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Chapter 12: Problem 7

Suppose that two competing firms, \(A\) and \(B\), produce a homogeneous good. Both firms have a marginal cost of \(\mathrm{MC}=\$ 50 .\) Describe what would happen to output and price in each of the following situations if the firms are at (i) Cournot equilibrium, (ii) collusive equilibrium, and (iii) Bertrand equilibrium. a. Because Firm \(A\) must increase wages, its \(\mathrm{MC}\) increases to \(\$ 80\). b. The marginal cost of both firms increases. c. The demand curve shifts to the right.

Short Answer

Expert verified
In summary, the results differ depending on the type of competition equilibrium and the specific parameter change in the market. Generally, changes in MC affect output and price in various ways. While a shift in the demand curve increases the market price and possibly the amount of output.

Step by step solution

01

Situation a: Cournot Equilibrium - Increase in MC for Firm A

Under Cournot competition, each firm independently chooses its quantity given what they believe is the other firm's quantity. When MC in firm A increases to $80, firm A will reduce its output to keep profitability. Consequently, firm B will increase its output as firm A now produces less. This will lower the price in the market.
02

Situation a: Collusive Equilibrium - Increase in MC for Firm A

In a collusive equilibrium, the firms collude to act like a single monopolist and try to maximize their joint profit. If MC of firm A increases but they continue colluding, the total output will decrease leading to an increase in the market price. There will be a reduction in the output of firm A but firm B’s output will remain the same.
03

Situation a: Bertrand Equilibrium - Increase in MC for Firm A

In a Bertrand competition, firms simultaneously set prices and consumers buy everything they want from the firm selling at a lower price. If firm A's MC increases, it will lead to an increase in its price. Since firm B has a lower price (assuming no increase in MC), the consumers will buy from firm B causing the output of firm A to fall to zero.
04

Situation b: Cournot Equilibrium - Increase in MC for both firms

If the MC of both firms A and B increases together, they will both reduce their outputs. This reduction in total output in the market will result in an increase in the market price.
05

Situation b: Collusive Equilibrium - Increase in MC for both firms

If the MC of both firms increases, the firms will reduce total output to maintain profitability leading to an increase in price.
06

Situation b: Bertrand Equilibrium - Increase in MC for both firms

If the MC of both firms increases, both firms A and B will increase their prices. As a result, the output will decrease.
07

Situation c: Cournot Equilibrium - Shift of Demand Curve

If the demand curve shifts to the right, this implies that the consumers' willingness to purchase the good has increased at each price level. Therefore, both firms A and B will increase their output and this will lead to an increase in market price.
08

Situation c: Collusive Equilibrium - Shift of Demand Curve

If the demand curve shifts to the right in a collusive equilibrium, the colluding firms will perceive this as an opportunity to increase prices. They increase the price, with the quantity supplied possibly either remaining the same or increasing due to the higher demand.
09

Situation c: Bertrand Equilibrium - Shift of Demand Curve

In a Bertrand Competition, if the demand curve shifts to the right, it means there are more consumers willing to pay for the products at any given price. Thus, both firms would be likely to increase their prices, leading to higher profits but the quantity supplied would remain the same.

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Most popular questions from this chapter

Two firms compete in selling identical widgets. They choose their output levels \(Q_{1}\) and \(Q_{2}\) simultaneously and face the demand curve $$P=30-Q$$ where \(Q=Q_{1}+Q_{2}\). Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm \(2^{\prime}\) s marginal cost to \(\$ 15 .\) Firm \(1^{\prime}\) s marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level Suppose that two identical firms produce widgets and

Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain.

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A monopolist can produce at a constant average (and marginal) cost of \(\mathrm{AC}=\mathrm{MC}=\$ 5 .\) It faces a market demand curve given by \(Q=53-P\) a. Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits. b. Suppose a second firm enters the market. Let \(Q_{1}\) be the output of the first firm and \(Q_{2}\) be the output of the second. Market demand is now given by $$Q_{1}+Q_{2}=53-P$$ Assuming that this second firm has the same costs as the first, write the profits of each firm as functions of \(Q_{1}\) and \(Q_{2}\) c. Suppose (as in the Cournot model) that each firm chooses its profit- maximizing level of output on the assumption that its competitor's output is fixed. Find each firm's "reaction curve" (i.e., the rule that gives its desired output in terms of its competitor's output). d. Calculate the Cournot equilibrium (i.e., the values of \(Q_{1}\) and \(Q_{2}\) for which each firm is doing as well as it can given its competitor's output). What are the resulting market price and profits of each firm? *e. Suppose there are \(N\) firms in the industry, all with the same constant marginal cost, \(\mathrm{MC}=\$ 5 .\) Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also, show that as \(N\) becomes large, the market price approaches the price that would prevail under perfect competition.
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