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Consider a non-renewable resource. There are two periods, now and later. The demand curve in each period (t = 1, 2) is Qt = 10 - Pt. The stock of the resource is 10 units. Extraction costs are approximately zero. The interest rate is 4 percent.
(a) A market equilibrium requires identifying price and quantity at all times. What are the four variables for which we need to find numerical values to find the equilibria?
(b) To find these four unknowns, we need four equations. These equations are (i) the two demand curves, (ii) the Hotelling price path, and (iii) a summing-up condition that says that the quantity used in both periods sums to the stock. Write down those four equations.
(c) Solve the four equations by substitution to find the equilibrium quantity harvested in each period and the equilibrium market price in each price. What is the solution (round your answers to two decimal places).
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TC = 1q^3 - 40q^2 + 840q + 1800 Price= $750
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