Question

In: Economics

1. Suppose there are two firms in a market producing differentiated products. Both firms have MC=0....

1. Suppose there are two firms in a market producing differentiated products. Both firms have MC=0. The demand for firm 1 and 2's products are given by:

q1(p1,p2) = 5-2p1+p2

q2(p1,p2) = 5-2p2+p1

a. First, suppose that the two firms compete in prices (i.e. Bertrand). Compute and graph each firm's best response functions. What is the sign of the slope of the firms' best-response functions? Are prices strategic substitutes or complements?

b. Solve for the Nash equilibrium prices and quantities when the two firms play Bertrand. Calculate the firm's profits.

c. Next, assume firms compete in quantities (i.e. Cournot). Solve for firm 1 and 2's inverse demand functions (i.e. solve the demand equations for p as a function of q).

d. Compute and graph each firm's best response functions. What is the sign of the slope of the firms' best-response functions? Are quantities strategic substitutes or complements?

e. Solve for the Nash equilibrium prices and quantities when the two firms play Cournot. Calculate the firm's profits.

f. Compare the market outcomes in parts (a) and (c). Is the equilibrium outcome more competitive under price or quantity competition?

Solutions

Expert Solution


Related Solutions

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...
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...
firms with market power offer differentiated products in order to:
firms with market power offer differentiated products in order to:
Suppose there are two firms facing a common market withdemand function p= 12 - Q. Suppose both firms’ marginal cost are mc= 2.
(Cournot Competition.) Suppose there are two firms facing a common market withdemand function p= 12 - Q. Suppose both firms’ marginal cost are mc= 2. Let’s assume that these two firms are playing the cournot competition game. (a) Write down the profit function of both firms. (b) Solve the best response function of the two firms. (c) Compute the Nash Equilibrium. (d) Now assume that the first firm has the first mover advantage. Calculate the new equilibrium (the Stackleburg equilibrium.)
22. Consider a monopolistically competitive market. Despite producing differentiated products, suppose that each existing firm (and...
22. Consider a monopolistically competitive market. Despite producing differentiated products, suppose that each existing firm (and any potential entrant) has the same total cost function, given by TC=2200+100Q+Q2. And despite producing differentiated products, suppose that each existing firm currently faces the same residual demand curve, given by Q=(320-P)/4.5 What will happen in the market over the long run?       A. Number of firms will increase and residual demand of existing firms will shift leftward.       B. Number of firms will...
Horizontal Mergers. Consider a market that initially has two firms selling differentiated products and competing in...
Horizontal Mergers. Consider a market that initially has two firms selling differentiated products and competing in prices. The cost of production of each firm is C(q)=0. Demand for the two goods is given by the following system: q1=420-4p1+p2 q2=420-4p2+p1 The goal of this question is to find by how much the prices of the goods will increase if the firms horizontally merge. To do this, we first derive the equilibrium prices before the merger, and then compare with the optimal...
Suppose there are two firms operating in a market. The firms produce identical products, and the...
Suppose there are two firms operating in a market. The firms produce identical products, and the total cost for each firm is given by C = 10qi, i = 1,2, where qi is the quantity of output produced by firm i. Therefore the marginal cost for each firm is constant at MC = 10. Also, the market demand is given by P = 106 –2Q, where Q= q1 + q2 is the total industry output. The following formulas will be...
There are two firms, A and B producing differentiated products. Their demand curves are: qA=100-2PA+3PB qB=120-2PB+2PA...
There are two firms, A and B producing differentiated products. Their demand curves are: qA=100-2PA+3PB qB=120-2PB+2PA and both have MC=5. Note that demand curves are not symmetric. Assuming that firms are engaged in Bertrand price competition: (a)Write down the profit function of firm A and find its price response function Hint: πA=(PA-5)(100-2PA+3PB) (b) Write down the profit function of firm B and find its price response function (c) Find equilibrium prices PA and PB; equilibrium quantities qA and qB; and...
There are two main company(A, B) in a market. Their products are identical. MC = $1/1...
There are two main company(A, B) in a market. Their products are identical. MC = $1/1 product. Qd = -1000P + 15000 (Demand curve) What is a payoff matrix by finding two company’s profit if two company make a cartel and split the market equally? What is a payoff matrix by finding two company’s profit if company A makes 1000 more product while company B keeps the previous agreement? What is the Nash equilibrium in the two situation? The cartel...
Suppose there are only two firms, firm1 and firm2, in the market. They both choose a...
Suppose there are only two firms, firm1 and firm2, in the market. They both choose a quantity to produce simultaneously. The market price is determined by the market demand: p =130-(Q1+Q2) where Q1 is the output quantity of firm1 and Q2 is the output quantity of firm2. Firm1’s total cost of production is 10Q1 and firm2’s total cost of production is 10Q2. That is, both firms have a constant marginal cost of 10. Task 1. What’s firm 1’s best response...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT