Q.1. (15 points) Use the 2-period extraction model demonstrating the Hotellings Rule (Anderson chapter 14), to derive mathematically and explain graphically (like figure 14.6) what will be economic rents in each period under the following scenarios. Suppose the initial market price of the resource is $30 and the marginal extraction cost in all periods is $10 and the resource can be extracted for 3 consecutive periods.

a. Interest rate is 5 percent.

b. Interest rate decreases from 5 percent to 2 percent (everything else remains same).

c. Marginal extraction cost increases in period 2 to $15 and remains constant in period 3. Interest rate is 5%.

Show your work in details. All work should be typed and not handwritten.