1 / 97

Chapter 36 Public Goods

Chapter 36 Public Goods. Public Goods -- Definition. A good is purely public if it is both nonexcludable and nonrival in consumption. Nonexcludable -- all consumers can consume the good. Nonrival -- each consumer can consume all of the good. Public Goods -- Examples.

Download Presentation

Chapter 36 Public Goods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 36Public Goods

  2. Public Goods -- Definition • A good is purely public if it is both nonexcludable and nonrival in consumption. • Nonexcludable -- all consumers can consume the good. • Nonrival -- each consumer can consume all of the good.

  3. Public Goods -- Examples • Broadcast radio and TV programs. • National defense. • Public highways. • Reductions in air pollution. • National parks.

  4. Reservation Prices • A consumer’s reservation price for a unit of a good is his maximum willingness-to-pay for it. • Consumer’s wealth is • Utility of not having the good is • Utility of paying p for the good is • Reservation price r is defined by

  5. Reservation Prices: An Example Consumer’s utility is Utility of not buying a unit of good 2 is Utility of buying one unit of good 2 atprice p is

  6. Reservation Prices; An Example Reservation price r is defined by I.e. by

  7. When Should a Public Good Be Provided? • One unit of the good costs c. • Two consumers, A and B. • Individual payments for providing the public good are gA and gB. • gA + gB c if the good is to be provided.

  8. When Should a Public Good Be Provided? • Payments must be individually rational; i.e.and

  9. When Should a Public Good Be Provided? • Payments must be individually rational; i.e.and • Therefore, necessarily and

  10. When Should a Public Good Be Provided? • And ifandthen it is Pareto-improving to supply the unit of good

  11. When Should a Public Good Be Provided? • And ifandthen it is Pareto-improving to supply the unit of good, so is sufficient for it to be efficient to supply the good.

  12. Private Provision of a Public Good? • Suppose and . • Then A would supply the good even if B made no contribution. • B then enjoys the good for free; free-riding.

  13. Private Provision of a Public Good? • Suppose and . • Then neither A nor B will supply the good alone.

  14. Private Provision of a Public Good? • Suppose and . • Then neither A nor B will supply the good alone. • Yet, if also, then it is Pareto-improving for the good to be supplied.

  15. Private Provision of a Public Good? • Suppose and . • Then neither A nor B will supply the good alone. • Yet, if also, then it is Pareto-improving for the good to be supplied. • A and B may try to free-ride on each other, causing no good to be supplied.

  16. Free-Riding • Suppose A and B each have just two actions -- individually supply a public good, or not. • Cost of supply c = $100. • Payoff to A from the good = $80. • Payoff to B from the good = $65.

  17. Free-Riding • Suppose A and B each have just two actions -- individually supply a public good, or not. • Cost of supply c = $100. • Payoff to A from the good = $80. • Payoff to B from the good = $65. • $80 + $65 > $100, so supplying the good is Pareto-improving.

  18. Free-Riding Player B Don’tBuy Buy Buy Player A Don’tBuy

  19. Free-Riding Player B Don’tBuy Buy Buy Player A Don’tBuy (Don’t’ Buy, Don’t Buy) is the unique NE.

  20. Free-Riding Player B Don’tBuy Buy Buy Player A Don’tBuy But (Don’t’ Buy, Don’t Buy) is inefficient.

  21. Free-Riding • Now allow A and B to make contributions to supplying the good. • E.g. A contributes $60 and B contributes $40. • Payoff to A from the good = $40 > $0. • Payoff to B from the good = $25 > $0.

  22. Free-Riding Player B Don’tContribute Contribute Contribute Player A Don’tContribute

  23. Free-Riding Player B Don’tContribute Contribute Contribute Player A Don’tContribute Two NE: (Contribute, Contribute) and (Don’t Contribute, Don’t Contribute).

  24. Free-Riding • So allowing contributions makes possible supply of a public good when no individual will supply the good alone. • But what contribution scheme is best? • And free-riding can persist even with contributions.

  25. Variable Public Good Quantities • E.g. how many broadcast TV programs, or how much land to include into a national park.

  26. Variable Public Good Quantities • E.g. how many broadcast TV programs, or how much land to include into a national park. • c(G) is the production cost of G units of public good. • Two individuals, A and B. • Private consumptions are xA, xB.

  27. Variable Public Good Quantities • Budget allocations must satisfy

  28. Variable Public Good Quantities • Budget allocations must satisfy • MRSA & MRSB are A & B’s marg. rates of substitution between the private and public goods. • Pareto efficiency condition for public good supply is

  29. Variable Public Good Quantities • Pareto efficiency condition for public good supply is • Why?

  30. Variable Public Good Quantities • Pareto efficiency condition for public good supply is • Why? • The public good is nonrival in consumption, so 1 extra unit of public good is fully consumed by both A and B.

  31. Variable Public Good Quantities • Suppose • MRSA is A’s utility-preserving compensation in private good units for a one-unit reduction in public good. • Similarly for B.

  32. Variable Public Good Quantities • is the total payment to A & B of private good that preserves both utilities if G is lowered by 1 unit.

  33. Variable Public Good Quantities • is the total payment to A & B of private good that preserves both utilities if G is lowered by 1 unit. • Since , making 1 less public good unit releases more private good than the compensation payment requires  Pareto-improvement from reduced G.

  34. Variable Public Good Quantities • Now suppose

  35. Variable Public Good Quantities • Now suppose • is the total payment by A & B of private good that preserves both utilities if G is raised by 1 unit.

  36. Variable Public Good Quantities • Now suppose • is the total payment by A & B of private good that preserves both utilities if G is raised by 1 unit. • This payment provides more than 1 more public good unit  Pareto-improvement from increased G.

  37. Variable Public Good Quantities • Hence, necessarily, efficient public good production requires

  38. Variable Public Good Quantities • Hence, necessarily, efficient public good production requires • Suppose there are n consumers; i = 1,…,n. Then efficient public good production requires

  39. Efficient Public Good Supply -- the Quasilinear Preferences Case • Two consumers, A and B.

  40. Efficient Public Good Supply -- the Quasilinear Preferences Case • Two consumers, A and B. • Utility-maximization requires

  41. Efficient Public Good Supply -- the Quasilinear Preferences Case • Two consumers, A and B. • Utility-maximization requires • is i’s public good demand/marg. utility curve; i = A,B.

  42. Efficient Public Good Supply -- the Quasilinear Preferences Case pG MUB MUA G

  43. Efficient Public Good Supply -- the Quasilinear Preferences Case pG MUA+MUB MUB MUA G

  44. Efficient Public Good Supply -- the Quasilinear Preferences Case pG MUA+MUB MC(G) MUB MUA G

  45. Efficient Public Good Supply -- the Quasilinear Preferences Case pG MUA+MUB MC(G) MUB MUA G* G

  46. Efficient Public Good Supply -- the Quasilinear Preferences Case pG MUA+MUB MC(G) MUB pG* MUA G* G

  47. Efficient Public Good Supply -- the Quasilinear Preferences Case pG MUA+MUB MC(G) MUB pG* MUA G* G

  48. Efficient Public Good Supply -- the Quasilinear Preferences Case pG MUA+MUB MC(G) MUB pG* MUA G* G Efficient public good supply requires A & B to state truthfully their marginal valuations.

  49. Free-Riding Revisited • When is free-riding individually rational?

  50. Free-Riding Revisited • When is free-riding individually rational? • Individuals can contribute only positively to public good supply; nobody can lower the supply level.

More Related