In the standard Bertrand duopoly model studied in class1 two rms produc ing the some good compete by choosing the price they charge. In the problem considered here, the rms still compete by choosing the price of their prod uct. But since these products are differentiated, the rms face diEerent demand functions. The demand function faced by rm 1 is a: = IUD2:11 +1121 where m is rm 1*s output, 191 is the price charged by rm 1, and I): is the price charged by rm 2. Likewise, the demand faced by rm 2 is y2=IDD2p2+p1. Firm 1 faces a constant marginal cost of production of 312}, and rm 2 faces a constant marginal cost of production of If]. The rms simultaneously choose their own price. {a} 1Write the formulas giving each rm's prot as a function of both prices. {b} Derive the best reply function of each rm. {c} Find the NashBertrand equilibrium prices. [d] Compute the associated prots