Consider a homogenous good market with the following market demand curve:
Q=100-p
Two firms produce output at constant marginal cost = 10. Derive the Nash equilibrium outcome in terms of prices, outputs and the profits of the two firms under the following alternative situations in a)-d)
a) Firms engage in Bertrand price competition with no capacity constraints.
b) Firms engage in Bertrand price competition and each firm has a maximum production capacity = 15. c) How would your answer in part (b) change if the capacity of each firm is 90?
d) Firms engage in Cournot quantity competition (i.e., determine their capacity assuming that the price is such that market demand equals industry capacity).
e) Compare the industry output in cases (a) and (d) to the socially optimal and the monopoly output levels.