Question

In: Economics

Two firms produce differentiated products and set prices to maximize their individual profits. Demand functions for...

Two firms produce differentiated products and set prices to maximize their individual profits. Demand functions for the firms are given by

Q1 =64–4P1 +2P2

Q2 =50–5P2 +P1

where P1, P2, Q1, Q2, refer to prices and outputs of firms 1 and 2 respectively. Firm 1’s marginal cost is $5 while firm 2’s marginal cost is $4. Each firm has a fixed cost of $50.

Assuming that the two firms decide on prices independently and simultaneously, calculate the best response function of each firm in terms of prices. Calculate the resulting equilibrium price quantity combination for each firm. Illustrate your answer with a suitable graph. Also calculate optimal profits of each firm.

Please show and explain all calculations.

Solutions

Expert Solution

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Consider two firms that sell differentiated products and compete by choosing prices. Their demand functions are...
Consider two firms that sell differentiated products and compete by choosing prices. Their demand functions are Q1 = 72 – 3P1 + 2P2 and Q2 = 72 – 3P2 + 2P1 where P1 and P2 are the prices charged by firm 1 and 2, respectively, and Q1 and Q2 are the corresponding demands. All production costs are assumed to be zero. (a) Suppose the two firms set their prices simultaneously and non-cooperatively. Find the resulting Bertrand-Nash equilibrium. What price does...
Two firms compete in a market by selling differentiated products. The demand equations are : q1...
Two firms compete in a market by selling differentiated products. The demand equations are : q1 = 75 – p1 +p2/2 q2 = 75 – p2 +p1/2 Assume that each firm has a marginal cost and average costs of 0 What market model do we use if each firm competes by simultaneously choosing price Are the two goods substitutes? . Solve for firm 1’s best response function. Solve for the equilibrium price and quantity. Would firm 1 still be able...
Two firms produce differentiated products with demand curves p1=a−q1−bq2 and p2=a−q2−bq1. They both face constant average...
Two firms produce differentiated products with demand curves p1=a−q1−bq2 and p2=a−q2−bq1. They both face constant average and marginal cost c and their profit functions are Π1=(p1−c)q1 and Π2=(p2−c)q2. Solve the Cournot game.
Q2. Consider a Bertrand game with differentiated products in which two firms simul- taneously choose prices....
Q2. Consider a Bertrand game with differentiated products in which two firms simul- taneously choose prices. The marginal cost for each firm is zero and there are no fixed costs. The demand functions for each firm are: Q1 = 80 − 2P1 + 2P2, Q2 = 80 − 2P2 + 2P1. where P1 is the price set by firm 1, P2 is the price set by firm 2, Q1 is the quantity demanded of firm 1’s product and Q2 is...
Two Cournot firms produce slightly different products. Product prices depend on both firms' outputs and are...
Two Cournot firms produce slightly different products. Product prices depend on both firms' outputs and are determined by the following equations P1 = 70 - 2Q1 - Q2, P2 = 100 - Q1- 2Q2. Both Firm 1 and Firm 2 have constant marginal cost of $10 and zero fixed cost. Firm 1 chooses Q1 and Firm 2 chooses Q2. (3pts) Find Firm 1's best response as a function of Firm 2's output Q2.   (3pts) Find Firm 2's best response as...
The major difference between monopolistic competition and perfect competition is that firms produce differentiated products in...
The major difference between monopolistic competition and perfect competition is that firms produce differentiated products in the former and homogeneous products in the latter. How does product differentiation generate the differences between the two models?
Two firms set prices in a market with demand curve Q = 6 − p, where...
Two firms set prices in a market with demand curve Q = 6 − p, where p is the lower of the two prices. If firm 1 is the lower priced firm, then it is firm 1 that meets all of the demand; conversely, the same applies to firm 2 if it is the lower priced firm. For example, if firms 1 and 2 post prices equal to 2 and 4 dollars, respectively, then firm 1–as the lower priced firm–meets...
Two firms set prices in a market with demand curve Q = 6 − p, where...
Two firms set prices in a market with demand curve Q = 6 − p, where p is the lower of the two prices. If firm 1 is the lower priced firm, then it is firm 1 that meets all of the demand; conversely, the same applies to firm 2 if it is the lower priced firm. For example, if firms 1 and 2 post prices equal to 2 and 4 dollars, respectively, then firm 1–as the lower priced firm–meets...
Consider two firms that provide a differentiated product, which they produce at the same constant marginal...
Consider two firms that provide a differentiated product, which they produce at the same constant marginal cost, MC = 3 (no fixed cost). The demand function for Firm 1 is q1 = 10 – p1 + 0.5p2 and for Firm 2 is q2 = 20 – p2 + 0.5p1, where p1 is Firm 1’s price and p2 is Firm 2’s price. a) Write the profit functions for these firms.( 8 marks) b) What are the equilibrium prices and quantities? (...
In a market, there are two firms, firm A and firm B, producing differentiated products. Denoting...
In a market, there are two firms, firm A and firm B, producing differentiated products. Denoting the prices with pA and pB, firm A faces a demand given by qA(pA,pB) = 380−2pA +4 α pB, where 0 ≤ α < 1, and firm B faces a demand given by qB(pA,pB) = 180 − 2pB + pA. Each firm has a constant marginal cost, cA =cB =10and no fixed costs. (a)   Suppose that the firms compete in prices simultaneously. Find the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT