Question # 1
Consider a two-period mine (periods 0 and 1) industry that is owned by a monopoly firm. Let interest rates, demand, extraction costs, and initial stock be give by: r = 5%, P(Qt) = 100 Qt/2, MC = $50/barrel, S0 = 150 barrel. (4+5+6 points)
(a) Set up the maximization problem and Lagrangian for this monopoly firm.
(b) Solve the above maximization problem using Lagrangian multiplier method. Calculate the scarcity rent. Test if you get negative rent.
(c) If scarcity rent is negative, then that means scarcity rent is zero. Use the correct method to solve this maximization problem.