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4. Public Goods 4. Public Goods

SO FAR… We have seen that the role of government in promoting efficiency is SO FAR… We have seen that the role of government in promoting efficiency is to intervene in the pricing mechanism of goods that create externalities. Now we will investigate a class of goods where it is usually more efficient for the government to supply instead of the private sector. Public Goods: =(Law and Order, defence, refuse collection, roads, education, public health, …)

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

Definition A Public Good has 2 properties: (1) If it has been provided to 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”

Example: TV Signals NON-RIVAL NON-EXCLUDABLE TERESTRIAL Pure Public Good BASIC CABLE Impure Public Good Example: TV Signals NON-RIVAL NON-EXCLUDABLE TERESTRIAL Pure Public Good BASIC CABLE Impure Public Good EXCLUDABLE SATELLITE Impure Public Good Pay-per-View Pure Private Good

CONSEQUENCES Non-excludable: Very difficult for the private sector to provide it and make a CONSEQUENCES Non-excludable: Very difficult for the private sector to provide it and make a profit. (Basic Research, Information, R&D) Non-rivalry: Do not want to exclude people as it is inefficient (The marginal cost of them getting the good is zero and they get positive benefit. )

The Free Rider Problem The fundamental problem of all public goods is I’d rather The Free Rider Problem The fundamental problem of all public goods is I’d rather someone else paid for the public goods I consumed. This is called the free-rider problem.

Prisoners’ Dilemma in Action Imagine it costs £ 4 to provide a clean street 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. If one of us pays £ 4 we are both better off. He Pays I Pay I Don’t Pay He Doesn’t Pay

Prisoners’ Dilemma in Action He Pays He Doesn’t Pay I Pay (-1, -1) (-1, Prisoners’ Dilemma in Action He Pays He Doesn’t Pay I Pay (-1, -1) (-1, 3) I Don’t Pay (3, -1) (0, 0) 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. If one of us pays £ 4 we are both better off.

Prisoners’ Dilemma in Action He Pays He Doesn’t Pay I Pay (-1, -1) (-1, Prisoners’ Dilemma in Action He Pays He Doesn’t Pay I Pay (-1, -1) (-1, 3) I Don’t Pay (3, -1) (0, 0) 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. If one of us pays £ 4 we are both better off.

Other Examples of Free Rider Problems In the USA people pay voluntary subscriptions for Other Examples of Free Rider Problems In the USA people pay voluntary subscriptions for the public broadcasting service – less than 10% do so. (In the UK it is mandatory to pay the TV licence fee. ) The town of Cambridge distributed 350 bikes around the town for people to use free of charge. (You had to return the bike to a special stand after using it. ) Within 4 days they had all gone.

When can private provision of public goods work You often find shops forming groups When can private provision of public goods work You often find shops forming groups to improve the environment they act in. e. g. Oxford Street Traders Association. Also rich neighbourhoods sometimes pay for security patrols, (e. g. Bishops Avenue, Hampstead) Why does this work? • People are not all the same – some people value the public good a lot. • Altruism • People feel good if they contribute to the public good (warm glow)

User Fees for Excludable Public Goods and for Publicly Provided Private Goods • Some 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 often publicly provided. Price/Fee Demand/Users’ Value # of users

User Fees for Excludable Public Goods and for Publicly Provided Private Goods How does 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

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

User Fees for Excludable Public Goods and for Publicly Provided Private Goods If you 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

User Fees for Excludable Public Goods and for Publicly Provided Private Goods If you 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 LOST VALUE Demand/Users Value COST OF BRIDGE FEE # of users

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

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

Marginal Benefit Non-Excludable Marginal Benefit = Marginal Benefit 1 + Marginal Benefit 2 + Marginal Benefit Non-Excludable Marginal Benefit = Marginal Benefit 1 + Marginal Benefit 2 + … + Marginal Benefit. N = S Marginal Benefiti

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

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

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

Equivalently S MU(pg) MC(pg) = MUi MC Equivalently S MU(pg) MC(pg) = MUi MC

Equivalently S MU(pg) MC(pg) = MUi MC Equivalently S MU(pg) MC(pg) = MUi MC

Equivalently S MU(pg) MC(pg) = MUi MC Equivalently S MU(pg) MC(pg) = MUi MC

Equivalently S MU(pg) MUi = MC(pg) MC Equivalently S MU(pg) MUi = MC(pg) MC

Equivalently S MRS = MRT This is called the Samuelson Condition after Paul Samuelson Equivalently S MRS = MRT This is called the Samuelson Condition after Paul Samuelson who first noticed it applied.

Mechanisms for Efficiently Providing the Public Good How do you get to provide people Mechanisms for Efficiently Providing the Public Good How do you get to provide people with the right quantity of the public good if: 1. When it is provided at zero MC people will tend to overstate their desire for it. 2. When it is provided at positive MC people will tend to understate their desire for it hoping to free ride.

Mechanisms for Efficiently Providing the Public Good How do you get to provide people Mechanisms for Efficiently Providing the Public Good How do you get to provide people the right quantity of the public good if: 1. When it is provided at zero MC people will tend to overstate their desire for it. 2. 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.

Example 1: Vickrey Auctions Assumptions: • One unit of a good to be sold. Example 1: Vickrey Auctions Assumptions: • One unit of a good to be sold. • People have independent and private values: v 1 , v 2 , …, vn. (This rules out situations where your value is affected by what others know. )

Example 1: Vickrey Auctions Assumptions: • One unit of a good to be sold. Example 1: Vickrey Auctions Assumptions: • One unit of a good to be sold. • People have independent and private values. (v 1 , v 2 , …, vn) Rules: • 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. (i. e. truthfully reveal your value)

Example 1: Vickrey Auctions Analysis: The highest bid from everyone else is B. My Example 1: Vickrey Auctions Analysis: The highest bid from everyone else is B. My value is v*. If I submit a bid b > B => I win and pay B (I get v*-B) If I submit a bid b < B => I lose and I get zero. Case 1: B>v* In this case winning (and bidding above B) will lose me money bidding v* is optimal here.

Example 1: Vickrey Auctions Case 1: B > v* In this case winning (and Example 1: Vickrey Auctions Case 1: B > v* In this case winning (and bidding above B) will lose me money bidding v* is optimal here. Case 2: B < v* In this case my payoff from winning (v* - B) is positive. This is also independent of what I bid. If I bid b=v* I will be sure I always win the auction in this case. WHATEVER THE OTHERS DO BIDDING v* IS BEST! (Note: this is not true if my value depends upon what you know. )

Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal 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 vi Note : they don’t have to report the truth vi ≠ vi*

Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal 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 vi Step 2 : Add up the reported values.

Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal 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 vi Step 2 : Add up the reported values. Step 3 : If Sum of Reports – Cost of Bridge >0 then build the bridge.

Clark-Groves Mechanism This is a process that will get individuals to truthfully to reveal 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 vi 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

Clark-Groves Mechanism Step 1 : Individuals report their value for the bridge vi Step Clark-Groves Mechanism Step 1 : Individuals report their value for the bridge vi 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 Step 4 : If the individual’s value was decisive, i. e. Sum of Others’ Reports < Cost of Bridge < Sum of all Reports

Clark-Groves Mechanism Step 1 : Individuals report their value for the bridge vi Step Clark-Groves Mechanism Step 1 : Individuals report their value for the bridge vi 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 Step 4 : If the individual’s value was decisive, i. e. Sum of Others’ Reports < Cost of Bridge < Sum of all Reports Charge the individual = Cost of Bridge – Sum of others’ reports

Clark-Groves Mechanism Optimal to tell the truth. Let U be the sum of the Clark-Groves Mechanism Optimal to tell the truth. Let U be the sum of the other’s reports and let v be my value. If U>Cost: I don’t care what I say so reporting truthfully is fine.

Clark-Groves Mechanism Optimal to tell the truth. If U+v > Cost > U: Then Clark-Groves Mechanism Optimal to tell the truth. If U+v > Cost > U: Then any report u such that U+u>Cost (or u>Cost-U) will get me utility v – (Cost –U) >0. (independent of report!) But any report u < Cost – U will get me utility =0. To ensure I get this positive utility should then report truthfully.

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