economic question

ECO 412: HW 1

Sean Fahle State University of New York at Buffalo

Spring 2016

Due date: Friday, February 19, 2016, at the beginning of class.

You are free to collaborate with your classmates on this assignment and are encouraged to do so. However, all students must individually write up and submit their own assignment. Late assignments may receive no credit.

1. Suppose the state is trying to decide how many miles of a very scenic river it should preserve. There are 1000 people in the community, each of whom has an identical demand function given by

Q = 40 − 0.4P

where Q is the number of miles preserved and P is the per-mile price he or she is willing to pay for Q miles of preserved river. (Hint: You will need to derive the market (aggregate) demand curve for a public good.)

(a) If the marginal cost of preservation is $25, 000 per mile per year, how many miles would be preserved in an efficient allocation?

(b) How large are the annual net benefits?

(c) What if substitute sites were available to the members of the community such that their demands were substantially more elastic? Suppose their individual demand functions for river preservation are:

Q = 40 − 1.2P

If the marginal cost of preservation is $25, 000 per mile per year, how many miles of the river would be preserved in an efficient allocation?

2. Suppose that the inverse demand for a depletable resource is

P = 8 − 0.4Q

and the marginal cost of extraction is $2. There are 20 units to be allocated between two periods. We covered this example in class with a discount rate of 0.10. Answer the following questions:

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In your answers, provide explicit calculations of dynamically efficient quantities, prices, and scarcity rent. Briefly provide an intuition for your results. Your answers should also include the graph from class in which the left axis represented the marginal value of extraction in period 1 and the right axis represented the (present value of the) marginal value of extraction in period 2. In each case, show how the proposed change to the model affects the graph.

(a) Relative to the example in class, how does the solution change if the discount rate is 0? How does it change if the discount rate is 0.20? What is the efficient allocation and price in the two periods? What is the marginal user cost (MUC) in each period?

(b) Relative to the example in class, what happens if the marginal cost of extraction rises to $4 in both periods? How much should be produced in each period? What is the MUC? Give an intuition for your result.

(c) Relative to the example in class, suppose the marginal cost were to decrease in the second period from $2 to $1. It remains $2 in the first period. Would more or less output be allocated to the second period in this model relative to the one we covered in class? Would the MUC be higher or lower? Why?

(d) Relative to the example in class, suppose that in the second period the demand curve shifted right due to population growth. The new inverse demand curve in period two is:

P = 10 − 0.4Q

What is the effect on the efficient allocation across periods? What is the effect on the present value of the MUC? Explain.

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