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.

We Play a Game

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

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

1 pt. for each contribution made by anyone. + 3 pts. for each round you don’t contribute.

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

Payoffs = 1 pt. for each contribution by anyone; 10 pts. for each round you don’.

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

Contribute 1 7 13 19 25Don’t 5 11 17 23 29

Assume n = 25

We Play a Game

Payoff: 1 pt. for each contribution made by anyone. + 10 pts. for each round you don’t contribute.

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

Payoffs = 1 pt. for each contribution by anyone; 10 pts. for each round you don’.

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

Contribute 1 7 13 19 25Don’t 5 11 17 23 29

Assume n = 25

We Play a Game

Payoff: 1 pt. for each contribution made by anyone. + 10 pts. for each round you don’t contribute.

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

We Play a Game

Public Goods Games

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”

Tragedy of the Commons

If property rights are well defined, there will be no problem with externalities. Hence, if property rights are not well defined, we can expect economic interactions to give rise to inefficiencies. This is especially so in the case of a common property resource:

•  Clean air• Clean water• Biodiversity• Antarctica

 

Externalities can arise when

resources are used without payment.

Tragedy of the Commons

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 lake. There are Y fish in the lake.

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

 

c1 = (Y – c2)/2  

 

c1

c2

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

2 – ½c1c2

FOC: ½Y – c1 – ½c2 = 0

c1 = (Y – c2)/2

Tragedy of the Commons

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

• 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 – ½c1c2

FOC: ½Y – c1 – ½c2 = 0

c1 = (Y – c2)/2

Tragedy of the Commons

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

• 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/4 Y/3 c1

c2

Y/3Y/4 c2 = (Y – c1)/2

Tragedy of the Commons

NE: c1 = c2 = Y/3

Social Optimum: c1 = c2 = Y/4

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

• 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/4 Y/3 c1

c2

Y/3Y/4 c2 = (Y – c1)/2

Tragedy of the Commons

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 lake, 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

C = 3 in the springD = 4 “ “

Tragedy of the Commons

If there are 12 fish in the lake, 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

Tragedy of the Commons

If there are 12 fish in the lake, 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?

Tragedy of the Commons

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 subject to free-riding and thus 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.