1. PUBLIC GOODS MICROECONOMICS Lecture 7th, November 7, 2003
Varian, H., Intermediate Microeconomics, 5th Edition, Norton, 1999.
Landsburg, S., Price Theory and Applications, 2th Edition, The Dryden Press, 1992.
Stiglitz, J., Economics of the Public Sector, 2th Edition, Norton, 1988.
Ana Simões nº 1849
Inês Azevedo nº 47427
Paulo Rebelo nº 5545
Tânia Sousa nº

2. Table of Contents I. What are Public Goods?
II. Why to provide Public Goods?
III. When to provide Public Goods?
IV. Which level of Public Goods to provide?
V. In what conditions is the right level of Public Goods unique?
VI. Should provision of Public Goods be private or public?
VII. Should provision of Nonrivalrous Goods be private?
VIII. Should provision of Nonexcludable Goods be private?
IX. When and how should Private Goods be publicly provided?
X. What is the difference between Private and Public Goods?
XI. Why do people Free Ride?
XII. How is public choice made?
XIII. Is voting a good social choice mechanism?
XIV. Why do people lie in Demand Revelation?
XV. How to enforce true Demand Revelation?
XVI. Summary
Microeconomics – Public Goods
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3. I. What are Public Goods? Nonrivalrous good
A good that, if consumed by one person, can be provided to others at no additional cost. It has a Low/Null marginal cost.
ex: pirated software, uncrowd theater
Nonexcludable good
A good which is impossible or very costly to exclude individuals from using it.
ex: national defense, lighthouse
Lower left is a pure public good.
Upper right is a pure private good.
x-axis: nonexcludable to excludable
y-axis: nonrivalrous to rilvarous
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4. I. What are Public Goods? Main characteristics of Public Goods:
Nonrivalrous (not desirable to ration), Nonexcludable (not feasible to ration).
The user of a common resource imposes a negative externality on other users, so that such property tends to be overused.
The creator of a public good creates a positive externality so that such goods tend to be under produced.
Rivalrous
Nonrivalrous
Excludable
Private Goods
Ice-creams
Clothes
Natural Monopolies
cable TV
Gas company
Small phone company
Non Excludable
Common Resources
Fisheries
Environment
Public Goods
National defense
Knowledgment
Lighthouse
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5. I. What are Public Goods? What are Public Goods?
The main characteristics of public goods are: Nonrivality and Nonexcludability.
As public goods are nonexcludable it is difficult to impose a price thus they are susceptible to market failures.
As they are Nonrivalrous and Nonexcludable:
Must be provided in the same amount to all affected consumers.
Each person may value it differently but they all have to consume the same amount.
Public goods could be either publicly (government or the adequate authority at that scale) or private provided. This balance changes from country to country and with time.
development of new technology, ex: cable TV.
changes in income per capita.
changes in personal tastes.
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6. II. Why to Provide Public Goods?A B
Utility possibilities frontier: a Pareto efficient allocation of resources
Utility possibilities frontier for two different groups, U1 andU2
Assuming that without Public Good, equilibrium is at point E.
With tax coercion needed to provide public goods both groups can be at a better position A.
Although, once the power of coercion is granted, can be used from one at the expense of another – point B.
Why to Provide Public Goods?
Because there is a potential for increasing utility.
Utility possibilities frontier with government providing public goods.
Utility possibilities frontier without government providing public goods.
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7. III. When to Provide Public Goods?
Example:
Two roommates, 1 and 2, trying to decide whether or not to purchase a TV. They are both able to watch it public good.
Is it worth to buy the TV?
Budget constraints
TV price constraint
w1, w2 - each roommate’s initial wealth
g1, g2 - each roommate’s contribution to the TV
x1, x2 - each roommate’s money left to private consumption
c - TV’s price
Microeconomics – Public Goods
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8. III. When to Provide Public Goods?
The utility function of roommate i will depend on his private consumption and the availability of the TV.
The roommates may value the TV differently: r1  r2.
The reservation price of each roommate will probably be a function of his/her wealth.
u1 ,u2 - each roommate’s utility function
x1 ,x2 - each roommate’s money left to private consumption
G - Availability of the TV (the public good)
0: no TV 1: TV
r1 ,r2 - each roommate’s reservation price
w1, w2 - each roommate’s initial wealth
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9. III. When to Provide Public Goods?
When is there a payment scheme (g1, g2) that both people are better off having the TV that not having it?
It has to represent a Pareto improvement:
Using reservation prices:
u1 ,u2 - each roommate’s utility function
x1 ,x2 - each roommate’s money left to private consumption
r1 ,r2 - each roommate’s reservation price
w1, w2 - each roommate’s initial wealth
g1, g2 - each roommate’s contribution to the TV
Microeconomics – Public Goods
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10. III. When to Provide Public Goods?
The payment scheme (g1, g2) that means that both people are better off having the TV then not having it is:
The acquisition will be on both roommates’ benefit if each can acquire the good for less than the maximum he would be willing to pay – necessary condition.
A sufficient condition is that the sum of the reservation prices is higher than the sum of their contributions.
The condition stated must be satisfied if the allocation without the TV (w1, w2, 0) is Pareto inefficient.
r1 ,r2 - each roommate’s reservation price
w1, w2 - each roommate’s initial wealth
g1, g2 - each roommate’s contribution to the TV
Microeconomics – Public Goods
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11. III. When to Provide Public Goods?
Whether or not it is Pareto efficient to provide the public good is a matter of the initial distribution of wealth.
Exception: quasi-linear preferences, where the reservation price is only a function of the public good utility:
When to Provide a Public Good?
When it is a Pareto Improvement. This only depends on each agent willingness to pay and on the total cost.
The willingness to pay depends usually on individual’s wealth with exception of quasi-linear preferences. x G
r1 ,r2 - each roommate’s reservation price
w1, w2 - each roommate’s initial wealth
u1 ,u2 - each roommate’s utility function
v1 ,v2 - each roommate’s utility function for the Public Good
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12. IV. Which level of Public Goods to provide?
How good is the TV purchased?
Budget constraint
Pareto efficient allocation given consumer 2’s level of utility
Optimality condition: the sum of the marginal rate of substitutions between the public and the private good equals the marginal cost of providing an extra unit of the public good
w1, w2 - each roommate’s initial wealth
x1, x2 - each roommate’s money left to private consumption
c - cost function for the TV quality (G)
u1 ,u2 - each roommate’s utility function
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13. IV. Which level of Public Goods to provide?
Maximisation of u1 utility given a u2 fixed utility:
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14. IV. Which level of Public Goods to provide?
The value at which the marginal cost of the public good equals the sum of the absolute values of the marginal rates of substitution between the private and public good.
MRS G* MC
MRS1 - roommate’s 1 marginal rate of substitution.
MRS2 - roommate’s 2 marginal rate of substitution.
MRS1+2 - sum of both marginal rates of substitution .
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15. IV. Which level of Public Goods to provide?
The sum of MRS equals the aggregate demand curve - how much the society will be willing to pay for an extra unit of Public Good. The aggregate demand curve is the vertical sum of the individual demand curves
How to build individual demand curves for Public Goods:
Suppose that for each extra unit of Public Good provided an individual tax price, p, is imposed on each individual. How much would each individual demand for each tax level, p?
Level of optimum expenditure on Public Good is the tangency between indifference curve and budget constraint
Indifference curves Budget constraint with p slope G1 x G w
-p1 E
x - private consumption
G - Public Good
p - Tax imposed
w - individual wealth
Microeconomics – Public Goods
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16. IV. Which level of Public Goods to provide?
How to build individual demand curves for Public Goods:
Budget constraint shifts as tax price decreases from p1 to p2 and right amount of public good changes from G1 to G2.
Raising and lowering the tax price permits that individual demand curves are traced.
Individual Demand for Public Goods
Budget constraint with p slope
Indifference curves
x - private consumption
G - Public Good
P - Tax imposed
w - Individual wealth P G1 G2 E E’ x G w
-p1
-p2 E p1 E’ p2 G G1 G2
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17. IV. Which level of Public Goods to provide?
How to build aggregated demand curves for Public Goods:
Aggregated demand curve is the sum of individual demand curves
Supply curve is the marginal cost of production - how much the society will have to pay for an extra unit of public good
Aggregate Demand for Public Goods Supply Curve
Which level of Public Goods to provide?
The efficient level: the level where marginal cost of production equals aggregate demand
G - Public Good
P - Total tax imposed P
pA+pB € pB pA G1 G G
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18. Marginal Rate of Substitution
V. In what conditions is the efficient level of public good unique for an individual?
What happens in the following preferences preferences?
Quasilinear Preferences Cobb-Douglas Preferences
Indifference curves
Marginal Rate of Substitution
Budget constraint
In quasilinear preferences whatever the budget constraint is, the amount of efficient Public Good remains the same. x x G G G* G* G*
xi- money left to private consumption of person i
G- total amount of money spent on public good
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19. V. In what conditions is the efficient level of public good unique for an individual?
Optimality condition in this case implies that marginal rates of substitution are independent of the amount of private good
In this case if there is a redistribution of wealth in the society the Pareto efficient amount of Public Good does not change. The same happens if aggregate wealth increases/decreases.
In what conditions is the right level of public good unique?
In the case of quasilinear preferences.
In general it is not: the optimal amount of Public Good will be different at different wealth allocations. It is not possible to separate efficiency considerations in the supply of public good from distributional considerations
Microeconomics – Public Goods
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20. VI. Should provision of Public Goods be private or public?
Are there problems associated with private provision of Public Goods? (the TV example):
If the sum of the roommates’ willingness's to pay exceeds the cost of the TV then acquiring the TV will be Pareto Efficient.
But whether or not they actually decide to acquire the good will depend on the particular method they adopt to make joint decisions.
If the two roommates truthfully reveal they how much they value the TV, then they will agree on buying it. But will they tell the truth?
If one of the roommates think that the other will buy the TV on his one he will have an incentive to lie - this is called FREE RIDE.
Due to free ride behaviour the private provision of Public Goods will always be insufficient
Are there problems associated with private provision of Public Goods?
Yes, because of free ride behaviour.
Microeconomics – Public Goods
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21. VI. Should provision of Public Goods be private or public?
Are there problems associated with public provision of Public Goods ?
A tax system has to be imposed to finance Public Goods.
These tax systems have effects on incentives to produce wealth and are costly to administer, increasing the cost of production:
Feasibility curve: maximum level of private consumption for each level of Public Goods for that Tax System
Production possibilities curve: maximum consumption level for each level of Public Goods
Laffer curve: decrease tax revenues x x G G
xi - money left for private consumption of person i
G - total amount of money spent on public good
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22. VI. Should provision of Public Goods be private or public?
Are there problems associated with public provision of Public Goods ?
The tax system imposes to each individual a marginal cost. This individual will only be better of if its marginal cost is lower than its marginal benefit
The tax system changes the distribution of income and therefore will probably change the efficient level of public good
Yes due to the distortions imposed by the tax system.
Theoretically this problem could be minimized by calculating the efficient level of public good for a given tax scheme structure: p1, p2
such that
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23. VI. Should provision of Public Goods be private or public?
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24. VII. Should provision of Nonrivalrous Goods be private?
If a nonrivalrous good is private owned then its use will be charged although the cost of an additional person using it is zero.
Example: a bridge that has a null marginal cost.
Comparing public with private supply:
If private owned it will have a P toll for each trip and if public owned will have a null tool. The triangle area (loss of welfare) will be saved but there will be costs associated with raising the revenue to pay ‘construction cost’.
What about software? - incentives for innovation
Qc - number of trips at max capacity
Qe - number of trips at toll p
Qm - number of trips at null price
p - toll
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25. VIII. Should provision of Nonexcludable Goods be private?
If an expensive excludable good is private the costs of excluding it increase its price - transaction costs
Example: a good with constant marginal costs of production, C
Comparing public with private supply:
The area ABCP* is saved; consumption increases from Qe to Qm where the area ABE measures the gain and the area EFQm the excessive consumption, there will be costs associated with raising the revenue to pay the good.
P* - price with transaction costs
Qe - consumption at price P*
Qm - consumption at null price
c - marginal costs of production
Microeconomics – Public Goods
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26. Should provision of nonrivalrous / Nonexcludable / Public Goods be private?
Should provision of Public Goods be private or public?
It should not be private because of free rider behaviour. If there is a private provision of Public Goods it will be unsufficient.
A public provision has costs associated with it due to the tax scheme imposed to raise the revenues.
Should provision of nonrivalrous Goods be private?
Depends. If Nonrilavarous Goods are private provided there will be a deadweight loss due to underutilization but if public provided there will be costs associated with raising the revenue to pay it.
Should provision of Nonexcludable Goods be private?
Depends. The gain associated with the elimination of transaction costs has to be compared with the loss due to excessive consumption and the loss created by the taxes needed to provide the good.
Microeconomics – Public Goods
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27. IX. When and How should Private Goods be Publicly Provided?
Private Goods Publicly Provided: there is a large marginal cost associated with each additional consumer - rivalrous goods.
When should Private Goods be Publicly Provided?
When there are large transaction costs - quasi-nonexcludable goods
When distributive considerations are important, ex: education
These goods are rivalrous therefore mechanisms to restrict consumption must exist to avoid inefficiencies (where marginal benefit is inferior to marginal cost of production).
Rationing systems: price, uniform provision, queuing
Queuing:
Allows for some adaptability between supply and needs.
Cost is paid in waiting time (cost of waiting time varies with consumer).
Waste of time spent in queuing -> social cost.
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28. IX. When and How should Private Goods be Publicly Provided?
Uniform Provision: the same quantity of the good to everyone
It does not allow for the adaptation to differences in individual’s needs
If the provided level is low enough and higher demand individual can acquire more this is not a problem, ex: social security
How should Private Goods be Publicly Provided?
They should be provided through rationing systems P
Demand curve for low demander
Demand curve for high demander
Marginal Cost of Production
Q1 - quantity demanded by the high demander
Q2 - quantity demanded by the low demander
Q* - uniform quantity provided c Q2 Q* Q1
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29. X. What is the difference between Private and Public Goods?
Public goods are nonrivalrous and nonexcludable while private goods are rivalrous and excludable
Private Goods
Public Goods
Consumers
Each decides for himself
Everyone is required to consume the same amount
Market
Capable of achieving a Pareto efficient allocation of private goods
Uncapable of achieving a Pareto efficient allocation of public goods
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30. XI. Why do people Free Ride?
How to get to the Pareto efficient outcomes of public goods?
w1, w2 - each person’s initial wealth
x1,,x2 - each person’s money left for private consumption
g1, g2 - each person’s contribution to the public good
u1 ,u2 - each person’s utility function
For simplicity c(G)=G (and thus MC=1)
Each person:
cares about the total amount of the public good provided
will make the optimal choice given the other person’s choice Nash equilibrium model.
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31. XI. Why do people Free Ride?
Nash equilibrium:
Part of Game Theory = general analysis of strategic interaction.
A’s optimal choice will depend on what he thinks B will decide == there is not a dominant strategy equilibrium.
dominant strategy - when there is one optimal choice of strategy for each player no matter what the other player does  equilibrium outcome of the game.
Nash equilibrium: if A’s choice is optimal, given B’s choice, and B’s choice is optimal given A’s choice.
When the other person’s choice is revealed, neither individuals wants to change his behaviour.
Player A
Player B
1,2
0,0
Option 2
2,1
Option 1
Option b
Option a
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32. XI. Why do people Free Ride?
How to get to the Pareto efficient outcomes of public goods?
If both people purchase both gods:
It is a Nash equilibrium model
The solution is just like an ordinary consumer maximization problem: the marginal rate of substitution between the public and the private goods (they purchase) should be 1 for each consumer.
BUT: Person 2 might decide that the amount already contributed by person 1 is sufficient and it would be unnecessary for him to contribute towards that public good. FREE RIDER PROBLEM – person 1 contributes while person 2 free-rides.
Optimization conditions
- guess about the other’s person contribution
x1,,x2 - each person’s money left for private consumption
g1, g2 - each person’s contribution to the public good
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33. X. Why do people Free Ride?
Free rider behaviour is the reluctance of individuals to contribute voluntary to the support of public goods.
People can only free-ride nonexcludable goods.
Examples: vaccination; family; etc.
Agent 1
Agent 2
Budget line of agent 2 without the contribution of 1
Budget line of agent 2 with the contribution of 1
Public good
Public good
G=g1
Private good
Private good x1 x2
He can’t consume more than x2 (no money), BUT he can consume G (without paying)
Any other point of this budget line has lower utility levels
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34. X. Why do people Free Ride?
Free rider behaviour vs the other also contributes
Agent 1
Agent 2
Public good
Public good
g2=DG
G=g1+g2
G=g1 x1
Private good
Dx2
Private good
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35. XI. Why do people Free Ride?
Numerical Example with a single-level good (TV):
Suppose that each person has a wealth of €500, each person values the TV at €100 and that the cost of the TV is €150.
Since the sum of the reservation prices is higher than the cost ( >150), it is Pareto Efficient to buy the TV.
Each roommate will decide separately whether to buy or not the TV. If player A buys the TV, he gets the benefit of 100€ and pays a cost of 150€, having the net benefit of -50€. In that situation, player B watches TV for free, having a net benefit of 100€.
Player A
Player B
0,0
100,-50
Doesn’t buy
-50,100
-50,-50
Buy
Microeconomics – Public Goods
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36. XI. Why do people Free Ride?
Strategy of Player B:
If player A buys the TV it is in player’s B best interest to free ride (100 > -50)
Player A
Player B
0,0
100,-50
Doesn’t buy
-50,100
-50,-50
Buy
If player A decides not to buy the TV, then it is in player’s B best interest not to buy the TV either
(0 > -50)
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37. XI. Why do people Free Ride?
The dominant strategy equilibrium for this game is for neither player to buy the TV.
Player A
Player B
0,0
100,-50
Doesn’t buy
-50,100
-50,-50
Buy
Dominant Strategy of Player B
Dominant Strategy of Player A
Dominant Strategy Equilibrium
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38. XI. Why do people Free Ride?
Comparison between free riding and prisoner's dilemma.
In both games the DSE doesn’t not correspond to the strategy that maximizes the sum of utilities.
Free riding:
Player A
Player B
0,0
100,-50
Doesn’t buy
-50,100
-50,-50
Buy
The strategy that maximizes the sum of the utilities is just one of the players to buy the TV (and both players to watch it).
Player A
Player B
-1,-1
-6, 0
Deny
0, -6
-3,-3
Confess
Prisoner’s dilemma:
The strategy that maximizes the sum of the players’ utilities is for each player to make the same choice.
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39. XI. Why do people Free Ride?
Strategy that maximizes the sum of the utilities:
Just one of the players buys the TV (and both players watch it).
Free ride may be optimal from an individual point of view, but it is Pareto inefficient from the viewpoint of the society as a whole.
Pareto improvement:
The other player makes a side payment.
Pareto improvement for this example:
Any payment between 50 and 100.
Player A
Player B
0,0
100,-50
Doesn’t buy
-50,100
-50,-50
Buy
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40. XI. Why do people Free Ride?
The maximization of one’s utility given the other’s expected behaviour is obtained by free riding.
What is the consequence?
The provision of a public good by anyone will tend to reduce the provision by the other person  too little of the public good supplied in a voluntary equilibrium, relative to an efficient provision of the public good.
What is the solution?
It is in interest of all to agree to be coerced to pay taxes for Government to provide Public Goods.
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41. XII. How is Public Choice Made?
Envolved actors: individuals, representatives and administrative agencies.
Elected
representatives
Economic Fluxes
Individual
Income Fluxes
Utility Fluxes
Free Rider
Behaviour
Taxes
Public Budget
Political Fluxes
Administrative
agencies
Private Goods
Public Goods
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42. XII. How is Public Choice Made?
Economic Fluxes
Political Fluxes
How much taxes?
How much public goods? or
Social Choice
What for?
What kind of public goods? or
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43. XI. What is the difference between Private vs Public Goods?
Public goods are nonrivalrous and nonexcludable while private goods are rivalrous and excludable
Private Goods
Public Goods
Consumers
Each decides for himself
Everyone is required to consume the same amount
Market
Capable of achieving a Pareto efficient allocation of private goods
Uncapable of achieving a Pareto efficient allocation of public goods
Decision Maker
Knows their own decisions (rational consumer)
Has to ascertain the preferences of those on whose behalf he is making the decision: social choice (ex.: command mechanism, voting system)
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44. Demand Revelation Voting Market or Auction Process
Predetermined Amount
Clark Tax
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45. XIII. Is voting a good social choice mechanism?
The Paradox of Cyclical Voting
Voting on 3 different expenditures:
Depending on the order of voted pairs of options, the outcome is different.
Social preferences are not transitive
Manuel Aipo
João Couve
Zé Cebola
First
Military
Research
Charity
Second
Third
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46. XIII. Is voting a good social choice mechanism?
How to avoid the “paradox of cyclical voting”?
Individual preferences must be single-peaked!
Example of multi-peaked preferences: school
single-peaked preferences
multi-peaked preferences
Net utility
Expenditure
Net utility
Expenditure
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47. XIII. Is voting a good social choice mechanism?
Example of single-peaked preferences
Median Voting Theorem: Whenever alternatives can be classified according to the proximity to the ideal choice for each voter, the majority selection will always coincide with the median voter preferred alternative.
It does not say anything about how much more people want or do not want of expenditure – it does not lead to an efficient outcome.
% of GNP
Manuel Aipo
João Couve
Zé Cebola
Military
50% 6%
10%
% GNP 60 40 20 11 8 5
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48. XIII. Is voting a good social choice mechanism?
Is voting a good social mechanism?
There are problems of cyclical voting
This can be avoided if preferences are single peaked
Single peaked preferences will lead to median outcomes
This will not in general lead to an efficient outcome
People may have an incentive to vote differently than their true preferences (lie on demand revelation) in order to manipulate the final outcome.
What about you? (Exam weight on the final mark)
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49. XIV. Why do people lie in Demand Revelation?
Market or auction processes:
For simplicity consider quasi-linear preferences - there is an unique optimal amount of the public good.
Each person is asked how much they value the public good knowing that their share of the cost will be proportional to their stated value.
It is efficient to provide the public good if the sum of the value that everybody places on the public good is larger that its cost.
Why do people lie in Market or auction processes?
As the declaration on how much a person values the good affects how much she/he has to pay, there is a natural incentive to shade the true value.
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50. XIV. Why do people lie in Demand Revelation?
Paying a fixed pre-determined amount
A pre-determined amount ci paid by everybody
Why do people lie in fixed pre-determined paying processes?
As the declaration on how much a person values the good does not affect how much she/he has to pay, there is a natural incentive to exaggerate the statements of the true value.
Why do people lie in Demand Revelation?
People lie because there is no COST for deviating from the truth.
ni - each person’s net value of the public good
vi - each person’s value of the public good
ci - each person’s pre-determined contribution
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51. XIII. Why do people lie in Demand Revelation?
Summary of Demand Revelation
Option
Conditions
Problem
Solution
Voting
Single peaked preferences to avoid cyclical voting.
Doesn’t lead to an efficient outcome.
Economic valuation of the different hypotheses.
Market or auction
Each person says how much and then pays proportionally.
Natural incentive to shade true value.
Everybody pays the same.
Pre-Determined Amount
Everybody pays the same. Revelation of the net value
Natural incentive to exaggerate – pivotal behaviour.
To tax the pivotal behaviour.
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52. XV. How to enforce true Demand Revelation?
Procedures that provide the right incentives to tell the truth about the value of a public good
200 men
1 ship
Several year’s wages in their own personal strongbox
Bad weather
All the coins are mixed together…
The Captain has to decide…
How can the coins be returned to their owners?
Reference: Typhoon, Joseph Conrad
The Captain
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53. XV. How to enforce true Demand Revelation?
Procedures that provide the right incentives to tell the truth about the value of a public good
Pivotal Agents – those who change the social choice
When the social decision is changed by the pivotal agent j, the total harm imposed to the other agents is:
In order to give person j the right incentives to decide whether or not to be pivotal, the social costs will be imposed on him: Grooves-Clarke tax
ni - each person’s net value of the public good
Hj - total harm imposed by pivotal agent j
Microeconomics – Public Goods
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54. XV. How to enforce true Demand Revelation?
Clark tax
Assign a cost to each agent, ci, which the individual will have to pay if it is decided that the public good will be provided;
Have each agent state a net value si (this may or may not be his true net value ni)
If the sum of the stated net values is positive, the public good will be provided. If it is negative, it won’t be.
Each pivotal agent will be required to pay a tax to the state. If person j changes the decision from provision to no provision (or vice versa), he will pay the tax.
si - each person’s stated net value of the public good
Hj - tax imposed by pivotal agent j
Microeconomics – Public Goods
7th of November 2003

55. XV. How to enforce true Demand Revelation?
Clark tax ci s1 s2 s3 s4 s5
Pivotal agent
Clark Tax=Hj
Person 1 2 3 4 5 c v 6
-14 s
-12
Tax 10
si - each person’s stated net value of the public good
Hj - tax imposed by pivotal agent j
ci - cost share paid by each person
vi - each person’s stated value of the public good
Microeconomics – Public Goods
7th of November 2003

56. XV. How to enforce true Demand Revelation?
Problems with the Clark Tax:
Only works with quasi-linear preferences because the amount to be paid c can’t influence individual demand for the public good.
Does not generate a Pareto efficient outcome
There is an optimal level of the outcome but private consumption is reduced by the tax.
The collected tax cannot go to anybody involved in the decision process, since that might affect their decisions.
However the tax collection is expected to be small because of small probability of having pivotal agents.
Microeconomics – Public Goods
7th of November 2003

57. XV. How to enforce true Demand Revelation?
Equity and efficiency trade off in the Clark Tax
The Pareto efficient amount of the Public good will be provided.
Since the payment scheme must be fixed in advance there will be situations where some people will be made worse off by providing the public good.
There is some payment scheme for which everyone is better off having the public good provided than not having it – it does not mean that for an arbitrary payment scheme everyone will be better off.
The tax ensures that if everyone would be better off having the good provided, then it will be provided. But that doesn’t imply that everyone will actually be better off.
How to enforce true Demand Revelation?
If the preferences are quasi-linear a Clark Tax can be imposed.
Microeconomics – Public Goods
7th of November 2003

58. XVI. Summary What are Public Goods?
Public goods are nonrivalrous and nonexcludable goods for which everyone must “consume” the same amount even if people value them differently.
Why to provide a Public Good?
Because there is a potential for increasing utility.
When to provide a Public Good?
If a public good is to be provided in some fixed amount or not provided at all, then a sufficient condition for provision to be Pareto efficient is that the sum of the willingness to pay exceeds the sum of the necessary contribution (cost of the public good).
Which level of Public Good to provide?
If a public good can be provided in a variable amount, then the necessary condition for a given amount to be Pareto efficient is that the sum of the marginal willingness's to pay should equal the marginal cost. The sum of the marginal willingness's to pay equals aggregated demand.
The efficient level will be the level where marginal cost of production equals aggregate demand.
Microeconomics – Public Goods
7th of November 2003

59. XV. Summary
In what conditions is the right level of public good unique?
In general it is not: the optimal amount of Public Good will be different at different wealth allocations. It is not possible to separate efficiency considerations in the supply of public good from distributional considerations.
In the case of quasilinear preferences there is an unique right level.
Should provision of Public Goods be private or public?
It should not be private because of free rider behaviour. If there is a private provision of Public Goods it will be insufficient.
A public provision has costs associated with it due to the tax scheme imposed to raise the revenues.
Should provision of Nonrivalrous Goods be private?
It depends. If Nonrilavarous Goods are private provided there will be a deadweight loss due to underutilization but if public provided there will be costs associated with raising the revenue to pay it.
Should provision of Nonexcludable Goods be private?
It depends. The gain associated with the elimination of transaction costs has to be compared with the loss due to excessive consumption and the loss created by the taxes needed to provide the good.
When should Private Goods be Publicly Provided?
When there are large transaction costs - quasi-nonexcludable goods
When distributive considerations are important, ex: education
Microeconomics – Public Goods
7th of November 2003

60. XV. Summary How should Private Goods be Publicly Provided?
They should be provided through rationing systems
Why do people free ride?
Because the maximization of one’s utility given the other’s expected behaviour is obtained by free riding.
What is the consequence of free riding behaviour?
The provision of a public good by anyone will tend to reduce the provision by the other person  too little of the public good supplied in a voluntary equilibrium, relative to an efficient provision of the public good.
What is the solution to free riding behaviour?
It is in interest of all to agree to be coerced to pay taxes for Government to provide Public Goods.
Microeconomics – Public Goods
7th of November 2003

61. XV. Summary What is the best way to demand revelation?
The process for demand revelation should lead to an efficient outcome and should have the right incentives for people not to understate or overstate their values (avoiding pivotal behaviour). The Clark Tax is a possible solution but not the optimal one since it leads to reduction in incomes and only works with quasi-linear preferences.
Microeconomics – Public Goods
7th of November 2003