The inverse demand curve for sugar is P = 100−Q. There are two firms, C and D, who produce sugar. Firms produce sugar using a technology with a cost function characterized by C(Qi) = 20Qi where Qi is the quantity produced by each firm. So, each firm marginal cost is equal to 20. Firms compete in prices and they make their price choices simultaneously (Bertrand competition). Firms can choose any price between 0 and ∞.
(a) What is the Bertrand-Nash equilibrium?
(b) Suppose firm D invests in a new technology and the cost function associated with this technology is characterized by C(QD) = 10QD. So, this technology allows firm D to reduce its marginal cost to 10. What is now the Bertrand-Nash equilibrium?
(c) Suppose that firm D has to pay to be able to lower its cost. How much is it willing to pay?