Suppose we allocate a fixed supply of a depletable resource between two periods in a dynamically efficient way. Assume further that the demand function is constant in the two periods and the marginal willingness to pay is given by the formula P = 8 - 0.33q while the marginal cost is constant at $1 per unit. The total supply is 20 units and the discount rate is 1%. What is the marginal user cost during the first period?

Suppose we allocate a fixed supply of a depletable resource between two periods in a dynamically efficient way. Assume further that the demand function is constant in the two periods and the marginal willingness to pay is given by the formula P = 8 - 0.33q while the marginal cost is constant at $1 per unit. The total supply is 20 units and the discount rate is 1%. What is the marginal user cost during the first period?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.10P: Wonopoly and natural resource prices Suppose that a firm is the sole owner of a stock of a natural...

See similar textbooks

Similar questions

Suppose we allocate a fixed supply of a depletable resource between two periods in a dynamically efficient way. Assume further that the demand function is constant in the two periods and the marginal willingness to pay is given by the formula P = 8 - 0.34q while the marginal cost is constant at $2 per unit. The total supply is 20 units and the discount rate is 1%. What is the marginal user cost during the first period?
Suppose the inverse demand function for a depletable resource is linear, P = 25 – 0.4q, and the marginal supply cost is constant at £5.i. If 40 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to period 1 and how much to period 2 when the discount rate is r = 0.15? Show your working ii. What is the marginal user cost in each period? Provide a one-sentence economic interpretation iii. Show in a diagram how the marginal user cost would change if an energy price shock were to raise the marginal cost in period 2 to £10
Consider a nonrenewable resource that can be consumed either today (period 1) or tomorrow (period 2) and has a finite supply of 4 units. Assume the inverse demand for the resource in both periods is: P_1 = 150 - 25Q_1 P_2 = 150 - 25Q_2 Assume the marginal cost of extracting the resource is constant at $50 and the social discount rate is 15 percent (r = .15). What is the efficient level of consumption in period 1? Please report your answer out to at least two digits (e.g., 3.24).
The inverse demand function for a depletable resource is P=8-0.4q and the marginal cost of supplying it is $2 If 20 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to the first period and how much to the second period when the discount rate is 5% and 10% (Hint Demand Function is the same in both periods) Given the discount rate, what would be the efficient price in the two periods? What would be the marginal user cost in each period? Assume a discount rate of 0% determine the efficient allocation amount between the two period Prepare a schedule of the discount rate and the efficient allocation for the two-period and graph the relationship. What can you say about the discount rate and the allocation between the two periods?
Suppose that there is a nonrenewable resource that can be consumed today (period 1) or tomorrow (period 2) and that it has a fixed supply of 2 units. Assume that the inverse demand for the resource in each period is given by: P1 = 25 - 5Q1 P2 = 25 - 5Q2 Moreover, assume that the resource's marginal extraction cost (MEC) is constant in both periods at $5 and that the social discount rate is 10% (i.e., r=0.10). Assuming that the resource is efficiently allocated, what is the consumer surplus in period 1?
The inverse demand function for a depletable resources is P=8-0.4q and the marginal cost of supplying it is $2 If 20 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to the first period and how much to the second period when the discount rate is 5% and 10% (Hint Demand Function is the same in both periods) Given the discount rate what would be the efficient price in the two periods? What would be the marginal user cost in each period? Assume a discount rate of 0% determine the efficient allocation amount between the two period Prepare a schedule of the discount rate and the efficient allocation for the two period and graph the relationship. What can you say about the discount rate and the allocation between the two periods?
Assume that a country is endowed with 8 units of oil reserve. There is no oil substitute available. How long the oil reserves will last ifa) the marginal willingness to pay for oil in each period is given by P=8-0.57q. (b) the marginal cost of extraction ofol s constant at $4 Per unit and c) discount rate is 1%?
What has been the general trend in nonrenewable resource prices in the past several decades? What change has been observed in recent years? Are these trends consistent with Hotelling’s rule? Discuss.
Suppose a depletable natural resource has no substitute. The resource can be extracted from the ground at a constant marginal cost. Furthermore, the marginal willingness to pay exceeds the marginal cost for the initial quantities of the resource, so it is worth extracting at least some of the resource. In a dynamically efficient allocation over many periods, when will most of the resource be extracted (earlier periods or later periods)? Why? At what point will the resource run out? Will the resource run out abruptly or smoothly? Why?
Consider a nonrenewable resource that can be consumed either today (period 1) or tomorrow (period 2) and has a finite supply of 15 units. Assume the inverse demand for the resource in both periods is: P_1 = 100 - 5Q_1 P_2 = 100 - 5Q_2 Assume the marginal cost of extracting the resource is constant at $25 and the social discount rate is 10 percent (r = .10). If the social discount rate is decreased to 5% (r = .05), how much less of the resource would be consumed in the first period, assuming a dynamically efficient allocation? Please report your answer out to at least two digits (e.g., 3.24). Hint: Solve for the efficient allocation of the resource at r = .1 and then at r = .05. The difference in period one consumption is your answer.
Consider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. The constant social marginal cost of extraction is 40 in each period and the total stock of the resource is Q = 300 units. Moreover, the social marginal beneÖt is MB(Qt) = 200 Qt, where Qt is the quantity of resource extracted in period t, for t = 0; 1. The discount factor is 0:8. (c) Suppose that there is a market to trade the resource. What is the equilibrium price corresponding to each period? Justify the answer.
Assume that the oil extraction company needs to extract Q units of oil (a depletable resource) reserve between two periods in a dynamically efficient manner. What should be a maximum amount of Q so that the entire oil reserve is extracted only during the 1st period if (a) the marginal willingness to pay for oil in each period is given by P = 30 - 0.5q, (b) marginal cost of extraction is constant at $3 per unit, and (c) discount rate is 2%?