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Assume that the inverse demand function for a two period depletable resource is P =24 - 0.2q and the constant marginal cost of supplying it is $6 (a = 24, b = 0.2, c = 6)

a. If 60 units are to be allocated between two periods, how much would be allocated to the first period and how much to the second period in a dynamic efficient allocation when the discount rate is zero?

b. What would be the efficient price in the two periods?

c. What would be the marginal user cost in each period?

d. Assume the discount rate is 5%, how much would be allocated to the first and second period?

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Joshua Stredder
Joshua StredderLv10
28 Sep 2019

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Related questions

Assume that the inverse demand function for a two period depletable resource is P =24 - 0.2q and the constant marginal cost of supplying it is $6 (a = 24, b = 0.2, c = 6)

a. If 60 units are to be allocated between two periods, how much would be allocated to the first period and how much to the second period in a dynamic efficient allocation when the discount rate is zero?

b. What would be the efficient price in the two periods?

c. What would be the marginal user cost in each period?

d. Assume the discount rate is 5%, how much would be allocated to the first and second period?

4. Suppose that South Africa is trying to find the efficient amount of coal to extract, which is a depletable resource. There are two periods and the inverse demand function is P = 15 - 0.5QD and the marginal cost of extraction is 5.

(a.) Use the static efficiency model to find the efficient allocation for the first time period. Also, compute the price of coal at that efficient allocation.

(b.) Now suppose that the total available quantity of coal is Q = 40. Is the static efficiency criteria sufficient? If yes, what is the efficient allocation of coal over the two periods? If no, why not?

(c.) Now suppose that the total available quantity of coal is Q = 35. Is the static efficiency criteria sufficient? If yes, what is the efficient allocation of coal over the two periods? If no, why not?

2. Suppose a demanding schedule is P = 100 - Q and a supply schedule is P = 20 + 2Q. What is the marginal net benefit curve?

MNB = 80 - Q

MNB = 80 - 3Q

MNB = 80 + Q

MNB = 120 - Q

MNB = 120 - 3Q

3. Suppose a demand curve is Q = 100 - P and a supply curve is Q = 0.5P - 25. What is the marginal net benefit curve?

MNB = 75 - 0.5Q

MNB = 125 - 1.5Q

MNB = 125 + 1.5Q

MNB = 50 + 3Q

MNB = 50 - 3Q

5. In a two time-period example, economic efficiency is maximized when ...

The marginal net benefits are maximized in both time periods

The discount rate is set equal to the marginal benefits

The marginal net benefit in the first time period is set equal to the present value of marginal net benefits in the second time period

The marginal net benefits in the first period are set equal to the discount rate in the second time period

The marginal net benefits in the first period are set equal to the user costs in the second time period

6. Assuming economic efficiency is maximized, when will more of a resource tend to be used in the first time period (as compared to future time periods)?

Whenever the discount rate is positive

Whenever the marginal net benefits in the present are positive

Whenever the discount rate is zero

Whenever the user costs are positive in the present

Whenever the marginal net benefits in the future are negative

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