Consider the model of Bertrand competition with differentiated products from the text. Let the demand curves for firms A and B be given by Equation 12.10 and Equation 12.11, and let the firms' marginal costs be constant, given by cA and cB. It can be shown that the best-response function for firm A is

PA = 1 + 2pB + cA / 4

and for firm B is

PB = 1 + 2pA + cB / 4.

a. Graph the two best-response functions. Find the Nash equilibrium assuming cA = cB = 0 algebraically and indicate it on the graph.

b. Indicate on the graph how an increase in cB

Would shift the best-response functions and change the equilibrium.

c. Indicate on the graph where analogue to the Stackelberg equilibrium might be, with firm A choosing price first and then firm B. Is it better to be the first or the second mover when firms choose prices?