1Public Goods and Free rider Public Goods and Free rider problemproblemPlanPlan4Can Markets Allocate Public Goods Efficiently?– Samuelson’s Condition for Efficient Provision of Public Goods– A Market for Apples– A Market for Parks4The Free rider problem4Developing formal tools: definitions– Nash equilibriumDefinition: Rivalry in consumption means that only one person can consume a good: the good is used up in consumption (it is depletable).Definition: Exclusion in consumption means that others can be prevented from consuming a good.Definition: Private goods have properties of rivalry and exclusion. Pure Public goods lack both rivalry and exclusion. Club goods lack rivalry but have property of exclusion. Common property lacks exclusion but does have the property of rivalryExclusion No exclusionRivalry Pure Privategoods: AppleCommons:FisheriesNo Rivalry Club goods:concertPure publicgood: cleanairBecause public goods lack rivalry, the aggregate demand is the aggregate willingness to pay curve: the vertical sum of the individual demand curves.Example: Efficient Provision of a Public Good0Price ($/unit)Quantity of public goodD1400300200100100302Example: Efficient Provision of a Public Good0Price ($/unit)Quantity of publicgoodD1D2400300200100100 20030Example: Efficient Provision of a Public Good0Price ($/unit)Quantity of publicgoodMC = 240MSBD1D2MC = 50400300200100100 20030ExampleConsumer 1: P1= 100 - QConsumer 2: P2= 200 - QHow would we determine the efficient level of the public god algebraically assuming the marginal cost of the public good is $240?Summing P1and P2, we obtain MSB = P1+ P2= 100 - Q + 200 - Q = 300 - 2QSetting MSB = MC, we have:300 - 2Q = 240 … or…Q* = 30Optimal Level of Provision of Optimal Level of Provision of Public Goods Public Goods 4Assume there are two individuals in the society, Adam and Eve, who have quasilinear preferences. They both enjoy a public good, say, parks. Let c(g) denote the cost of constructing a park covering g yards. The optimal size for the park should satisfy()()()gcguguEAg−+maxOptimal Provision of Public Optimal Provision of Public GoodsGoods4The maximization implies that if the size of the park is optimal, the sum of the marginal valuations by Adam and Eve should equal to the marginal cost of construction. In other words, the sum of Adam and Eve’s valuations of the last yard of the park should equal to the cost of enlarging the park by one yard.3Market Market Provision of Public GoodsProvision of Public Goods4Example. Assume that the marginal cost of providing another yard of the park is constant and is equal to 10. Adam’s and Eve’s valuations (willingness to pay) is depicted below.Adamg$1068 20Eveg$1042 20The OutcomeThe Outcome4Adam and Eve get the 10(=8+2) yard park, instead of the optimal 20 yd.4Note that we assumed that “in the market” the contributions are “simultaneous” and that the price should be the same for everyone.Is this story a familiar one? Is this story a familiar one? 4 Two roommates share a kitchen. Both of them like to have it clean. If they clean it together, they spent 15 minutes. If any of them cleans it on his own, it takes an hour and “destroys” the happiness from having it cleaned.Definition: a free rider benefits from an action of other(s) without paying for that action.Solutions to the free rider problem•social pressure (small numbers)•government action (compulsion)•transformation into private good (metering)1. When one agent's actions affect another agent, the agent exerts an externality.2. When externalities are present the competitive market may not attain the Pareto Efficient outcome.3. We can restore optimality by assigning property rights to the cause of the externality (The Coase Theorem).4. If we follow this approach, efficiency is achieved regardless of who receives the property rights; however, the property rights affect the income distribution.5. When transaction costs are high or there is asymmetric or incomplete information, allocating property rights may not restore optimality. 6. Other methods of restoring optimality include direct regulation and fees.7. Private goods have the properties of rivalry and exclusion. Other types of goods exist that do not have these properties.8. Goods that lack rivalry and exclusion are called pure public goods.49. The demand for pure public goods is the vertical sum of the individual willingness to pay for the good. 10. Pure public goods tend to be undersupplied by the