CHAPTER 35 PUBLIC GOODS Excludable goods people can

CHAPTER 35 PUBLIC GOODS

Excludable goods: people can be excluded from consuming it; n Non-rival goods: one person’s consumption does not reduce the amount available to others; n Public goods: goods that are non-excludable and non-rival; n ¨ Street area; ¨ National defense; ¨ Radio broadcasting.

Pareto efficiency Assumption: two persons; n Initial endowments: w 1 and w 2; n Preference: u 1(x 1, G) and u 2(x 2, G); n Public good: G=0, 1; n Private contributions: g 1 and g 2; n Cost of the good: c. n

Pareto efficiency Budget constraint: xi+gi=wi; n The reservation prices: ui(wi-ri, 1)=ui(wi, 0); n For allocation (x 1, x 2, 1) to be feasible: n ¨ g 1+g 2 c. n For allocation (x 1, x 2, 1) to Pareto-dominate (w 1, w 2, 0): ¨ ui(wi-gi, ¨ ri gi. 1)=ui(xi, 1) ui(wi, 0)=ui(wi-ri, 1);

Pareto efficiency Necessity: r 1+r 2 c; n Sufficiency: r 1+r 2 c. n ¨ We can design a payment plan (g 1, g 2) such that: n ri gi; n n g 1+g 2=c. The caveat: ¨ The initial distribution of (w 1, w 2) matters.

Pareto efficiency n Quasilinear preferences: ui(xi, G)=xi+vi(G); ¨ The reservation prices: wi-ri+vi(1)=ui(wi-ri, 1)=ui(wi, 0)=wi+vi(0); n ri=vi(1)-vi(0). n ¨ The reservations prices are independent of (w 1, w 2).

Private provision n The game 2 Buy 1 Not to buy u 1(w 1 -c, 1) u 2(w 2 -c, 1) u 1(w 1 -c, 1) u 2(w 2, 1) u 1(w 1, 1) u 2(w 2 -c, 1) u 1(w 1, 0) u 2(w 2, 0)

Private provision n Case 1: r 1+r 2<c ¨ ui(wi, 0)=ui(wi-ri, 1)>ui(wi-c, 1); ¨ No private provision: Pareto efficiency. 2 Buy 1 Not to buy u 1(w 1 -c, 1) u 2(w 2 -c, 1) u 1(w 1 -c, 1) u 2(w 2, 1) u 1(w 1, 1) u 2(w 2 -c, 1) u 1(w 1, 0) u 2(w 2, 0)

Private provision n Case 2: r 1+r 2 c; ri<c ¨ ui(wi, 0)=ui(wi-ri, 1)>ui(wi-c, 1); ¨ No private provision: Pareto inefficiency. 2 Buy 1 Not to buy u 1(w 1 -c, 1) u 2(w 2 -c, 1) u 1(w 1 -c, 1) u 2(w 2, 1) u 1(w 1, 1) u 2(w 2 -c, 1) u 1(w 1, 0) u 2(w 2, 0)

Private provision n Case 3: r 1 c; r 2<c ¨ u 2(w 2, 0)=u 2(w 2 -r 2, 1)>u 2(w 2 -c, 1): no provision ¨ u 1(w 1, 0)=u 1(w 1 -r 1, 1) u 1(w 1 -c, 1); ¨ Consumer 2 free-rides on consumer 1. 2 Buy 1 Not to buy u 1(w 1 -c, 1) u 2(w 2 -c, 1) u 1(w 1 -c, 1) u 2(w 2, 1) u 1(w 1, 1) u 2(w 2 -c, 1) u 1(w 1, 0) u 2(w 2, 0)

Private provision n Case 4: r 1 c; r 2 c ¨ ui(wi, 0)=ui(wi-ri, 1) ui(wi-c, 1) ¨ One free-rides on the other; ¨ Randomized provision by both consumers: potential inefficiency. 2 Buy 1 Not to buy u 1(w 1 -c, 1) u 2(w 2 -c, 1) u 1(w 1 -c, 1) u 2(w 2, 1) u 1(w 1, 1) u 2(w 2 -c, 1) u 1(w 1, 0) u 2(w 2, 0)

Variable levels n Pareto efficiency ¨ F. O. C. : ¨ The sum of the marginal willingness to pay equals the marginal cost of the public good.

Variable levels

Variable levels n Private provision ¨ F. O. C. : ¨ The consumer with the smaller demand free-rides.

Variable levels

Voting A mechanism to determine the provision of public goods. n Each individual has a preference over the amount of the public good; n The plurality rule: The candidate with the most votes wins; n Down’s (1957) theorem: the winner is the median voter if the preferences are singlepeaked. n

Voting

Voting

Groves-Clarke tax n Assumption: ¨ Quasilinear preferences; ¨ True values vi are private information. n The mechanism: ¨ Arbitrarily assigned ci; ¨ Each consumer reports si; ¨ Provide the public good if isi 0, tax on the pivotal consumer: - j isj; ¨ Do not Provide the public good if isi<0, tax on the pivotal consumer: j isj.

Groves-Clarke tax n Truth revealing is a weakly dominant strategy: ¨ What n if the public good should be provided? If ni - j inj and j inj<0: ¨ si - j inj: payoffs=ni+ j inj; ¨ si<- j inj: payoffs=0. n If ni - j inj and j inj 0: ¨ si - j inj: payoffs=ni; ¨ si<- j inj: payoffs=- j inj.

Groves-Clarke tax n Truth revealing is a weakly dominant strategy: ¨ What n if the public good should not be provided? If ni<- j inj and j inj 0: ¨ si - j inj: payoffs=ni; ¨ si<- j inj: payoffs=- j inj. n If ni<- j inj and j inj<0: ¨ si - j inj: payoffs=ni+ j inj; ¨ si<- j inj: payoffs=0.