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 problem below.
Raising rival’s costs: Suppose that firm 1 can spend x dollars 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?