UNIT IV: GAMES & INFORMATION

UNIT IV: GAMES & INFORMATION

• Decision under Uncertainty• Externalities and Public Goods• Review• FINAL: 8/2

7/28

Markets Imperfections

• Monopoly and Market Power• Duopoly and Imperfect Information• Asymmetric Information• Externalities• Public Goods

Externalities

Externalities are the effects of consumption and production that are not accounted for in the market (e.g., steel industry creating air pollution).

When externalities are present, the price of a good may not reflect its true social cost. As a result, firms may produce too much (or too little) and the market outcome may be inefficient.

Remedies include government regulations, taxes, legal recourse, and bargaining among those affected., and bargaining among those affected.

Externalities

Consider a farmer and a rancher that produce on neighboring land. The rancher’s cattle stray onto the farmer’s land, causing damage to his crops.

Number in Herd Annual Crop Loss Crop Loss per Add/l

(Steer) (Tons) Steer (Tons)

1 1 1

2 3 2

3 6 3

4 10 4

Marginal Social Cost

Externalities

Consider a farmer and a rancher that produce on neighboring land. The rancher’s cattle stray onto the farmer’s land, causing damage to his crops.

Should the rancher be prohibited from grazing his cows to prevent damage to the farmer’s crops?

Coase noted that while this prohibition would remove the cost to the farmer, it would also impose a cost on the rancher (and on society). He called this the reciprocal nature of the externality.

Externalities

We know that in a market equilibrium, both consumers (MRS = Px/Py) and firms (MR = MC) are optimizing, and we used these conditions to derive Demand and Supply curves.

that burning gasoline causes pollution which is harmful to peoples health, and that this harm is measured to be $1 for each gallon gasoline burned. What is the optimal level of gasoline consumption, taking this externality into account?

P

P*

Q* Q

QD = MSB

QS = MSC

The supply curve accounts for the total social cost of production; the demand curve

Externalities

In the presence of a negative production externality (e.g. pollution), the marginal social cost (MSC) is higher than the marginal cost of production (MC).

MSC PP = 4 - 1/3QD

MSB = (4 - 1/3QD) - 1

Suppose that burning gasoline causes pollution which is harmful to peoples health, and that this harm is measured to be $1 for each gallon gasoline burned. What is the optimal level of gasoline consumption, taking this externality into account?

P

P1

Q* Q1 Q

QD = MSB

QS = MC

MSC The industry’s competitive output (Q1) is greater than the efficient output (Q*), where MSC = MSB.

Price does not reflect the externality.

Remedies

There are several ways to remedy, or internalize an externality:

MSC PP = 4 - 1/3QD

MSB = (4 - 1/3QD) - 1


P

P1

Q* Q1 Q

QD = MSB

Impose a tax (emissions fee) on producers equal to the cost of the externality, so that their cost fully reflects the true social cost.

MSC = MC + Tax

MSC

Tax

Remedies


MSC PP = 4 - 1/3QD

MSB = (4 - 1/3QD) - 1


P

P1

Q* Q1 Q

QD = MSB

QS = MC

A tax on consumers would also achieve the efficient level of output, Q*.

MSCTax

Remedies


MSC PP = 4 - 1/3QD

MSB = (4 - 1/3QD) - 1


P

Q* Q1 Q

QD = MSB

QS = MC

So would a price ceiling …

MSC

Remedies


MSC PP = 4 - 1/3QD

MSB = (4 - 1/3QD) - 1


P

Q* Q1 Q

QD = MSB

QS = MC

Or a maximum output, or emissions standard.

MSC

Remedies

In each case, the efficient level of output is achieved.But producer surplus (profits), consumer surplus, and government revenue may change:

MSC PP = 4 - 1/3QD

MSB = (4 - 1/3QD) - 1


P

Q* Q1 Q

QD = MSB

QS = MC

MSC

A

C

B

A = Consumer surplus

B = ???

C = Producer surplus

Remedies

Emissions Fees v. Emissions Standards

Comparing the costs and benefits of different regulatory schemes can be very difficult, because policy makers need to know the cost each firm faces in reducing its emissions.

Fees work best when the goal is to minimize cost per unit of abatement. “Get the biggest bang for the buck.” With incomplete information, there is less certainty about emissions levels but more about abatement costs.

The preferable policy, therefore, will depend upon the nature of uncertainty and the shapes of the cost curves.

Coase Theorem

Consider a pair of roommates, one a smoker and the other a non-smoker. Smoke is a good for the first and a “bad” for the second.

If there are well-established “property rights,” (e.g., smoker’s right to smoke, non-smoker’s right to enjoy clean air), the 2 can bargain over the outcome and both end up better off as a result. The non-smoker, for example, could pay the smoker to smoke less, or the smoker could pay the non-smoker to compensate for her smoking.

Coase Theorem: If bargaining costs are zero, the 2 will reach an efficient outcome independent of the structure of property rights.

Externalities: Summary

“In the presence of an externality, there is a unique efficient level of production, but there is no unique efficient price.”

As a practical matter, measuring the effect of an externality is difficult, and scientific evidence is not always clear cut.

An alternative, with lower informational requirements, would be to allow those affected to bargain over the outcome (e.g., tradable property rights).

Common Resource Problems

Externalities can arise when resources are used without payment. This can arise in cases of common property resources:

• Clean air• Clean water• Biodiversity• Antarctica


Two fishermen fish from a single lake. Each year, there are a fixed number of fish in the lake and two periods during the year that they can be harvested, spring and fall. Each fisherman consumes all the fish he catches each period, and their identical preferences are described by the following consumption function:

Ui = CsCf

where Cs = spring catch; Cf = fall catch.

Each spring, each fisherman decides how many fish to remove from the lake. In the fall, the remaining fish are equally divided between the two.

Consider two fishermen deciding how many fish to remove from a commonly owned pond. There are Y fish in the pond.

• Period 1 each fishery chooses to consume (c1, c2).• Period 2 remaining fish are equally divided ½[Y – (c1+c2)].

c1 = (Y – c2)/2

Y/3 c1

c2

Y/3c2 = (Y – c1)/2

U1 = c1(½[Y - (c1+ c2 )]) = ½Yc1 - ½c1

2 - ½c2c1

FOC: ½Y - c1 - ½c2 = 0 = ½Yc1 – ½c1

2 – ½c1c2

FOC: ½Y – c1 – ½c2 = 0

c1 = (Y- c2)/2



• Period 1 each fishery chooses to consume (c1, c2).• Period 2 remaining fish are equally divided (Y – (c1+c2))/2).

c1 = (Y – c2)/2

Y/4Y/3 c1

c2

Y/3Y/4 c2 = (Y – c1)/2

NE: c1 = c2 = Y/3

Social Optimum: c1 = c2 = Y/4



• Period 1 each fishery chooses to consume (c1, c2).• Period 2 remaining fish are equally divided (Y – (c1+c2))/2).

c1 = (Y – c2)/2

Y/4Y/3 c1

c2

Y/3Y/4 c2 = (Y – c1)/2

If there are 12 fish in the pond, each will consume (Y/3) 4 in the spring and 2 in the fall in a NE. Both would be better off consuming (Y/4) 3 in the fall, leaving 3 for each in the spring.


If there are 12 fish in the pond, each will consume (Y/3) 4 in the spring and 2 in the fall in a NE. Both would be better off consuming (Y/4) 3 in the fall, leaving 3 for each in the spring.

C 9, 9 7.5,10

D 10,7.5 8, 8

C D

A Prisoner’s Dilemma

What would happen if the game were

repeated?


C = 3 in the springD = 4 “ “

Imagine the fisherman make the following deal: Each will Cooperate (consume only 3) in the spring as long as the other does likewise; as soon as one Defects, the other will Defect for ever, i.e., they adopt trigger strategies.

This deal will be stable if the threat of future punishment makes both unwilling to Defect, i.e., if the one period gain from Defect is not greater than the discounted future loss due to the punishment:

(T – R) < (R/(1-) – P/(1-))


Public Goods

Public goods are extreme cases of externalities, where all consumers can enjoy the good even if they don’t pay for it. A pure public good, such as national defense, exhibits both

Public goods are often undersupplied (or not supplied) by the market, and the government must step in.

nonrivalry: the consumption of the good by one individual does not inhibit another’s enjoyment of the good; and

nonexcludability: it is impossible to prevent an individual from enjoying the benefits of the good even if she has contributed nothing to its provision.

Public Goods

Public goods are extreme cases of externalities, where all consumers can enjoy the good even if they don’t pay for it.

qme = qyou = QS

Because public goods are nonrival in consumption, it is always efficient to increase the number of people who consume a public good. Any pricing scheme that excludes some individuals from the consumption of a public goods is necessarily inefficient.

nonrivalry: the consumption of the good by oneMarket Failure

Public Goods

Public goods are extreme cases of externalities, where all consumers can enjoy the good even if they don’t pay for it.

q1 = q2 = QS

When we looked at efficiency of competitive markets, we assumed only private goods:

Private goods: MRT = MRSPublic goods: MRT = MRS1 + MRS2

nonrivalry: the consumption of the good by one

Public Goods

Demand for a public good is the vertical sum of individual demand curves.

q1 = q2 = QS

When we looked at efficiency of competitive markets, we assumed private good:

Private good: MRT = MRSPublic goods: MRT = MRS1 + MRS2

nonrivalry: the consumption of the good by one

$

Q* Q

MSC

D = MSB

d1

d2

The efficient provision of a public good occurs where:

MSB = MSC.

Public Good Game

At each round of the game, you will have the chance to contribute to a public good (e.g., clean air; national defense).

The game is repeated for several rounds, and payoffs are calculated as follows:

1 pt. for each contribution made + 4 pts. for each round you don’t contribute.

See Holt and Laury, JEP 1997: 209-215.

Payoffs 1 pt. for each contribution made. + 4 pts. for each round you don’t contribute.

You play: Contribution Rate (n-1)0% 25 … 50 … 75 100%

Contribute 1 4 7 10 13Don’t 4 7 10 13 16

Assume n = 13

N-person Prisoner’s Dilemma: Don’t Contribute is a dominant strategy. But if none contribute, the outcome is inefficient.

Public Good Game

N-person Prisoner’s Dilemma: Don’t Contribute is a dominant strategy. But if none contribute, the outcome is inefficient.

Public Good Game

Typically, contribution rates:

• 40-60% in one-shot games & first round of repeated games

• <30% on announced final round• Decease with group size• Increase with “learning”

Public Goods: Summary

• Public goods are extreme cases of externalities, where all consumers can enjoy the good even if they don’t pay for it. A pure public good, such as national defense, exhibits both nonrivalry and nonexcludability.

• Public goods are often undersupplied (or not supplied) by the market, and the government may be needed to step in.

• Experiments show that people do contribute to the provision of public goods, even when “rationally” they should not.

Markets Imperfections

• Monopoly and Market Power• Duopoly and Imperfect Information• Asymmetric Information• Externalities• Public Goods

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8/2 FINAL EXAM

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UNIT IV: GAMES & INFORMATION