OPTIMAL PROVISION OF Chapter 7: Public Goods PUBLIC GOODS

„ Outline „ Pure public goods have two traits:

„ Optimal provision of public goods. „ They are non-rival in consumption: The marginal cost of another person consuming the good is zero, „ Under-provision generally characterizes markets with public goods, absent government intervention. and does not affect your opportunity to consume the good. „ Private sector provision. „ They are non-excludable: There is no way to „ Crowd out deny someone the opportunity to consume the „ Problems good. „ Table 1 gives some examples.

If a IcegoodIce cream cream is both is is rival, rivalalso andbecauseexcludable, excludable, ThismyCableSomeIt istable excludable, TV goods showsis non-rival, are examples since“impure” because the ofpubliccable pure my consumptionTablebecause 1it Iis can aof private simplyit precludes good.not share youpubliccompanygoods frommyconsumption goods, because can impuresimply they of it publicrefuse arein no non-rival, way goods,to hook consumingYetForOther itexample, is non-excludablegoodsice the cream a sameare crowded with“impure” ice you.because cream.sidewalk publicFinally,It Theitisdiminishes butNational isis also they andpure non-excludable,up areprivatedefense publicthe your (to system. someconsumption. goods.goods is a classicextent) becauseare both goodsonlyrivalDefiningclearly way because because forvery you difficultthey your to pure consumeare enjoyment to rival, prohibit and butitexample.once is is non-rivalnotto impure an area It isexcludable.and is non-rival protected, non-excludable. public because everyone goods my pedestriansreducedmake as from excludable.more using pedestriansice cream. the sidewalk. alsoconsumption“consumes” of that national protection. defense Optimal Provision of Private Goods use the same sidewalk. protectionIs the does good not diminish rival your in consumption of it. consumption? „ Consider a private good, like ice cream. Yes No „ Yes Ice cream Cable tv „ Figure 1 shows the market for ice cream Is the cones, assuming that the alternative use of good No Crowded city National defense the money is buying cookies at $1 each. sidewalk excludable „ This makes cookies the numeraire good. ?

1 Adding up Ben’s and Jerry’s Price At a priceBenAdding of has $3, up an neither Ben’s individual, andperson Jerry’s individual demands at each S=SMC of ice demandsJerrydownward-sloping individualalso much has an icedemands individual, cream. demand give price gives society’s demand. cream downward-slopingcurvesociety’s for ice demand cream. demand at $3. curveAt a price for ice of Adding$2,cream.Leading both up people toBen’s a competitive and Jerry’s Optimal Provision of Private Goods $3 demand moreequilibriumindividual ice cream. at demands $2. Ben give& Jerry consumesociety’s different demandThere quantities. at $2.is a market supply curve „ In this figure, as price adjusted, each person changed his associated with producing ice quantity consumed. cream. $2 „ For a private good, consumers demand different quantities at the same market price. „ We can also represent this relationship mathematically. Ben has preferences over cookies D DJERRY BEN SMB =DBEN+JERRY (C) and ice cream (IC):

0 Q Q Q Quantity JERRY BEN TOTAL UCICB ( , ) of ice cream „ As does Jerry: Figure 1 Demand for a private good UCICJ (),

Optimal Provision of Private Goods Optimal Provision of Private Goods

„ Utility maximization requires that each of „ The private market equilibrium in this case is their indifference curves is tangent to the socially efficient. budget constraint. Moreover, suppliers set „ The MRS for any quantity of ice cream equals P=MC. For Ben, we have: the SMB of that quantity–the marginal value MUPMCB ICICIC===MRS B to society equals the marginal value to any B IC, C P MC MUC CC individual in the perfectly competitive market. „ For Jerry we have: MUPMCJ ICICIC===MRS J J IC, C MUC PMCCC

2 Price of AddingAdding up Ben’sup Ben’s and and Jerry’s Jerry’s missiles willingnesswillingness to to pay pay gives for each society’squantity demand gives society’s for 1 missile. demand. Optimal Provision of Public Goods As does Jerry. $6 There is a market supply curve Leading to a competitiveAddingassociated up Ben’s with andproducing Jerry’s „ Now consider the tradeoff between a public equilibrium at 5 missiles.willingness Ben & tomissiles pay gives society’s Ben hasJerry a downward consume sloping the same Q. WhileBen’s Jerry’swillingness willingness to pay fortodemand paythe for the 5th missile. demand Dcurve for missiles. S=SMC good, like missiles, and a private good like $4 forJERRY thefirst first missile missile is $2. is $4. WhileBen’s Jerry’swillingness willingness to pay forto paythe cookies. $3 for thefifth fifth missile missile is $1. is $2. SMB=D „ Figure 2 shows the market for missiles, $2$2 BEN+JERRY DBEN assuming that the alternative use of the $1 money is buying cookies at $1 each. 0 1 5 Quantity of missiles

Figure 2 Demand for a public good

Optimal Provision of Public Goods Optimal Provision of Public Goods

„ Unlike the case of private goods, where „ We can also represent this relationship aggregate demand is found by summing the mathematically. Ben has preferences over individual demands horizontally, with public cookies (C) and missiles (M): UCMB ( , ) goods, aggregate demand is found by „ To Ben, the marginal missile is worth MU B summing vertically. M B B = MRS MC, MU C „ That is, holding quantity fixed, what is each „ Jerry’s preferences are UCM(), person’s willingness to pay? J „ To Jerry, the marginal missile is worth

J MU M J J = MRS MC, MU C

3 Optimal Provision of Public Goods Optimal Provision of Public Goods

„ The social marginal benefit (SMB) of the next „ That is, social efficiency is maximized when missile is the sum of Ben and Jerry’s marginal the marginal costs are set equal to the sum of i rates of substitution: ∑ MRS MC, the marginal rates of substitution (rather than i „ where “i” represents each person in society. each individual’s MRS). „ Efficiency requires „ This is because the good is non-rival. Since a unit can be consumed by all consumers, i MCM ∑ MRSMC, = society would like the producer to take into i MCC account all consumers’ preferences.

PRIVATE PROVISION OF PUBLIC GOODS: Private-sector Underprovision Private-sector Underprovision

„ In general, the private sector underprovides „ Ben and Jerry benefit equally from a firework that is public goods because of the free rider provided by either of them. „ What matters is the total amount of fireworks. problem. „ Each person chooses combinations of ice cream and „ Consider two people, Ben and Jerry, and two fireworks in which his own MRS equals the ratio of price. consumption goods, ice cream and fireworks. „ For both Ben and Jerry, they set: „ Set the prices of each good at $1, but fireworks are a public good. Assume that MRSFIC, ==1, MU IC MU F Ben and Jerry have identical preferences. i „ Whereas optimal provision requires:∑ MRS FIC, = 1 i

4 Private-sector Underprovision The Free Rider Problem in Practice

„ With identical preferences, the optimal condition is: „ There are some interesting examples of the free- rider problem in practice. ⎛⎞MU F MU IC 2⎜⎟== 1, which implies MU F „ Only 7.5% of public radio listeners in New York ⎝⎠MU IC 2 contribute to the stations–that is, there is a lot of free- riding. In the United Kingdom, the BBC charges an „ Recall that marginal utilities diminish with increasing annual licensing fee for all television owners. consumption of a good. „ Many users of file sharing services never contribute „ In this example, optimal provision would require uploaded files; they only download files. Some of these that fireworks are consumed until their utility equals services, like Kazaa, give download priority to those who half the marginal utility of ice cream. contribute. „ Thus, each individually buys too much ice cream privately.

When Is Private Provision Likely to Overcome the Free Rider Problem? Some individuals care more than others

„ Under what circumstances are private market „ When some individuals have especially high demand forces likely to solve the free rider problem? for a public good, private provision may emerge (but not necessarily provide efficiently – in „ Intense preferences. particular, the public good is still likely to be „ Altruism. underprovided). „ „ Utility from one’s own contribution to the public The key intuition is that the decision to provide a good. public good is a function of the enjoyment that the individual gets from the total amount of the public good, net of cost. „ If a person gets a lot of enjoyment, or has a lot of money, he will choose to purchase more of the public good even though it benefits others.

5 PUBLIC PROVISION OF PUBLIC Altruism and Warm Glow GOODS

„ A second reason is that there is evidence that many „ In principle, the government could solve the individuals are altruistic, caring about the outcomes of optimal public goods provision problem and others as well as themselves. then either provide the good directly or „ A third reason is that that individuals may provide for a mandate individuals to provide the amount. public good is due to warm glow. „ In practice, three problems emerge: „ The warm glow model is a model of public good provision in which individuals care about both the total amount of the public „ Crowd-out. good and their particular contributions as well. „ Measuring costs and benefits. „ For example, they may get some psychological benefit from knowing they helped a worthy cause. „ Determining the public’s preferences. „ In this case, the public good becomes more like a private good, though it also does not fully solve the underprovision problems.

Private Responses to Public Provision: Private Responses to Public Provision: The Problem of Crowd-Out The Problem of Crowd-Out

„ In some cases, the private market may already „ For example, in the fireworks example with Ben and be providing a socially inefficient level of the Jerry, if one assumes: „ Ben and Jerry care only about the total number of private good. fireworks provided. „ In this case, public provision may crowd-out „ Government provision will be financed by charging equal amounts to each of them. some of the private provision–as the „ And the government provides no more fireworks than government provides more of the public were being provided privately beforehand. good, the private sector provides less. „ Then each dollar of public provision will crowd out private provision one-for-one.

6 Private Responses to Public Provision: Private Responses to Public Provision: The Problem of Crowd-Out The Problem of Crowd-Out

„ The full crowd-out in the fireworks example „ If noncontributors are forced to help pay for is rare, though partial crowd-out is much the good (but it is still below the social more common and can occur when: optimum), then the contributors’ effective

„ People who don’t contribute to the public good income levels are higher than before. are taxed to finance its provision. „ As a result of this income effect, contributors „ Or when individuals derive utility from their buy more if the public good is a normal good, individual contributions as well as the total offsetting the crowd-out to some extent. amount of the public good provided.

Public Provision of Public Goods: Private Responses to Public Provision: Measuring the costs and benefits of public The Problem of Crowd-Out goods

„ Alternatively, as discussed previously, there „ Another problem for government provision may not be full crowd-out if an individual is measuring costs and benefits of the public cares about his own contributions (the warm good. This entails the field of cost-benefit glow model). analysis, discussed in the next lesson. „ In this case, an increase in government „ For example, improving a highway involves contributions will not fully crowd out giving. valuations of commuting time saved as well reduced traffic fatalities.

7 How Can We Measure Preferences for the Public Good?

„ Finally, our model of optimal public good provision assumes the government knows each person’s preferences over public and private goods. „ In practice, this runs into problems with preference revelation, preference knowledge, and preference aggregation. „ These issues are addressed in the field of political economy. „ Let me work two problems…

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