Bertrand Price Competition Model: Suppose there are two firms, Firm 1 and Firm 2. They produce...

Bertrand Price Competition Model:

Suppose there are two firms, Firm 1 and Firm 2. They produce a slightly differentiated product. The demand for the two products is given respectively by:
Q1 = 12 – 2P1 + P2 Q2 = 12 – 2P2 + P1

Suppose each firm’s TFC = $20 and MC = $1 The firm’s compete in prices. Firm 1 chooses P1 to maximize its profit and Firm 2 chooses P2 to maximize profits. Find P1, P2, Q1, Q2

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Two firms, 1 and 2, are engaged in Bertrand price competition. There are10possible buyers, each of...

Two firms, 1 and 2, are engaged in Bertrand price competition. There are10possible buyers, each of whom is willing to pay up to $4, and no more, for an item the firms sell .Firms 1 and 2 have identical unit costs of $2. However, each firm has a capacity of 8units, so that it cannot satisfy the whole market by itself (it can only satisfy 8 possible buyers, at most).The firms simultaneously announce prices, p1 and p2 respectively and the...

Consider Cournot model of quantity competition between two firms, firm 1 and firm 2. Suppose the...

Consider Cournot model of quantity competition between two firms, firm 1 and firm 2. Suppose the inverse demand for the firms product is given by ?=40(?+2)−(?+1)(?1+?2)p=40(A+2)−(B+1)(q1+q2), where ??qi denotes the quantity of firm ?i, ?=1,2i=1,2, ?A is 6 and ?B is 9. Each firm's average cost is equal to ?+2c+2, where ?c is 4. a) Derive and accurately plot each firm's best response function. b) Find the (Nash) equilibrium quantities, price, profits and consumer surplus. c) Suppose next that each...

1. According to the model of Bertrand price competition, competing firms will set prices according to...

1. According to the model of Bertrand price competition, competing firms will set prices according to which rule: marginal revenue equal marginal cost marginal revenue equal to average cost price equal to marginal revenue price equal to marginal cost price equal to average cost 2. There are 2 firms that sell a certain software, Microsoft and Oracle. Microsoft invented the software and so they act as a market leader by first deciding how much of the software they are going...

Suppose there are only two firms in the market, firm 1 and firm 2. They produce...

Suppose there are only two firms in the market, firm 1 and firm 2. They produce identical products. Firm 1 has a constant marginal cost where AC1 =MC1 =20, and firm 2 has a constant marginal cost AC2 =MC2 =8. The market demand function is given by Q = 100 - 0.5P. a) Find the Cournot Nash Equilibrium price and quantity, write down the profits for each firm. (Use "q1" to represent output level for firm 1, and "profit1" to...

Suppose two firms are in Bertrand Competition. Both firms have a specific marginal cost of c...

Suppose two firms are in Bertrand Competition. Both firms have a specific marginal cost of c = 5. a.) Show that ( p∗1 , p∗2 ) = (5,5) is the unique Nash equilibrium. b.) Now, suppose that the firms can only set their prices to the nearest cent (i.e., their pric- ing decision is now discrete instead of continuous). There are now three Nash equilibria: (p∗1, p∗2)= (5,5) from before, and two more. Describe the two new Nash equilibria. c.)...

Consider a price competition model with two firms, 1 and 2, whose demand functions are as...

Consider a price competition model with two firms, 1 and 2, whose demand functions are as follows: Q1 =48−3P1 +2P2 Q2 =80−4P2 +3P1 Each firm incurs costs; C1(Q1) = 8Q1 and C2(Q2) = 13Q2. a) Write down firms 1’s and 2’s profit functions. b) Compute and graph firms 1’s and 2’s best response functions as a function of the other firm’s prices. c) Find the Nash equilibrium of the game. d) Calculate the profit of each firm in the Nash...

Two firms sell an identical product and engage in simultaneous-move price competition (i.e., Bertrand competition). Market...

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...

Consider Bertrand Competition with demand curve P = 56 − 2 Q. There are two firms....

Consider Bertrand Competition with demand curve P = 56 − 2 Q. There are two firms. Firm 1 has MC=12. Firm 2 has MC=8. What is the equilibrium number of units transacted in this market (Round to the nearest integer)?

1. In a Bertrand model with identical firms and a non-differentiated product, price will increase in...

1. In a Bertrand model with identical firms and a non-differentiated product, price will increase in response to: a-) an increase in the number of firms. b-) a decrease in the number of firms. c-) an increase in marginal cost. d-) a decrease in marginal cost. 2. Which of the following is not a feature of the Cournot model? a Group of answer choices b In a Cournot equilibrium, neither firm can change its production and make more profit. c...

problem 1. Suppose two firms facing a demand D(p) compete by setting prices simultaneously (Bertrand Competition)....

problem 1. Suppose two firms facing a demand D(p) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost c1 and Firm 2 has a marginal cost c2. Assume c1 < c2, i.e., Firm 1 is more efficient. Show that (unlike the case with identical costs) p1 = c1 and p2 = c2 is not a Bertrand equilibrium. how do you solve this?

Subjects