Public Goods. Topics in Political Economy. Ana Fernandes University of Bern. Spring 2010

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1 Public Goods Topics in Political Economy Ana Fernandes University of Bern Spring Public Goods Earlier in the course, we saw that markets achieve efficiency for private goods goods that benefit oneperson When goods are nonrival in consumption and can be enjoyed by many simultaneously, we do not expect an efficient outcome Because many people benefit simultaneously, public goods could well be called collective goods The collective nature of benefits suggests the need for collective means of decision making, such as voting We will now briefly look into public goods and their provision Next, we will address voting as a means of reaching collective decisions with regard to the provision of public goods and redistributive taxation

2 1.1 Properties of Public Goods Benefits from Private and Public Goods For a private good, an amount consumed by one person is not available for the consumption of others If individual i consumes amount x i 0 and X is the total quantity available of a private good, it follows that: nx X = x i i=1 Private goods are therefore divided or distributed among the population Consumption of private goods is rival in that amount x i consumed by individual i cannot be consumed by anyone else(e.g.a hamburger) For public goods, no such division takes place Total quantity G of a public good is also the quantity g i available to each of the n individuals: G = g 1 = g 2 =... = g n The quantity of a public good available to one person is also the quantity available to everybody This means that public goods are nonrival in consumption: consumption by one individual does not diminish or lessen the consumption of others (e.g. national defense) Although the amount consumed is the same, how individuals value that amount of course varies For example, when a Mozart symphony is played, some people will enjoy it, some will prefer Jazz and others still would prefer silence...

3 Characteristics of Pure and Congestible Public Goods Public goods may be subject to congestion For example, highways are a public good up to the point where additional cars affect the usage of other vehicles already on the highway If traffic istooheavy,therewillbetraffic jams or cars will have to slow down We say that public goods are pure when Individual benefits from a public good are independent of the number of users When individual benefit declines with the number of users(or after the number of users goes above some threshold), the public good is said to be congestible Figure 3.1a shows how individual benefit and the number of users are related for a pure public good In 3.1b we see the same relationship for a congestible public good There, the public good is pure up to a number n 1 of users, after which congestion begins and individual consumption declines When more than n 2 consumers use the public good, individual benefit is negative When more than n 2 cars are on the highway, people would be prepared to pay to have other drivers leave the highway

4 When public goods are congestible, it is usually possible to exclude people from consumption In the highway case, for example, toll booths can be set to charge people from using the highway The toll can be set high enough so as to reduce the number of users to a level considered adequate The possibility of exclusion allows markets to be created in which people pay in order to benefit The government therefore has no necessary responsibility in the supply of public goods As in the case of gyms, movie theaters, concerts, sports events, transportation, private schools, private hospitals and so on, in general, Congestible public goods can be privately and competitively supplied Since markets for congestible public goods resemble markets for private goods, we will focus our attention on pure public goods (or on congestible ones when the number of users is below the congestion threshold)

5 Exclusion People cannot always exclude themselves from the consumption of pure public goods nor it is always possible to exclude people (for example in the cases of the benefits from national defense or the rule of law) However, Where exclusion is possible, exclusion from a pure public good is inefficient We see this by examining the total benefit ton people from a pure public goods: nx W n = B i C i=1 When an additional person benefits, the fixed cost C of supplying the public good remains unchanged However, with n +1beneficiaries, total benefit from the public good increases to: W n+1 = n+1 X i=1 B i C Thus, the change in total benefit from the public good is the personal benefit to the additional person: Therefore, W = B n+1 > 0 Allowing an additional person to benefit from an available public good is Pareto-improving: someone is better off and no one is worse off

6 The marginal cost of use of an existing public good by an additional person is zero: MC use =0 Efficient use requires that MB use = MC use Therefore, efficient use requires free use or free access to existing public goods: P use =0 The cost of supplying a public good differs from the cost of use A bridge is costly to build However, once the building costs have been incurred and it has been built, the cost of use of a noncongested bridge is zero The efficient price of use of the bridge is therefore zero Efficient use requires that access to pure public goods be free The Dilemma of Exclusion Though efficiency requires that access to public goods be free, their provision must still be financed Ifpeopleareabletobenefit from pure public goods once they are provided, they have no incentive to contribute to the costs of their provision If feasible, exclusion might then be exercised as a means of giving people incentives to contribute to public good provision For example, if fire fighters only put off firesofhousesofpeoplewho contribute to the fire squad, people have an incentive to do so Although exclusion is inefficient as seen earlier, it might be the means for giving people incentives to pay for public goods

7 1.2 Voluntary Personal Payment for Public Goods We next address the question: How effective can a society be in supplying public goods without a government that has the authority to tax? Figure 3.3a shows demand for a private good Total market demand is the horizontal sum individual demands MB 1 and MB 2 of two people At the market equilibrium price P E, person 1 purchases quantity q1 and person 2 the quantity q2 At price P E,marketdemandisQ = ³ q1 + q 2 Figure 3.3b shows the total demand for a public good, definedintermsof either quantity or quality For a public good, the quantity or standard available to one person is also that available to everyone else Therefore, collective (or total) demand for a public good is found by asking: How much are all beneficiaries of a public good willing to pay in total for a given common quantity or standard? In figure 3.3b, person 1 s marginal willingness to pay for the public good at common quantity G is P 1 Person 2 s marginal willingness to pay is P 2 Combined marginal willingness to pay at quantity G is ³ P 1 + P 2 = P

8 Point F in figure 3.3b is on the combined demand function P MB of persons 1 and 2 The combined or collective demand function is found by vertically summing MB 1 and MB 2 at different quantities or standards of the public good For private goods, as the amount of a good consumed by one individual is not available for the consumption of another, the summation is horizontal At a given price, we add up the quantities demanded by different individuals and which will be consumed by each individual on his own For public goods, the quantity consumed is the same across people Therefore, for a given amount G of public good provided, we add up the valuation that different individuals have of that quantity It makes no sense to add horizontally individual marginal benefit curves since the same common quantity G will be available to all Supply There is no difference between supply functions for private and public goods As for private goods, the inputs required for the production of public goods are generally competitively supplied in markets

9 Efficient Voluntary Payments for Public Goods Figure 3.4 combines a competitive supply function for a public good with total willingness to pay, P MB At point E, where quantities demanded and supplied are equal, payment of price P E of the public good is shared Person 1 pays the personal per-unit price P E 1 and person 2 pays P E 2 Personal per-unit prices in figure 3.4 are determined by each person s marginal benefit at the equilibrium quantity G E We see that P E 1 = MB 1, P E 2 = MB 2 Adding up the personal per-unit prices and personal marginal benefits from the previous expression, we get: P E = P E 1 + P E 2 = X i MB (1) Because the inputs for public goods are competitively supplied: P E = MC (2) Combining (1) and (2), we get that, at point E, X MB = MC (3) i Condition (3) is satisfied when people voluntarily pay for public goods according to personal benefit

10 Condition (3) also ensures efficient provision of public goods as follows Total benefit from the public good is W = X i B C Total benefit is maximized when X MB i = MC i Condition (3) describing the outcome of voluntary payments at point E is therefore the condition for maximum W We conclude that: Voluntary payment for public goods according to personal benefit maximizes W and so is efficient There was no reason to expect otherwise Personal payment in competitive markets is efficient for private goods The only difference regarding public goods is that total demand is derived by vertical rather than horizontal summation of individual demands Of course we are assuming that people have an incentive to pay for public good provision

11 Asymmetric Information and Under-Supply of Public Goods For private goods, individuals face a common market price and choose different personal quantities For public goods, individuals have the same quantity but are asked to pay different personal prices based on personal benefit Personal benefit, however, is subjective private information Personal payment for public goods thus involves asymmetric information: only people themselves know their private benefit By taking advantage of asymmetric information and understating true personal benefit, people can reduce the personal price they pay Figure 3.5a shows the personal gain from understating true marginal benefit By claiming lower than true MB,thepersoninfigure 3.5a reduces the personal price when the quantity supplied is G from P 1 to P 2 In a competitive market for private goods, there can be no personal benefit from misrepresenting personal preferences or willingness to pay: By misrepresenting preferences for private goods, people can only reduce their benefit (by getting an amount which is less than what they would like to consume at the given price) But misrepresentation of MB for public goods when payment is voluntary leads to a reduction in the personal price paid

12 The consequences of deception by only one person in a large population is negligible Figure 3.5b shows the downward shift in the combined P (untrue MB) function of the population when many people deceptively claim low personal benefit The quantity G 0 of the public good that is provided is less than the efficient quantity G E We conclude that Personal incentives to understate benefit suggest that voluntarily financed public goods will be under-supplied relative to the efficient quantity or standard The term free riding describes relying on others to pay Under-supply of voluntarily financed public goods arises because of free riding incentives The Ideal Lindahl Consensus The ideal efficient outcome for voluntarily financed public goods is known as the Lindahl solution, achieved through a Lindahl mechanism In the Lindahl solution, people are described as paying a share of the cost of public goods according to their true preferences Noonefreerides The Lindahl solution emphasizes the need for consensus on the quantity or standard of the public good Ideally, people should not be compelled to pay for a quantity or standard of a public good that they do not want; therefore, it is desirable that there be consensus about the quantity or standard

13 We previously described a market for public goods by expressing total demand as the sum of MBs and supply in terms of the MC of inputs To demonstrate the Lindahl solution, we now change how we look at demand and supply In figure 1, the horizontal axis measures the common quantity of a public good No one is excluded from benefit sothereisanefficient price of use of zero Still, there is the need to pay for the public good The public good is competitively supplied at given market price P Person 1 pays a share s 1 of the price P of the public good Therefore, person 1 s cost share or personal price is determined as P 1 = s 1 P The schedule OO in figure 1 is person 1 s demand expressed as a function of his share s 1 The higher the share s 1 paid by person 1, the lowest the quantity of the public good desired by this person The schedule LL isthedemandofperson2,alsoexpressedasafunction player 1 s share Because shares add to unity in this two person environment, s 2 =1 s 1 Therefore, the greater the share of the price paid for by person 1, the more quantity of the public good is desired by person 2

14 At s 1 =1, person 1 is paying fully for the provision of the public good He then wishes to consume a small amount of it Person 2, on the other hand, wishes to consume a lot, and, in particular, a greater amount than person 1 When s 1 =0, it is person 2 s turn to pay for the public good Person 1 wishes to consume more of the public good than person 2 does in this case From the continuity and monotonicity of demand functions, they must crossonlyonce The point E where they cross determines both the equilibrium quantity of public good provision and the way the cost is shared Figure 1 can be interpreted in terms of demand and supply: Demand of one person is supply for the other Because a public good provides collective benefit no matter who pays, payment by one person for the public good is free supply for the other In the Lindahl solution, shown in figure 1, there is consensus about demand for the public good That is, given share s 1 that person 1 pays of P and the corresponding s 2, both persons agree on the quantity of the public good that ought to be provided, G The Lindahl solution is therefore characterized by the consensus quantity demanded G and cost shares s 1 and s 2

15 We next show that the Lindahl-consensus solution results in the supply of an efficient quantity or standard of the public good We confirm that supply of the consensus quantity G is efficient by showing that the Lindahl solution replicates the efficiency condition for public good supply: X MB i = MC (4) In figure 1, at quantity or standard G, i P i = s i P = MB i (G ), i =1, 2 Summing for the two people, we have: (P 1 + P 2 )=(s 1 + s 2 ) P = X MB With P = MC because of competitive supply of the public good and because ³ s 1 + s 2 =1,theefficiency condition (4) follows from the previous equation Therefore: The Lindahl voluntary-payment consensus results in efficient supply of public goods through voluntary personal payments

16 However, the efficient Lindahl solution requires people to be truthful about their benefits expressed in the willingness to pay curves In figure 2, understatement of personal benefits of person 1 changes the determination of personal cost shares from point E to E At E, person 1 has a lower cost share than at point E and, consequently, the cost-share of person 2 has increased Person 2 confronts the same incentive to misrepresent personal benefit The mutual incentives to understate true benefit once more result in inefficient under-supply of the public good Strategic Behavior Understatement of personal benefit introduces strategic consideration Person 1 would not want to understate benefit toomuch Excessive understatement of personal benefits may push the other person s contribution beyond a level where he would no longer want to continue making contributions Likewise, if person 2 were to raise person 1 s contributions beyond an acceptable level for person 1, person 1 would stop contributing to financing the public good

17 The Lindahl Solution as a Benchmark The Lindahl solution is a normative portrayal of ideal truthful behavior of beneficiaries of public goods People are thus viewed as trusting and trustworthy The Lindahl solution is, however, contrary to the premise that people maximize utility or do the best for themselves By misrepresenting their preferences and thus reducing their cost shares, people would be better off if taking the behavior of others as given We shall not assume that the Lindahl solution is feasible We can nonetheless use the Lindahl solution as a benchmark for efficient payment and supply of public goods The question of interest becomes whether there is some way of achieving the efficient Lindahl consensus outcome In particular, we would like to know whether governments can replicate the efficient Lindahl consensus outcome