Suppose two firms selling an identical product engage in Cournot competition. There are 100 potential customers and the industry demand is 100 − p. Firms choose quantities qi ∈ [0, 50], which leads to a price that equalizes supply and demand. Firms maximize their profits. This applies to all four problems below.
Part A – Suppose the firms choose their quantities simultaneously. Each firm’s marginal cost is $10. Find the Nash equilibrium of this game.
Part B – Now, suppose that firm 1 can spend $X to increase the other firm’s marginal cost to $20 (leaving its own marginal cost unchanged). Then, given the new costs, the firms choose their quantities simultaneously. What is the most money (i.e., the largest X), that firm 1 would be willing to spend on this?
Part C – As in the baseline game, each firm’s marginal cost is $10. Suppose that, unbeknownst to firm 2, firm 1 can observe the quantity chosen by firm 2 before it chooses its own quantity. (For example, firm 1 has a spy in firm 2’s headquarters and firm 2 does not suspect this is even possible.) How do the profits of each firm change? Along with an exact numerical answer, provide an intuition for the direction of the change(s), if any.
Part D – As in the baseline game, each firm’s marginal cost is $10. Suppose that everyone knows that firm 1 can observe the quantity chosen by firm 2 before it chooses its own quantity. How do the profits of each firm change? Along with an exact numerical answer, provide an intuition for the direction of the change(s), if any.
Sample Solution
