Question

. Two firms sell an identical product and engage in simultaneous-move price competition (i.e., Bertrand competition). Market demand is Q = 20 – P. Firm A has marginal cost of $1 per unit and firm B has marginal cost of $2 per unit. In equilibrium, firm A charges PA = $1.99(…) and firm B charges PB = $2.00 A clever UNC alum has patented a cost-saving process that can reduce marginal cost to zero. The UNC alum is willing to license her invention to one (and only one) of the firms. She will invite the firms to bid for the license. The firms submit their bids simultaneously to the inventor. The firm with the higher bid wins the license and pays its bid, and the losing firm keeps its old technology and pays nothing. The firm that wins the auction gets MC = 0. The firm that loses keeps its original marginal cost (MCA = 1 or MCB = 2). After the auction, the firms engage in one additional round of price competition. a. What is the maximum each firm is willing to pay for the license? In other words, how much value does each firm get from winning the auction instead of losing it? Explain and/or provide sufficient calculations to support your answer. b. Which firm do you expect will win the auction? At what price (bid)? Assume that each firm is willing to pay (bid) a price that could be as high as its value from the license, i.e. the values you found in part (a), but each firm would prefer a lower price to win if possible.

Answer 1

According to BERTRAND MODEL there are two firms which are producing homogeneous product or identical product.Both are competing with price. They try to increase their sale with decrese in price.

Q=Q¹+Q²

^{P_{1 =}}F(P₂)

P¹<P² Q¹=Q

P¹>P² Q=0 ,Q²=Q

P¹=P² Q/2 According to this model price is variable ,if one firm will reduce the price other will also follow the same.But they will not lower the price than MC. MC will never become 0,so price will also be never equal to zero.so

when Q= 20-P

FIRM A Q=20-1.99=18.01

FIRM B Q=20-2= 18 SO The firm is having less price than A firm.so they are getting profit in duopoly model.

Hence,no any firm will get the auction with zero MC.