Question

In: Economics

IV. Public Goods Consider an economy with 3 types of individuals, who differ only in their...

IV. Public Goods

Consider an economy with 3 types of individuals, who differ only in their preferences for a public good (monuments, or M). Individuals of type I get a fixed benefit of 100 from the existence of monuments, whatever their number. Individuals of type II get marginal benefits of MBII=30-3M, and individuals of type III get marginal benefits of MBIII=90-9M. There are 50 people of each type.

1. What is the marginal benefit of group I, i.e., MBI ? (Hint: type I individuals get a fixed benefit, regardless of the number of monuments).

2. What is the social marginal benefit function for this public good? (Hint: note the number of individuals of each type)

3. If each monument costs $3600 to build, how many monuments should be built?

Solutions

Expert Solution

1) in short, marginal benefit in this case is defined as the benefits derived from providing one more monuments. And because individuals in group I gets a fixed benefit from the monuments regardless of their number, individuals in group I gets a fixed benefit of 100 if there were 2/3/or any number of monuments.

Thus, MB​​​​​I of one more monument= 0

2) Social Marginal Benefit (SMB) = MB​​​​​I + MB​​II+MB​​​​​III = 50x0 + 50(30-3M) + 50(90-9M) = 1500- 150M + 4500-450M = 300M+6000 = 300(M+20)

3) equating SMB to the cost of monuments,

300M + 6000 = 3600M

3300M = 6000

M = 60/33 = 2 approximately


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