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Question: The following questions ask you how the solution we obtained inclass changes as we vary the para...

The following questions ask you how the solution we obtained in
class changes as we vary the parameters of the problem. In each
case, calculate the efficient quantities, prices, and scarcity
rents for both time periods. In your answers, include the figure
above and show how it changes as the parameters of the problem
vary.

(a) How does the solution change if the discount rate is 0? How
does it change if the discount rate is 0.20?

(b) How does the solution change if the marginal cost of
extraction rises to $4 in both periods?

(c) How does the solution change if the marginal cost of
extraction were to decrease in the second period from $2 to $1?
Marginal cost in the first period in unchanged.

(d) How does the solution change if, in the second period, the
demand curve shifted right due to population growth? The new
inverse demand curve in period two is:

P2 = 10 − 0.4Q2

Demand in the first period is unchanged.

Show transcribed image text 1. Suppose that the inverse demand for a depletable (non-renewable) resource is 0.4Q There are 20 units to be allocated between two time periods, t 1, 2. Qu is the number of units of the resource extracted and consumed in period t. P is the per-unit price of the resource in period t. We covered this example in class with a discount rate of 0.10 and a marginal cost of extraction of $2. There it was shown how to compute the dynamically) efficient rate of extraction of the resource, the price, and the scarcity rent in each period The solution was: 5 W 3 3 UU Z 2 1 10 15 20 15 10 MUC2 MUC 0.1 10.238 9.762 3.905 4.095 1.905 2.095

1. Suppose that the inverse demand for a depletable (non-renewable) resource is 0.4Q There are 20 units to be allocated between two time periods, t 1, 2. Qu is the number of units of the resource extracted and consumed in period t. P is the per-unit price of the resource in period t. We covered this example in class with a discount rate of 0.10 and a marginal cost of extraction of $2. There it was shown how to compute the dynamically) efficient rate of extraction of the resource, the price, and the scarcity rent in each period The solution was: 5 W 3 3 UU Z 2 1 10 15 20 15 10 MUC2 MUC 0.1 10.238 9.762 3.905 4.095 1.905 2.095