Question

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 10 units. assume that the inverse demand for the resource in each period is given by: p1 = 70 - 5q1 p2 = 70 - 5q2 moreover, assume that the marginal extraction cost is constant in both periods at $5 and that the social discount rate is 8% (i.e., r=0.08). if the social discount rate is increased to 12% (i.e., r=0.12), then how much more of the resource would be consumed in the first period? (hint: solve for the efficient allocation of the resource in first period q1 at r=0.08 and again at r=0.12. the difference between these two values is your answer.) please round your intermediary calculations (e.g., prices and quantities) and your final answer to two decimal places if necessary.

A) 1.50 units
B) 2.00 units
C) 2.50 units
D) 3.00 units

Answer 1

After calculating the efficient allocation of the resource in the first period at both social discount rates, it is determined that the increase in social discount rate from 8% to 12% does not result in any additional units consumed in the first period. Regardless of the social discount rate, all 10 units are consumed in the first period due to the limited supply.

Step-by-step explanation:

To calculate the efficient allocation of the resource in the first period at both social discount rates (r=0.08 and r=0.12), we must first determine the price in each period that equates marginal extraction cost (MEC) to the marginal user cost (MUC) and then apply the inverse demand functions provided. The marginal extraction cost is constant at $5 for both periods.

For r=0.08: MUC1 = MEC/(1+r) = $5/1.08 = $4.63 approximately. Using the inverse demand function p1 = 70 - 5q1, we solve for q1 by setting the price equal to MEC plus MUC1, giving q1 = (70 - MEC - MUC1) / 5 = (70 - $5 - $4.63) / 5 = 12.07 which we can approximate to 12 units, but since there's only 10 units total, we consume all in the first period.

When r is increased to 0.12, MUC1 becomes MEC/(1+r) = $5/1.12 = $4.46 approximately. Using the inverse demand function again and the new MUC1, q1 = (70 - $5 - $4.46) / 5 = 12.11, which we again approximate to 12 units due to the fixed supply of 10 units, so still all is consumed in period 1. Therefore, there is no increase in consumption in the first period with the rate change; the answer is 0 units.

However, if we are to calculate the difference nontrivially (ignoring the limit of 10 units total), we would find that there would theoretically be an increase, however since we consume all 10 units at both rates, in practical application, this difference would not exist. If we disregard the resource limit, the consumption increase would be q1 (at r=0.12) minus q1 (at r=0.08), but both allocations are 12 when rounding to two decimal places, yielding a difference of 0.