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 prices are publicly known. If p1=p2<=4; the first five buyers buy from firm 1 and the remaining 5from firm 2. Then firm 1's profit becomes (p1-2)*5 and similarly for firm 2.If p1< p2<=4; the first eight buyers buy from firm 1 and the remaining 2 from firm 2.If p2< p1<=4; then only the first two buyers buy from firm 1 and the remaining 8 from firm 2. If a firm charges a price above $4, it does not get any buyers. The prices p1;,p2 are restricted to be $0,$1, $2, $3, $4..

Find all the Nash equilibria in pure strategies for this game.

Expert Solution

Rahul Sunny answered 2 years ago

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

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...

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...

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)?

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.)...

Two firms are price-competing as in the standard Bertrand model. Each faces the market demand function...

Two firms are price-competing as in the standard Bertrand model. Each faces the market demand function D(p)=50-p. Firm 1 has constant marginal cost c1=10 and firm 2 has c2=20. As usual, if one of the firms has the lower price, they capture the entire market, and when they both charge exactly the same price they share the demand equally. 1. Suppose A1=A2={0.00, 0.01, 0.02,...,100.00}. That is, instead of any real number, we force prices to be listed in whole cents....

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...

Suppose two firms are engaged in Stackelberg Competition. The demand curve is P = 56 -...

Suppose two firms are engaged in Stackelberg Competition. The demand curve is P = 56 - 2Q and MC=20. What is the equilibrium market quantity?

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?

Suppose there are three identical firms engaged in quantity competition. The demand is P = 1...

Suppose there are three identical firms engaged in quantity competition. The demand is P = 1 − Q where Q = q1 + q2 + q3. To simplify, assume that the marginal cost of production is zero. Compute the Cournot equilibrium (i.e., quantities, price, and profits).

Question