Jack and Mike harvest timber and sell it to local sawmills. Harvesting timber requires a special government permit. Jack and Mike have the only two permits and are therefore the only two producers of timber in this market. Harvested timber is a homogenous product. Total market demand for timber is given by Q=200 000 - 5P, where Q denotes total quantity measured in tons. Jack and Mike both have a constant marginal cost of $200 per ton. Fixed costs are zero.
a) Calculate the Cournot equilibrium outputs (i.e. assuming that Jack and Mike make simultaneous output decisions). What is the market price?
b) Suppose that the government grants Jack the legal right to harvest timber before Mike. Calculate the Stackelberg solution in which Jack makes his production decision before Mike. What is the resulting market price?
c) Now suppose that Jack can sell Mike the legal right to harvest timber first (i.e., the right to make the output decision first). By using your answers from part (b), calculate the maximum amount Mike would be willing to pay for the legal right to move first on one occasion. What is the minimum amount Jack would be willing to accept in order to sell this legal right?
d) Suppose now that there are N producers in the industry (including Jack and Mike), all with the same constant marginal cost of $200 per ton; and all choosing output simultaneously. Find the Cournot equilibrium.
(Hint: Use the fact that this is a symmetric game where in equilibrium all firms choose the same output.) How much will each firm produce, and what will be the market price? Also, show that as N becomes large the market price approaches the price that would prevail under perfect competition.