Answer to Question #259589 in Microeconomics for life

Question

(8 points) Consider a Bertrand duopoly. Both firms produce an identical good at the same constant marginal cost of $0.80. Demand is given by 𝑄𝑄=100−𝑃. If the two firms charge the same price, they share market demand equally.

The firms are located in Singapore, where the smallest currency denomination is $0.05. The firms thus can only choose prices in increments of $0.05.

a) (1 point) Suppose that both firms choose the same price, 𝑝. What is the profit of a firm as a function of 𝑝?

b) (2 points) Now suppose that one firm unilaterally deviates from the arrangement in (a) by charging a price $0.05 lower than 𝑝𝑝. What is that firm’s profit as a function of 𝑝?

c) (5 points) A Nash equilibrium occurs when no firm has an incentive to deviate by lowering its price. Using your answers in (a) and (b), set up an inequality that characterizes the Nash equilibrium. Then solve for the Nash equilibria in this game. (Hint: there are three equilibria)

Answer 1

a.

$MC=p\\0.8=100-p\\100-0.8=p\\p=99.2\\Q=100-99.2\\q=0.8\\ Profi=0.8×99.2\\=79.36$

b.

$Profi=0.5×99.2\\=49.6$