4.12 Private Provision of Public Goods: Experiments Testing Free Rider Behavior 4.7 OPTIMAL PROVISION OF PRIVATE GOODS

Transcription

1 Module 4 Lecture 16 Topics 4.7 Optimal Provision of Private Goods 4.8 Optimal Provision of Public Goods 4.9 Samuelson Rule 4.10 Free Rider Problem 4.11 Private Provision of Public Goods Private-Sector Underprovision: a Numerical Example The Free Rider Problem in Practice 4.12 Private Provision of Public Goods: Experiments Testing Free Rider Behavior Marwell and Ames OPTIMAL PROVISION OF PRIVATE GOODS In the case of private goods, equilibrium is determined by the interplay of supply and demand As prices adjust, each person changes his quantity consumed according to own preferences. For a private good, consumers demand different quantities at the same market price. 1

2 Figure 16.1 Consider a private good B and the market for it. The alternative use of money is buying the numeraire are individual preferences of A & B. curves for A &B respectively coming from private Adding up for good Y we get, which is same as the demand curve. Market supply is S. Competitive equilibrium price PE. is the market clearing quantity, But A & B derive their demand from the individual demand curve.. The private market equilibrium in this case is socially efficient. The MRS for any quantity of Y equals the SMB of that quantity the marginal value to society equals the marginal value to any individual in the perfectly competitive market. 4.8 OPTIMAL PROVISION OF PUBLIC GOODS Now consider the market for military spending as opposed to Food spending. Demand for a public good is determined by the Willingness To Pay That is, holding quantity fixed, what is each person s willingness to pay? 2

3 Figure 16.2 Demand for a public Good for Missiles demand curve for Missiles We want to know if individuals are willing to pay for missiles. Suppose we need 1 missile A is willing to pass for 1 missile B is willing to pass for 1 missile Adding the two willingness to pay we get, For the 5 th missile, A is willing to pay For the 5 th missile, B is willing to pay For the 5 th missile Total Adding A & B s WTP for each quantity of the public good we get, society s Demand curve or society s WTP. is the market supply curve Competitive equilibrium =5 missiles, B & A consume 5 missiles each. Unlike the case of private goods, where aggregate demand is found by summing the individual demands horizontally, with public goods, aggregate demand is found by summing individual demand curve vertically. 4.9 SAMUELSON RULE: Optimal Provision of Public Goods Private Goods: social efficiency is maximized when the marginal costs are set equal to the marginal rate of substitution for each individual 3

4 Public Goods: social efficiency is maximized when the marginal costs are set equal to the sum of the marginal rates of substitution (rather than each individual s MRS). Two goods P and G Two individuals A&B To A: The marginal public good is worth To B: Now = Marginal benefit derived from consumption of G. The social marginal benefit from the next unit of public good G is The social MC is the same as before: derived from the production function of G.. Efficiency requires Samuelson Rule (1954)} as opposed to private good case when This is because the good is nonrival: Since a unit can be consumed by all consumers, society would like the producer to take into account all consumers preferences. This is because the good is non-rival. Excludability plays no role in the analysis. Only relevant for determining feasible provision mechanisms 4

5 4.10 FREE RIDER PROBLEM All of the individual members of a group can benefit from the efforts of each member and all can benefit substantially from collective action. For example, if each of us pollutes less, we all benefit from the reduction of harmful gases in the air we breathe. If all of us prefer the state of less pollution over the state of pollution, then the provision of cleaner air is a collective good for us. Unfortunately, my polluting less does not matter enough for anyone -- especially me -- to notice. Therefore, I may not contribute my share toward not polluting. I may be a free ride on the beneficial actions of others PRIVATE PROVISION OF PUBLIC GOODS In general, the private sector under-provides public goods because of the free rider problem PRIVATE-SECTOR UNDERPROVISION: A NUMERICAL EXAMPLE Consider two people, A and B, with identical preferences Two consumption goods private and public, Roads and Cars. Set the prices of each good at 1. A and B benefit equally from Road that is provided by either of them since road is a public good. Each person chooses combinations of Car and Roads in which his own MRS equals the ratio of price. Recall that marginal utilities diminish with increasing consumption of a good. In this example, optimal provision would require that Roads are consumed until their utility equals half the marginal utility of Cars. Thus, each individually buys too much Car privately & provides too few roads privately. Strong positive externality in private provision of roads leads to underprovision 5

6 THE FREE RIDER PROBLEM IN PRACTICE There are some interesting examples of the free-rider problem in practice. Many users of file sharing services, like youtube, never contribute uploaded files; they only download files. To overcome this problem some of these services though give download priority to those who contribute PRIVATE PROVISION OF PUBLIC GOODS: EXPERIMENTS TESTING FREE RIDER BEHAVIOR MARWELL AND AMES 1981 Groups of 5 subjects, each given 10 tokens. Can invest tokens in either an individual or group account. Money deposited in own account returned 1-1. Money deposited in the public account was first pooled, then multiplied by some factor greater than one, and then distributed equally among all subjects. Thus tokens given to group account paid out money at higher rate but the group sum was divided equally between all contributors irrespective of their donation to the fund Nash equilibrium is 100% individual contribution but Pareto efficient outcome is 100% group contribution. Rationality implies that all subjects will follow the individual strategy. For empirical evidence: Compute fraction invested in group account under various treatments. Experiment run on various groups of high school and college students & economics PhD students. Finding: 40 to 60% of tokens were still invested in the public good. Only one group free-rode a lot: 1st year econ graduate students (20% donation rate). 6

7 Stephen Marglin, The Dismal Science: Thinking like an economist undermines community Two follow up questions: What is a fair investment in the public good? 75 percent of the noneconomists answered 1/2 or more, 25 percent answered all. Are you concerned about fairness in making your investment decision? Almost all noneconomists answered yes. More than one-third of the economists either refused to answer the question regarding what is fair. Those who did respond were much more likely to say that little or no contribution was fair. They were about half as likely as other subjects to indicate concerned with fairness in making their decisions. Criticism Difference in age Difference in gender composition of their group of economics graduate students These experiments may be of limited applicability or fail external validity: Individuals may behave differently in a contrived laboratory setting. The stakes are often small, so the cost of being altruistic is low. College undergraduates may not be representative of the population more generally. 7