Let the inverse demand curve be D(Q) = 56 − 2Q, Q = q1 + q2. Costs for each firm are a constant variable cost of 2, a unit capacity charge of 18, and setup costs of f .
a. Graph the first mover’s marginal cost function, given that capacity (k) is equal to 4. Derive the first mover’s marginal revenue function. On the same graph draw the first mover’s marginal revenue function for q2 equal to 6, 15, and 23.
b. Derive the first mover’s best-response function when its marginal cost is 2 and 20. Graph these best-response functions; then for k = 8 show the first mover’s best-response function. Derive and graph the second mover’s best-response function.
c. What is the equilibrium to the quantity subgame when k = 8? Explain why the first mover will not install a capacity less than 6 or greater than 12.
d. For fixed costs of 75, 50, 32, and 15, find the subgame perfect equilibrium. Explain intuitively your results!
e. For all values of f except 75, what would the subgame perfect equilibrium be if the first mover was capable of selling his capacity after the second mover decides to enter/stay out?
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