4113 PM Wed Oct 13 0 umass,moonamicom 309 Game theory Assignment 4 fall 2021 1. Two prot maximizing rms produce complementary goods (printers and ink, for instance). The demand functions are given by QA = 524PA2PB QB = 522PA4PB where Q A and Q3 are the quantities of goods A and B, and PA and P3 are the respective prices. The unit cost for each producer is 2. (a) (10) Write an expression for the prots of rm B as a function of the prices PA and PB. Treating prices as the choice variables (Bertrand competition), what is rm B's best response if rm A chooses the price PA? Illustrate rm B's best response function in a gure with PA and PB on the two axes. Find the Nash equilibrium. Suppose that the two rms were to merge and maximize their joint prots. The merged company would charge prices that are lower than the Nash equilibrium prices. You don't need to show this but explain in words why this would be the case. '5' 75%