拔高尼科爾森系列課件ch20-externalities and public googs

1、Chapter 20EXTERNALITIES ANDPUBLIC GOODSCONTENTSDefining externalities Externalities and Allocative InefficiencySolutions to the Externality ProblemAttributes of Public GoodsPublic Goods and Resource AllocationLindahl pricing and resource goodsDefining externalitiesExternalityAn externality occurs wh

2、enever the activities of one economic agent affect the activities of another economic agent in ways that are not reflected in market transactionschemical manufacturers releasing toxic fumesnoise from airplanesmotorists littering roadwaysInterfirm ExternalitiesConsider two firms, one producing good x

3、 and the other producing good yThe production of x will have an external effect on the production of y if the output of y depends not only on the level of inputs chosen by the firm but on the level at which x is producedy = f(k,l;x)y/x0Externalities in UtilityExternalities can also occur if the acti

4、vities of an economic agent directly affect an individuals utilityexternalities can decrease or increase utilityIt is also possible for someones utility to be dependent on the utility of anotherutility = US(x1,xn;UJ)Us/Uy,=)0Public Goods ExternalitiesPublic goods are nonexclusiveonce they are produc

5、ed, they provide benefits to an entire groupit is impossible to restrict these benefits to the specific groups of individuals who pay for themExternalities and Allocative InefficiencyExternalities and Allocative InefficiencyExternalities lead to inefficient allocations of resources because market pr

6、ices do not accurately reflect the additional costs imposed on or the benefits provided to third partiesWe can show this by using a general equilibrium model with only one individualExternalities and Allocative InefficiencySuppose that the individuals utility function is given byutility = U(xc,yc) w

7、here xc and yc are the levels of x and y consumedThe individual has initial stocks of x* and y*can consume them or use them in productionExternalities and Allocative InefficiencyAssume that good x is produced using only good y according toxo = f(yi)Assume that the output of good y depends on both th

8、e amount of x used in the production process and the amount of x producedyo = g(xi,xo)Externalities and Allocative InefficiencyFor example, y could be produced downriver from x and thus firm y must cope with any pollution that production of x createsThis implies that g1 0 and g2 0Externalities and A

9、llocative InefficiencyThe quantities of each good in this economy are constrained by the initial stocks available and by the additional production that takes placexc + xi = xo + x*yc + yi = yo + y*Finding the Efficient AllocationThe economic problem is to maximize utility subject to the four constra

10、ints listed earlierThe Lagrangian for this problem isL = U(xc,yc) + 1f(yi) - xo + 2g(xi,xo) - yo + 3(xc + xi - xo - x*) + 4(yc + yi - yo - y*)Finding the Efficient AllocationThe six first-order conditions areL/xc = U1 + 3 = 0L/yc = U2 + 4 = 0L/xi = 2g1 + 3 = 0L/yi = 1fy + 4 = 0L/xo = -1 + 2g2 - 3 =

11、0L/yo = -2 - 4 = 0Finding the Efficient AllocationTaking the ratio of the first two, we findMRS = U1/U2 = 3/4The third and sixth equation also imply thatMRS = 3/4 = 2g1/2 = g1Optimality in y production requires that the individuals MRS in consumption equals the marginal productivity of x in the prod

12、uction of yFinding the Efficient AllocationTo achieve efficiency in x production, we must also consider the externality this production poses to yCombining the last three equations givesMRS = 3/4 = (-1 + 2g2)/4 = -1/4 + 2g2/4 MRS = 1/fy - g2Finding the Efficient AllocationThis equation requires the

13、individuals MRS to equal dy/dx obtained through x production1/fy represents the reciprocal of the marginal productivity of y in x productiong2 represents the negative impact that added x production has on y outputallows us to consider the externality from x productionInefficiency of the Competitive

14、AllocationReliance on competitive pricing will result in an inefficient allocation of resourcesA utility-maximizing individual will opt forMRS = Px/Py and the profit-maximizing producer of y would choose x input according toPx = Pyg1Inefficiency of the Competitive AllocationBut the producer of x wou

15、ld choose y input so thatPy = PxfyPx/Py = 1/fyThis means that the producer of x would disregard the externality that its production poses for y and will overproduce x (not consider externality) fy x0)y = 2,000ly0.5 (for x x0) where x0 represents the rivers natural capacity for pollutants, 0Productio

16、n ExternalitiesAssuming that newsprint sells for $1 per foot and workers earn $50 per day, firm x will maximize profits by setting this wage equal to the labors marginal productlx* = 400If = 0 (no externalities), ly* = 400Production ExternalitiesWhen firm x does have a negative externality ( 0), its

17、 (x) profit-maximizing decision will be unaffected (lx* = 400 and x* = 40,000)； (ly* = 400 and y* = 40,000)But the marginal product of labor will be lower in firm y because of the externalityProduction ExternalitiesIf = -0.1 and x0 = 38,000, firm y will maximize profits byBecause of the externality,

18、 ly* = 87 and y output will be 8,723Production ExternalitiesSuppose that these two firms merge and the manager must now decide how to allocate the combined workforceIf one worker is transferred from x to y, output of x esx = 2,000(399)0.5 = 39,950 and output of y esy = 2,000(88)0.5(1,950)-0.1 = 8,79

19、6Production ExternalitiesTotal output increased (23 feet) with no change in total labor inputThe earlier market-based allocation was inefficient because firm x did not take into account the effect of its hiring decisions on firm yProduction ExternalitiesIf firm x was to hire one more worker, its own

20、 output would rise tox = 2,000(401)0.5 = 40,050the private marginal value product of the 401st worker is equal to the wageBut, increasing the output of x causes the output of y to fall (by about 21 units)The social marginal value product of the additional worker is only $29Solutions to the Externali

21、ty ProblemSolutions to theExternality ProblemThe output of the externality-producing activity is too high under a market-determined equilibriumIncentive-based solutions to the externality problem originated with Pigou, who suggested that the most direct solution would be to tax the externality-creat

22、ing entitySolutions to theExternality ProblemQuantity of xPriceS = MCDx1p1Market equilibrium will occur at p1, x1If there are external costs in the production of x, social marginal costs are represented by MCMCSolutions to theExternality ProblemQuantity of xPriceS = MCMCDx2taxA tax equal to these ad

23、ditional marginal costs will reduce output to the socially optimal level (x2)p2The price paid for the good (p2) now reflects all costsA Pigouvian Tax on NewsprintA suitably chosen tax on firm x can cause it to reduce its hiring to a level at which the externality vanishesBecause the river can handle

24、 (no) pollutants with an output of x = 38,000, we might consider a tax that encourages the firm to produce at that levelA Pigouvian Tax on NewsprintOutput of x will be 38,000 if lx = 361Thus, we can calculate t from the labor demand condition(1 - t) 1MPl = (1 - t)1,000(361)-0.5 = 50t = 0.05Therefore

25、, a 5 percent tax on the price firm x receives would eliminate the externalityTaxation in the General Equilibrium ModelThe optimal Pigouvian tax in our general equilibrium model is to set t = -pyg2the per-unit tax on x should reflect the marginal harm that x does in reducing y output, valued at the

26、price of good yTaxation in the General Equilibrium ModelWith the optimal tax, firm x now faces a net price of (px - t) and will choose y input according topy = (px - t)fyThe resulting allocation of resources will achieveMRS = px/py = (1/fy) + t/py = (1/fy) - g2Taxation in the General Equilibrium Mod

27、elThe Pigouvian tax scheme requires that regulators have enough information to set the tax properlyin this case, they would need to know firm ys production functionPollution RightsAn innovation that would mitigate the informational requirements involved with Pigouvian taxation is the creation of a m

28、arket for “pollution rights”Suppose that firm x must purchase from firm y the rights to pollute the river they sharexs choice to purchase these rights is identical to its output choicePollution RightsThe net revenue that x receives per unit is given by px - r, where r is the payment the firm must ma

29、ke to firm y for each unit of x it producesFirm y must decide how many rights to sell firm x by choosing x output to maximize its profitsy = pyg(xi,xo) + rxoPollution RightsThe first-order condition for a maximum isy/xo = pyg2 + r = 0r = -pyg2The equilibrium solution is identical to that for the Pig

30、ouvian taxfrom firm xs point of view, it makes no difference whether it pays the fee to the government or to firm yThe Coase TheoremThe key feature of the pollution rights equilibrium is that the rights are well-defined and tradable with zero transactions costsThe initial assignment of rights is irr

31、elevantsubsequent trading will always achieve the same, efficient equilibriumThe Coase TheoremSuppose that firm x is initially given xT rights to produce (and to pollute)it can choose to use these for its own production or it may sell some to firm yProfits for firm x are given byx = pxxo + r(xT - xo

32、) = (px - r)xo + rxTx = (px - r)f(yi) + rxTThe Coase TheoremProfits for firm y are given byy = pyg(xi,xo) - r(xT - xo)Profit maximization in this case will lead to precisely the same solution as in the case where firm y was assigned the rightsThe Coase TheoremThe independence of initial rights assig

33、nment is usually referred to as the Coase Theoremin the absence of impediments to making bargains, all mutually beneficial transactions will be completedif transactions costs are involved or if information is asymmetric, initial rights assignments will matterAttributes of Public GoodsAttributes of P

34、ublic GoodsA good is exclusive if it is relatively easy to exclude individuals from benefiting from the good once it is producedA good is nonexclusive if it is impossible, or very costly, to exclude individuals from benefiting from the goodAttributes of Public GoodsA good is nonrival if consumption

35、of additional units of the good involves zero social marginal costs of productionAttributes of Public GoodsSome examples of these types of goods include:Public GoodA good is a pure public good if, once produced, no one can be excluded from benefiting from its availability and if the good is nonrival

36、 - the marginal cost of an additional consumer is zeroPublic Goods and Resource AllocationPublic Goods andResource AllocationWe will use a simple general equilibrium model with two individuals (A and B)There are only two goodsgood y is an ordinary private goodeach person begins with an allocation (y

37、A* and yB*)good x is a public good that is produced using yx = f(ysA + ysB)Public Goods andResource AllocationResulting utilities for these individuals areUAx,(yA* - ysA)UBx,(yB* - ysB)The level of x enters identically into each persons utility curveit is nonexclusive and nonrivaleach persons consum

38、ption is unrelated to what he contributes to productioneach consumes the total amount produced Public Goods andResource AllocationThe necessary conditions for efficient resource allocation consist of choosing the levels of ysA and ysB that maximize one persons (As) utility for any given level of the

39、 others (Bs) utilityThe Lagrangian expression isL = UA(x, yA* - ysA) + UB(x, yB* - ysB) - KPublic Goods andResource AllocationThe first-order conditions for a maximum areL/ysA = U1Af - U2A + U1Bf = 0L/ysB = U1Af - U2B + U1Bf = 0Comparing the two equations, we findU2B = U2APublic Goods andResource Al

40、locationWe can now derive the optimality condition for the production of xFrom the initial first-order condition we know thatU1A/U2A + U1B/U2B = 1/f(consumpation) MRSA + MRSB = 1/fdy/dx (production)The MRS must reflect all consumers because all will get the same benefits公共品的邊際成本等于N個個體愿意為公共品提供的相對價格（以

41、私人品衡量）之和。Failure of aCompetitive MarketProduction of x and y in competitive markets will fail to achieve this allocationwith perfectly competitive prices px and py, each individual will equate his MRS to px/pythe producer will also set 1/f equal to px/py to maximize profitsthe price ratio px/py will

42、 be too lowit would provide too little incentive to produce xFailure of aCompetitive MarketFor public goods, the value of producing one more unit is the sum of each consumers valuation of that outputindividual demand curves should be added vertically rather than horizontallyThus, the usual market de

43、mand curve will not reflect the full marginal valuationInefficiency of aNash EquilibriumSuppose that individual A is thinking about contributing sA of his initial y endowment to the production of x （voluntary）The utility maximization problem for A is thenchoose sA to maximize UAf(sA + sB),yA - sAIne

44、fficiency of aNash EquilibriumThe first-order condition for a maximum isU1Af - U2A = 0U1A/U2A = MRSA = 1/fBecause a similar argument can be applied to B, the efficiency condition will fail to be achievedeach person considers only his own benefitsA0，free ride problem The Roommates DilemmaSuppose two

45、roommates with identical preferences derive utility from the number of paintings hung on their walls (x) and the number of granola bars they eat (y) with a utility function ofUi(x,yi) = x1/3yi2/3 (for i=1,2)Assume each roommate has $300 to spend and that px = $100 and py = $0.20The Roommates Dilemma

46、We know from our earlier analysis of Cobb-Douglas utility functions that if each individual lived alone, he would spend 1/3 of his e on paintings (x = 1) and 2/3 on granola bars (y = 1,000)When the roommates live together, each must consider what the other will doif each assumed the other would buy

47、paintings, x = 0 and utility = 0The Roommates DilemmaIf person 1 believes that person 2 will not buy any paintings, he could choose to purchase one and receive utility ofU1(x,y1) = 11/3(1,000)2/3 = 100 while person 2s utility will beU2(x,y2) = 11/3(1,500)2/3 = 131Person 2 has gained from his free-ri

48、ding positionThe Roommates DilemmaWe can show that this solution is inefficient by calculating each persons MRSAt the allocations described,MRS1 = 1,000/2 = 500MRS2 = 1,500/2 = 750The Roommates DilemmaSince MRS1 + MRS2 = 1,250, the roommates would be willing to sacrifice 1,250 granola bars to have o

49、ne additional paintingan additional painting would only cost them 500 granola barstoo few paintings are boughtThe Roommates DilemmaTo calculate the efficient level of x, we must set the sum of each persons MRS equal to the price ratioThis means thaty1 + y2 = 1,000 xThe Roommates DilemmaSubstituting

50、into the budget constraint, we get0.20(y1 + y2) + 100 x = 600 x = 2y1 + y2 = 2,000The allocation of the cost of the paintings depends on how each roommate plays the strategic financing gameLindahl Pricing ofPublic GoodsLindahl Pricing ofPublic GoodsSwedish economist E. Lindahl suggested that individ

51、uals might be willing to be taxed for public goods if they knew that others were being taxedLindahl assumed that each individual would be presented by the government with the proportion of a public goods cost he was expected to pay and then reply with the level of public good he would preferLindahl

52、Pricing ofPublic GoodsSuppose that individual A would be quoted a specific percentage (A) and asked the level of a public good (x) he would want given the knowledge that this fraction of total cost would have to be paidThe person would choose the level of x which maximizesutility = UAx,yA*- A f -1(x)Lindahl Pricing ofPublic GoodsThe first-order condition is given byU1A - AU2B(1/f)=0 MRSA = A/fFaced by the same choice, individual B would opt for the level of x which satisfiesMRSB = B/fLi