- 1. An oil producer has 60 barrels of oil to extract and sell in two periods. Assume that the cost of producing the 60 barrels of oil is $0.05/barrel. He will sell the oil either in period 0 and period 1. The demand curve in the two periods are P0 = 5 – 0.05Q0 in period 0 and P1 = 5 – 0.033Q1 in period 1. The discount rate is 10%.
(i) If the producer has monopoly power in the market, what’s his extraction plan?
(ii) If the government levies 5% tax on the Hotelling rent in period 0, no tax in period 1, what’s his extraction plan in this scenario? (hint: if tax rate is t%, the agent taxed receives r(1-t) from revenue or taxing object r).
(iii) If the government levies 5% tax on the Hotelling rent in both periods, what’s his extraction plan? Any surprised findings?
2. Based on the hand-out Excel model, solve the following optimal extraction problems through simulations: (i) R0 = 12; (ii) under (i) δ = 0.04 and 0.06 respectively. What’s the impacts of δ on optimal extraction paths? Why? Submit three Excel print-out results.