Consider an owner of a mine which can operate for two periods in a perfectly competitive market. The price in the first period is p0 and in the second period, it is p1. The interest rate is r and there are constant marginal costs for mining MC for both periods. The market demand curve is qt=a-but. The initial stock of minerals in the mine is R0.
(a) Write down the Hotelling rule with the perfect competition with constant marginal costs. (1 mark)
(b) If a=24, b=0.5, R0=10, r=0.08 and MC=8 find the mining path and the price. (4 marks)
(c) Suppose that the owner of the mine is a monopoly write down the Hotelling rule for a monopoly with constant marginal costs of mining. (1 mark)
(d) Find the mining and price path (4 marks).
(e) Now back to the competitive market explain what you would expect for the mining path if the second period MC increased. (4 marks)
(f) Test your intuition by solving with MC0=8, MC1=9 (4 marks)

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