Question

Fred and Barney get new wireless communications systems and start taking orders from customers by phone. When a customer calls, each fisherman quotes a price for his respective type of fish. The customer then places an order for his or her preferred quantity, and the fisherman adds that amount to his planned daily catch. Assuming that Fred and Barney quote prices without knowing the other’s price quote, what are the equilibrium prices? To figure this out, you need to know the quantities demanded as a function of the prices. Solving the inverse demand equation system from problem (2) above for the ordinary demand system yields:

Qb = 1066.67 - 133.33pb + 66.67pc, Qc = 1066.67 - 133.33pc + 66.67pb.

Assume that Fred catches cod (so pc = pF and Qc = QF) and Barney catches bluefish (so pb = pB and Qb = QB), and that they simultaneously and non-cooperatively choose prices.

(a) What is Fred’s profit as a function of his price pF and Barney’s price pB? What is Fred’s best response function?

(b) What is Barney’s profit as a function of his price pB and Fred’s price pF? What is Barney’s best response function?

(c) What are the Bertrand-Nash equilibrium price levels pFBN and pBBN?

(d) What are the equilibrium catch sizes for cod and bluefish QcBN and QbBN ?

(e) What are the equilibrium profits for Fred and Barney? πFBN and πBBN ?

Answer 1