Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10000 − 100P where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Joe’s marginal cost is $40 per cubic yard and Rebecca’s marginal cost is $25 per cubic yard. Competition in this market is described by the Cournot model. That is, the firms simultaneously decide the quantity to produce and the price clears the market given the quantity produced.
(a) What is Joe’s best response function?
(b) What is Rebecca’s best response function?
(c) Graph Joe and Rebecca’s best response functions on the same graph, with QJoe on the horizontal axis and QRebecca on the vertical axis.
(d) What are Joe and Rebecca’s Nash equilibrium outputs?
(e) What is the resulting price?
(f) What are the Joe and Rebecca’s markups, respectively?
(g) How much profit do they each earn?