Z ) or y K + y p C K (y K ) C F (y F, Z ) The rst-order conditions for maximizing the above pro t are: 1 = dc K (y K ) + C F (y F, Z (y K )) Z 0 (y K ) dy K Z 1 = C F (y F, Z ) y F (Institute) Energy & Environmental Economics a.y / 29

21 The market solution If instead each rm maximizes its own pro t, we have with the rst-order condition max y K C K (y K ) dc K (y K ) dy K = 1 and with rst-order condition max y F C F (y F, Z ) 1 = C F (y F, Z ) y F (Institute) Energy & Environmental Economics a.y / 29

22 The immediate conclusion we get from the comparison is that the market solution does not coincide with the socially optimal solution: this means that, although each rm maximizes its own pro t in the market setting, as a whole they might earn more if they behaved according to the socially otpimal solution. The di erence lies in the rst-order condition concerning chemical production: (socially optimal) 1 = dc K (y K ) + C F (y F, Z (y K )) Z 0 (y K ) dy K Z (market) 1 = dc K (y K ) dy K (Institute) Energy & Environmental Economics a.y / 29

23 It is easy to see that in the socially optimal solution, the marginal cost of producing chemicals has two components: one which stems out of the costs of the chemical plant (Private Marginal Cost dc K (y K ) dy K ), the other stemming out of sh production (Social Marginal Cost C F (y F,Z (y K )) Z Z 0 (y K )). The latter component disappears as we turn to the market solution, since the chemical m disregards the damaging e ects of chemical production on the shery industry. (Institute) Energy & Environmental Economics a.y / 29

24 PMC+SMC PMC P=1 Y K (social) Y K (private) (Institute) Energy & Environmental Economics a.y / 29

25 a1 A2 A6 A9 A10 A7 A3 A4 A8 A5 In the market solution Consumer surplus: a1 + a2 + a3 + a4 Pro t: a6 + a7 + a8 + a9 + a10 Social cost: a3 + a4 + a10 + a7 + a8 + a5 Net Welfare:(a1 + a2 + a3 + a4) + (a6 + a7 + a8 + a9 + a10) (a3 + a4 + a10 + a7 + a8 + a5) = (a1 + a2) + (a6 + a9) a5 (Institute) Energy & Environmental Economics a.y / 29

26 In the optimal solution Consumer surplus: a1 Pro t: a2 + a3 + a6 + a7 + a9 + a10 Social cost: a3 + a7 + a10 Net Welfare: a1 + (a2 + a3 + a6 + a7 + a9 + a10) (a3 + a7 + a10) = a1 + a2 + a6 + a9 (Institute) Energy & Environmental Economics a.y / 29

27 The bargaining solution to the externality problem Suppose that the shery rm is now entitled to sell to the chemical rm rights to pollute,at some price w per unit of pollution. The pro t function for the shery rm now changes as follows max y F C F (y F, Z ) + wz where Z here is both the amount of pollution and the numer of polluting rights sold to the chemical rm (the latter can pollute the lake only to the extent that it has bought a corresponding number of rights). The rst-order conditions are and 1 = C F (y F, Z ) y F w = C F (y F, Z ) Z the shery sells polluting rights until the marginal revenue from selling rights equals the increase in shing cost due to additional pollution. (Institute) Energy & Environmental Economics a.y / 29

28 The pro t function for the chemical rm now changes as follows max y K C K (y K ) wz (y K ) 1 = dc K (y K ) dy K + wz 0 (y K ) At an equilibrium 1 = dc K (y K ) + C F (y F, Z ) Z 0 (y K ) dy K Z 1 = dc K (y K ) + C F (y F, Z ) Z 0 (y K ) dy K Z i.e. the socially optimal solution (Institute) Energy & Environmental Economics a.y / 29

29 The interesting thing is that the same outcome appears if we assign R rights to pollute to the chemical rm, and let the shing rm buy such rights order to prevent pollution. The pro t function for the chemical rm becomes max y K C K (y K ) + w R R where R are the pollution rights that the chemical rm keeps for itself. The following constraint must hold The rst-order condition is R = Z (y K ) 1 = dc K (y K ) dy K + wz 0 (y K ) (Institute) Energy & Environmental Economics a.y / 29

30 The shing rm maximizes with the rst-order condition max y F C F (y F, Z ) w R R 1 = C F (y F, Z ) y F and w = C F (y F, Z ) Z (Institute) Energy & Environmental Economics a.y / 29