We have seen that the role of government in promoting efficiency is to intervene in the pricing mechanism of good that create externalities.

Transcription

1 4. Public Goods

2 SO FAR We have seen that the role of government in promoting efficiency is to intervene in the pricing mechanism of good that create externalities. Now we will investigate a class of good where it is usually more efficient for the government to supply instead of the private sector. Public Goods

3 Outline 1. Definition and Description 2. Free-riding 3. Optimal Provision: 4. Problems of Preference Revelation

4 Definition A Public Good has 2 properties: (1) If it has been provided to one consumer it is difficult/impossible to stop another from enjoying it too. Non-Excludable (2) The amount of the good I enjoy has no affect on the amount you enjoy. Non-rival

5 Example: TV Signals NON-RIVAL RIVAL NON-EXCLUDABLE TERESTRIAL BASIC CABLE EXCLUDABLE SATELLITE CABLE/PPP

6 CONSEQUENCES Non-excludable: Very difficult for private sector to provide it. Information and R&D Non-rivalry Do not want to exclude people as it is inefficient.

7 Prisoners Dilemma in Action Imagine it costs 4 to provide a clean street outside my house. Either I or my neighbour can pay for it. We both value clean streets at 3. He Pays He Doesn t Pay If one of us pays 4 we are both better off. I Pay I Don t Pay

8 Prisoners Dilemma in Action Imagine it costs 4 to provide a clean street outside my house. Either I or my neighbour can pay for it. He Pays He Doesn t Pay We both value clean streets at 3. If one of us pays 4 we are both better off. I Pay (-1,-1) (-1,3) I Don t Pay (3,-1) (0,0)

9 Prisoners Dilemma in Action Imagine it costs 4 to provide a clean street outside my house. Either I or my neighbour can pay for it. He Pays He Doesn t Pay We both value clean streets at 3. If one of us pays 4 we are both better off. I Pay (-1,-1) (-1,3) I Don t Pay (3,-1) (0,0)

10 Conclusion: Individual Incentives Don t Work Here. Need a government to provide the good.

11 User Fees for Excludable Public Goods and for Publicly Provided Private Goods Some public goods are excludable roads bridges etc. Some goods (education, water) have large cost of supplying additional individuals are are often publicly provided. Price/Fee Demand/Users Value # of users

12 User Fees for Excludable Public Goods and for Publicly Provided Private Goods How does welfare get maximized? The best possible is to allow everyone to travel and to somehow pay for the bridge. Price/Fee Demand/Users Value # of users

13 User Fees for Excludable Public Goods and for Publicly Provided Private Goods Welfare = Cost of the Bridge Price/Fee Demand/Users Value # of users

14 User Fees for Excludable Public Goods and for Publicly Provided Private Goods If you charge a fee to recoup the cost of the bridge welfare goes down. Price/Fee Demand/Users Value COST OF BRIDGE FEE # of users

15 User Fees for Excludable Public Goods and for Publicly Provided Private Goods If you charge a fee to recoup the cost of the bridge welfare goes down. Price/Fee Demand/Users Value LOST VALUE COST OF BRIDGE FEE # of users

16 Impure Public Goods Anything with a positive consumption externality. Congested goods: Roads Club Goods: Excludable with congestion = Museum Local Public Goods: Parks,etc

17 Efficient Provision of Public Goods How much Public Goods should the Government provide? Marginal Benefit of the Public Good MC of the PG

18 Marginal Benefit Non-Excludable Marginal Benefit = Marginal Benefit 1 + Marginal Benefit Marginal Benefit N = Σ Marginal Benefit i

19 How do we know whether we have the socially optimal quantity of public goods? Marginal Benefit from the public good = Σ MU(pg) Marginal Cost of Providing one more unit of Public Good = MC(pg)

20 How do we know whether we have the socially optimal quantity of public goods? Marginal Benefit from the public good = Σ MU(pg) Marginal Cost of Providing one more unit of Public Good = MC(pg) Marginal Benefit from the Private good = MU i Marginal Cost of Providing one more unit of Private Good = MC

21 Right Mix if MB(public good) = MB(private good) MC(public good) MC(private good)

22 Equivalently Σ MU(pg) = MU i MC(pg) MC

23 Equivalently MU(pg) = MU i MC(pg) MC

24 Σ MRS = MRT Equivalently

25 Mechanisms for Efficiently Providing the Public Good How do you get to provide people the right quantity of the public good if: When it is provided at zero MC people will tend to overstate their desire for it. When it is provided at positive MC people will tend to understate their desire for it hoping to free ride. We want to find Incentive Compatible Mechanisms i.e. provision schemes where it is in everyone s interest to correctly report how much they value the good.

26 Example 1 Vickrey Auctions One unit of a good to be sold. People have private values. Rule: Bids are submitted and the highest bid gets the object. The winner pays the amount bid by the second highest bidder. Optimal strategy = bid how much you value the object.

27 Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal their preferences for the public good. Step 1 : Individuals report their value for the bridge v i (Note : they don t have to report the truth v i v i *

28 Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal their preferences for the public good. Step 1 : Individuals report their value for the bridge v i Step 2 : Add up the reported values.

29 Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal their preferences for the public good. Step 1 : Individuals report their value for the bridge v i Step 2 : Add up the reported values. Step 3 : If Sum of Reports Cost of Bridge >0 Build Bridge

30 Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal their preferences for the public good. Step 1 : Individuals report their value for the bridge v i Step 2 : Add up the reported values. Step 3 : If Sum of Reports Cost of Bridge >0 Build Bridge If Sum of Reports Cost of Bridge <0 Don t Build

31 Clark-Groves Mechanism tep 1 : Individuals report their value for the bridge v i tep 2 : Add up the reported values. tep 3 : If Sum of Reports Cost of Bridge >0 Build Bridge If Sum of Reports Cost of Bridge <0 Don t Build tep 4 : If the individual s value was decisive, i.e. Sum of Others Reports < Cost of Bridge < Sum of all Reports

32 Clark-Groves Mechanism tep 1 : Individuals report their value for the bridge v i tep 2 : Add up the reported values. tep 3 : If Sum of Reports Cost of Bridge >0 Build Bridge If Sum of Reports Cost of Bridge <0 Don t Build tep 4 : If the individual s value was decisive, i.e. Sum of Others Reports < Cost of Bridge < Sum of all Reports harge the individual = Cost of Bridge Sum of others reports

33 Clark-Groves Mechanism roperties: 1) Voter only pays when decisive. 2) Payments < benefits received 3) Optimal to tell the truth. 4) As population grows less of a problem with excess revenue.