Public goods g (and priva priv t a e t ones) From Fr Eff Ef ic i i c e i n e t n marke mark t e s to Market Failure

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1 Public goods (and private ones) FromEfficient markets to Market Failure

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4 One more In 2008, US Army had more than 1 million soldiers. 543,000 were active duty. US Navy hd had about t460, sailors. About 335,000 were active duty. USMC had about 198,000 marines. US Air Force had about 400,000 personnel. About 330,000 were active duty. US Coast Guard had about 40,000 active duty personnel. WHAT ARE ALL THESE PEOPLE DOING

5 Outline Public and Private goods Markets Private goods equilibrium i Public goods equilibrium Solution Voluntary participation Privatize. Tax

6 Public and Private goods Private Goods Rival in consumption If you eat the apple I can not eat it Excludable If you have the apple you can prevent me from having it. Pure private goods have additional properties (divisibility, transferability) Non Rival Public Goods If I listen to the radio waves so can you Non Excludable If you produce the radio wave you can t stop anyone from listening

7 Excludable Non Excludable Rival Consumption goods Fishing grounds Non Rival Scrambled radio Clean Air Scarcity creates Rivalry Excludable Non Excludable Rival Wild Sl Salmon 2010 Wild Sl Salmon in 1980 Non Rival Wild Salmon in 1600 Technology creates excludability Rival Excludable Range in the US West 1800s Non Excludable Range in the US West 1860s Non Rival Digital Radio 2010 Radio in 1930

8 Demand for private goods At quantity demanded Marginal willingness to pay=price Total demand at a given price is the sum of individual demands. this comes out of the rivalry. If want to satisfy the demand of two people I have to produce enough for each of them. If price is $1 and x want 4 apples and Y wants 3 I have to have 7 apples to sell. Logic different If X is willing to pay $1 for one jazz radio station and Y is willing to pay $2 for one jazz radio station I can satisfy each of them with 1 radio station

9 Private demand D(1) D(2) 400 D(3) D(4) 300 D(10) 200 D(20)

10 Demand for Public Good D(1) 4000 D(2) D(3) 2500 D(4) 2000 D(10) 1500 D(20)

11 Private demand sum across Public demand sum up 600 D(1) 600 D(2) D(1) 500 D(3) D(4) 500 D(2) D(3) D(4) 400 D(10) D(20) 400 D(10) D(20)

12 Problems with these goods The non rival means that there is usually a high social willingness to pay (sum of each person s s the marginal willingness to pay) But the non excludable get in the way. Why because individuals id are rational. So they want to get stuff at least cost Why pay for something if someone else will

13 Provision of public goods 1. Voluntary Population of n individuals, all identical Max U(G,c) where G is public goods c is consumption sbjt to g+c Y where G=G i +g U(G, c) =G α +c Voluntary contributions optimize! Under private provision, G is a constant

14 Private provision is inefficient G is a constant and individual contributions are falling with n. What should we do? Total utility is ng α so we want to max ng α G Not transparent but G is increasing in n. (and so is g)

15 al contribution α= G g Total public good Individu Population

16 Solutions Taxation! That solves the voluntary part but not the efficient level pbs Preference elicitation Survey Voting Mechanism design

17 Remember Ask people who they are Now assume α i is distributed between Clearly l then Marginal willingness to pay So if you expect everyone else to contribute you will say the lowest possible feasible

18 Voting There is going to be a vote on the size of the public good. Given our assumptions, individuals will vote for what ever option is closest to their preferred G Find the voter that t has the median preference (half the population wants a smaller G and half a bigger one).

19 Voting Recall that the efficient solution would be to sum individual demand With a distribution of preferences, that would be integrating over the preferences. If the mean demand and the median demand are the same then voting will produce the efficient outcome (but only then). What would like to do is to elicit individual preferences and then integrate

20 Mechanism design Suppose we implement the following scheme Tll Tell everyone that t (1) their contribution tib ti g will depend on the average of everyone else reports (2) the choice of G will depend on the average report. (1) implies what you say does not affect what you pay => everyone has a (weak) incentive to be honest. (2) implies that if everyone is honest, then we get the efficient outcome. More on this in EC 106, 118, 131, 132.