1. Imagine that there is a public good that will be simultaneously consumed by a

Question

1. Imagine that there is a public good that will be simultaneously consumed by a number of people and that the marginal cost of providing a unit of this public good is $162,000. Each person has the following marginal value schedule for this good: Q MV 1 $20 2 $17 3 $14 4 $11 5 $ 8 6 $ 5 7 $ 2 A. What is the optimal number of units to provide if the population is 10,000? B. What is the optimal number of units to provide if the population is 20,000? C. In general, how does the optimal provision of a public good change as the population increases? Why? D. What will be the optimal numbers in parts A and B if the marginal cost is cut in half?

Explanation / Answer

What is the optimal number of units to provide if the population is 10,000?

It is optimal to provide till Marginal value > Marginal cost

So, for each person , it is optimal to provide 2 units

Hence for 10,000 , it is optimal to provide 20,000 units

B. What is the optimal number of units to provide if the population is 20,000?

If the population is 20,000 then optimal provision = 2*20,000 = 40,000 Units

C. In general, how does the optimal provision of a public good change as the population increases? Why?

Because, since the public good is non excludable, so as population increases, the optimal provision should alsoo increase

D. What will be the optimal numbers in parts A and B if the marginal cost is cut in half?

If MC gets half then in A , Optimal Provision = 5*1000 = 5,000 units

and in B, 5*2,000 = 10,000 units

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