Suppose that firms’ marginal and average costs are constant and equal to c and that inverse market demand is given by P = a – bQ, where a,b>0
a) Calculate the profit maximizing price-quantity combination for a monopolist. Also calculate the monopolist’s profit.
b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities for their identical products simultaneously. Also compute market output, market price and industry profits.
c) Calculate the Nash equilibrium prices for Bertrand duopolists, which choose prices for their identical products simultaneously. Also compute firm and market output as well as firm and industry profits.
d) Suppose now there are n identical firms in a Cournot model. Compute the Nash equilibrium quantities as functions of n. Also compute market output, market price, firm and industry’s profits.