Monopolistic Competition and Oligopoly
CHAPTER 12 MONOPOLISTIC COMPETITION AND OLIGOPOLY REVIEW QUESTIONS 1. What are the characteristics of a monopolistically competitive market? What happens to the equilibrium price and quantity in such a market if one firm introduces a new, improved product? The two primary characteristics of a monopolistically competitive market are (1) that firms compete by selling differentiated products which are highly, but not perfectly, substitutable and (2) that there is free entry and exit from the market.
When a new firm enters a monopolistically competitive market (seeking positive profits), the demand curve for each of the incumbent firms shifts inward, thus reducing the price and quantity received by the incumbents. Thus, the introduction of a new product by a firm will reduce the price received and quantity sold of existing products. 2. Why is the firm’s demand curve flatter than the total market demand curve in monopolistic competition? Suppose a monopolistically competitive firm is making a profit in the short run. What will happen to its demand curve in the long run?
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The flatness or steepness of the firm’s demand curve is a function of the elasticity of demand for the firm’s product. The elasticity of the firm’s demand curve is greater than the elasticity of market demand because it is easier for consumers to switch to another firm’s highly substitutable product than to switch consumption to an entirely different product. Profit in the short run induces other firms to enter; as firms enter the incumbent firm’s demand and marginal revenue curves shift inward, reducing the profit-maximizing quantity.
Eventually, profits fall to zero, leaving no incentive for more firms to enter. 3. Some experts have argued that too many brands of breakfast cereal are on the market. Give an argument to support this view. Give an argument against it. Pro: Too many brands of any single product signals excess capacity, implying an output level smaller than one that would minimize average cost. Con: Consumers value the freedom to choose among a wide variety of competing products. (Note: In 1972 the Federal Trade Commission filed suit against Kellogg, General Mills, and General Foods.
It charged that these firms attempted to suppress entry into the cereal market by introducing 150 heavily advertised brands between 1950 and 1970, crowding competitors off grocers’ shelves. This case was eventually dismissed in 1982. ) 4. Why is the Cournot equilibrium stable (i. e. , why don’t firms have any incentive to change their output levels once in equilibrium)? Even if they can’t collude, why don’t firms set their outputs at the joint profit-maximizing levels (i. e. , the levels they would have chosen had they colluded)?
A Cournot equilibrium is stable because each firm is producing the amount that maximizes its profits, given what its competitors are producing. If all firms behave this way, no firm has an incentive to change its output. Without collusion, firms find it difficult to agree tacitly to reduce output. Once one firm reduces its output, other firms have an incentive to increase output and increase profits at the expense of the firm that is limiting its sales. 5. In the Stackelberg model, the firm that sets output first has an advantage. Explain why.
The Stackelberg leader gains the advantage because the second firm must accept the leader’s large output as given and produce a smaller output for itself. If the second firm decided to produce a larger quantity, this would reduce price and profit. The first firm knows that the second firm will have no choice but to produce a smaller output in order to maximize profit, and thus, the first firm is able to capture a larger share of industry profits. 6. Explain the meaning of a Nash equilibrium when firms are competing with respect to price. Why is the equilibrium stable?
Why don’t the firms raise prices to the level that maximizes joint profits? A Nash equilibrium in price competition occurs when each firm chooses its price, assuming its competitor’s price as fixed. In equilibrium, each firm does the best it can, conditional on its competitors’ prices. The equilibrium is stable because firms are maximizing profit and no firm has an incentive to raise or lower its price. Firms do not always collude: a cartel agreement is difficult to enforce because each firm has an incentive to cheat. By lowering price, the cheating firm can increase its market share and profits.
A second reason that firms do not collude is that such collusion violates antitrust laws. In particular, price fixing violates Section 1 of the Sherman Act. Of course, there are attempts to circumvent antitrust laws through tacit collusion. EXERCISES 1. 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. Monopolistic competition is defined by product differentiation. Each firm earns economic profit by distinguishing its brand from all other brands.
This distinction can arise from underlying differences in the product or from differences in advertising. If these competitors merge into a single firm, the resulting monopolist would not produce as many brands, since too much brand competition is internecine (mutually destructive). However, it is unlikely that only one brand would be produced after the merger. Producing several brands with different prices and characteristics is one method of splitting the market into sets of customers with different price elasticities, which may also stimulate overall demand. 2. Consider two firms facing the demand curve P = 10 – Q, where Q = Q1 + Q2.
The firms’ cost functions are C1(Q1) = 4 + 2Q1 and C2(Q2) = 3 + 3Q2. a. Suppose both firms have entered the industry. What is the joint profit-maximizing level of output? How much will each firm produce? How would your answer change if the firms have not yet entered the industry? If both firms enter the market, and they collude, they will face a marginal revenue curve with twice the slope of the demand curve: MR = 10 – 2Q. Setting marginal revenue equal to marginal cost (the marginal cost of Firm 1, since it is lower than that of Firm 2) to determine the profit-maximizing quantity, Q: 0 – 2Q = 2, or Q = 4. Substituting Q = 4 into the demand function to determine price: P = 10 – 4 = $6. The profit for Firm 1 will be: (1 = (6)(4) – (4 + (2)(4)) = $12. The profit for Firm 2 will be: (2 = (6)(0) – (3 + (3)(0)) = -$3. Total industry profit will be: (T = (1 + (2 = 12 – 3 = $9. If Firm 1 were the only entrant, its profits would be $12 and Firm 2’s would be 0. If Firm 2 were the only entrant, then it would equate marginal revenue with its marginal cost to determine its profit-maximizing quantity: 10 – 2Q2 = 3, or Q2 = 3. 5. Substituting Q2 into the demand equation to determine price:
P = 10 – 3. 5 = $6. 5. The profits for Firm 2 will be: (2 = (6. 5)(3. 5) – (3 + (3)(3. 5)) = $9. 25 b. What is each firm’s equilibrium output and profit if they behave noncooperatively? Use the Cournot model. Draw the firms’ reaction curves and show the equilibrium. In the Cournot model, Firm 1 takes Firm 2’s output as given and maximizes profits. The profit function derived in 2. a becomes (1 = (10 – Q1 – Q2 )Q1 – (4 + 2Q1 ), or [pic] Setting the derivative of the profit function with respect to Q1 to zero, we find Firm 1’s reaction function: [pic]
Similarly, Firm 2’s reaction function is [pic] To find the Cournot equilibrium, we substitute Firm 2’s reaction function into Firm 1’s reaction function: [pic] Substituting this value for Q1 into the reaction function for Firm 2, we find Q2 = 2. Substituting the values for Q1 and Q2 into the demand function to determine the equilibrium price: P = 10 – 3 – 2 = $5. The profits for Firms 1 and 2 are equal to (1 = (5)(3) – (4 + (2)(3)) = 5 and (2 = (5)(2) – (3 + (3)(2)) = 1. [pic] Figure 12. 2. b c.
How much should Firm 1 be willing to pay to purchase Firm 2 if collusion is illegal but the takeover is not? In order to determine how much Firm 1 will be willing to pay to purchase Firm 2, we must compare Firm 1’s profits in the monopoly situation versus those in an oligopoly. The difference between the two will be what Firm 1 is willing to pay for Firm 2. Substitute the profit-maximizing quantity from part a to determine the price: P = 10 – 4 = $6. The profits for the firm are determined by subtracting total costs from total revenue: (1 = (6)(4) – (4 + (2)(4)), or (1 = $12.
We know from part b that the profits for Firm 1 in the oligopoly situation will be $5; therefore, Firm 1 should be willing to pay up to $7, which is the difference between its monopoly profits ($12) and its oligopoly profits ($5). (Note that any other firm would pay only the value of Firm 2’s profit, i. e. , $1. ) Note, Firm 1 might be able to accomplish its goal of maximizing profit by acting as a Stackelberg leader. If Firm 1 is aware of Firm 2’s reaction function, it can determine its profit-maximizing quantity by substituting for Q2 in its profit function and maximizing with respect to Q1: pic], or [pic], or [pic] Therefore [pic] [pic] Substituting Q1 and Q2 into the demand equation to determine the price: P = 10 – 4. 5 – 1. 25 = $4. 25. Profits for Firm 1 are: (1 = (4. 25)(4. 5) – (4 + (2)(4. 5)) = $6. 125, and profits for Firm 2 are: (2 = (4. 25)(1. 25) – (3 + (3)(1. 25)) = -$1. 4375. Although Firm 2 covers average variable costs in the short run, it will go out of business in the long run. therefore, Firm 1 should drive Firm 2 out of business instead of buying it. If this is illegal, Firm 1 would have to resort to purchasing Firm 2, as discussed above. 3.
A monopolist can produce at a constant average (and marginal) cost of AC = 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. The monopolist wants to choose quantity to maximize its profits: max ( = PQ – C(Q), ( = (53 – Q)(Q) – 5Q, or ( = 48Q – Q2. To determine the profit-maximizing quantity, set the change in ( with respect to the change in Q equal to zero and solve for Q: [pic] Substitute the profit-maximizing quantity, Q = 24, into the demand function to find price: 24 = 53 – P, or P = $29.
Profits are equal to ( = TR – TC = (29)(24) – (5)(24) = $576. b. Suppose a second firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1 + Q2 = 53 – P. Assuming that this second firm has the same costs as the first, write the profits of each firm as functions of Q1 and Q2. When the second firm enters, price can be written as a function of the output of two firms: P = 53 – Q1 – Q2. We may write the profit functions for the two firms: [pic] or [pic] and [pic] or [pic] TR=QP MR=TR(Q? )-TR(Q??? ) Profit=Pr=TR-TC
MC=2 VC= ? MC? Q = 2Q .Q …. P …. TR …. TC . Profit . MR 20 …. 2 …. 40 … 120 … -80 .. -17 19 …. 3 …. 57 … 114 … -57 .. -15 18 …. 4 …. 72 … 108 … -36 .. -13 17 …. 5 …. 85 … 102 … -17 .. -11 16 …. 6 …. 96 ….. 96 …… 0 … -9 15 …. 7 … 105 …. 90 …. 15 … -7 14 …. 8 … 112 …. 84 …. 28 … -5 13 …. 9 … 117 …. 78 …. 39 … -3 12 … 10 .. 120 …. 72 …. 48 … -1 11 … 11 .. 121 …. 66 …. 55 …. 1 10 … 12 .. 120 …. 60 …. 60 …. 3 9 …. 13 … 117 …. 54 …. 63 …. 5 8 …. 14 … 112 …. 48 …. 64 …. 7