1. Consider a simple two period model of production of a depletable resource. Th

Question

1. Consider a simple two period model of production of a depletable resource. The sum of production in each period is equal to the total resource endowment, or O q, +q Assume the marginal cost of extraction in each q2. period is given as c 3 Also, assume a royalty, r, is levied on the sale of the resource in each period. Finally, inverse linear demand given as p a -bg Oy, where y is income. Assume the interest rate, r, is 8%, income in the first period is 500, 1,000, a 65, b -0.1, 0.15, 0 0.02 and r 0.2. a. Solve for qu g, p and p. Assume there is no growth in income from period 1 to period 2.

Explanation / Answer

Equation 1 : 65 - 0.1q1 + 0.15 *500 = 0.02q1 + 0.2

Equation 2 : 65 - 0.1q2 + 0.15 *500 = 0.02q2 + 0.2*1.08

q1 + q2 = 1000

Solving these equations, we will get

p1 = p2 = 90

q1 = q2 = 500

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