1 City University of Hong Kong Semester B, 2020-21 EF4480 Industrial Organization Midterm - Solutions 1. True or False: Even with the same costs and market demand, monopolists that choose price earn lower profits than monopolists that choose quantity. Answer: FALSE. Monopolists face the same problem whether they choose price or quantity because the demand function is invertible in price and quantity. Thus, profits are identical. 2. The monopolist's marginal revenue curve lies to the left of any downward sloping demand curve. Answer: TRUE. As derived in class, for each marginal sale the monopolist receives the price but loses revenue on inframarginal consumers. Thus, the marginal revenue is less than price and the curve lies to the left. 3. In the two-firm linear demand case (with constant marginal costs) with homogeneous goods, let the superscript “c” denote Cournot, “s” denote Stackelberg, and “b” denote Bertrand. How does Deadweight Loss (DWL) compare across the models? (a) DWLb > DWLs > DWLc (b) DWLb > DWLc > DWLs (c) DWLs > DWLc > DWLb (d) DWLs > DWLb > DWLc (e) DWLc > DWLs > DWLb (f) DWLc > DWLb > DWLs Answer: (e) This is a result straight from class. Bertrand has no DWL, and Cournot leads to the least quantity produced and thus the most DWL. 4. A monopolist's consumers belong to two groups: those with a high willingness to pay (H) and those with a low willingness to pay (L). Let the demand for these groups be PH = 200 – QH and PL = 100 – 2QL, respectively. The monopolist has a constant marginal cost of $40. A. What is the profit-maximizing price and quantity if the monopolist must charge both groups the same price? What is the quantity sold to each consumer group? What is the monopolist's profit? What is total social welfare? B. Suppose the monopolist can separate the two consumer groups and charge each group a separate price (that is, the monopolist can price discriminate between the two groups). What is the profit-maximizing price and quantity for each group? What is the monopolist's profit? What is total social welfare? C. Has total social welfare increased once the monopolist can separate the groups? D. Give an example of a market that price discriminates in this way. State both the market and the different consumer groups. Answer: A. The monopolist’s total demand when it must charge one price is This study source was downloaded by 100000842097825 from CourseHero.com on 02-24-2022 02:30:15 GMT -06:00https://www.coursehero.com/file/88830122/EF4480-Midterm-Solutionpdf/2 𝑄= {QH+ QL; 𝑖𝑓 𝑃≤100QH; 𝑖𝑓 100≤𝑃≤2000; otherwise 𝑄= {250 - 1.5P; 𝑖𝑓 𝑃≤100200 - P; 𝑖𝑓 100≤𝑃≤2000; otherwise The monopolist can choose to sell to the whole market or just the high types. If the monopolist sells to both types, then the problem is: maxp (250-1.5𝑝)(p-40) First order condition of the problem implies: −1.5(𝑝 − 40)+ 250 −1.5𝑝=0 ⇒ p*=310/3 But we cannot have price above 100. The maximal price allowed if selling to both types is 100. At this price, the profit is 6000. If, instead, the monopolist only sells to high types, we have: maxp (200-𝑝)(p-40) First order condition of the problem implies: −1(𝑝 − 40)+ 200 − 𝑝=0 ⇒ p*=120 In this case, the optimal price is above 100 and below 200, so it is feasible. The profit is 6400. Therefore, the monopolist will only sell to the high demand consumer group. We have: QH=80, QL=0, P=120, and profit is 6400. Total social surplus (TS) is the sum of consumer surplus (CS) and producer surplus (PS), which is TS=CS+PS=3200+6400=9600. B. For the high types, the problem is the same as above, and we get QH=80, PH=120, CS=3200, and profit is 6400. For the low types, the problem is: maxp (50-0.5𝑝)(p-40) First order condition of the problem implies: −0.5(𝑝 − 40)+ 50 − 0.5𝑝=0 ⇒ PL=120 Thus, QL=15, CS=225, and profit is 450. The monopolist’s total profit is 6400+450=6850. Total social welfare is TS=CS+PS=(3200+225)+6850=10275. C. Total social welfare changed from 9600 to 10275. Thus, total social welfare increased. D. There are many examples of third-degree price discrimination, including: (1) Movie theaters - give discounts to students and senior citizens. In fact, many places give discounts to students and senior citizens including museums, amusement parks, newspaper and magazine subscriptions, etc. (2) Professional sports leagues – often will have promotional days where women or children enter for half of the price. This study source was downloaded by 100000842097825 from CourseHero.com on 02-24-2022 02:30:15 GMT -06:00https://www.coursehero.com/file/88830122/EF4480-Midterm-Solutionpdf/3 5. Suppose there are three identical firms in an industry. Each has a constant marginal cost c and the industry's demand curve is given by Q = 1 – P. (Hint: in a three player game, Nash equilibrium requires each player chooses an optimal strategy, given the other two players’ strategies.) A. Derive the Cournot equilibrium (quantities, price, profits). B. Would all three firms want to merge into a monopoly? Explain. C. Now suppose that just two of the firms were to merge with each other, making the industry a duopoly with each firm having marginal cost c. Compute the equilibrium outcome in this case. D. Would the non-merging firm want the merger to happen? Answer: For this question, you can simply apply the Cournot formulas for a three-firm market and a two-firm market. However, in the solution below, I will give the full details of the derivation. A. To derive the Cournot equilibrium we start with the profit functinos: 𝜋𝑖=(P-c)qi=(1-qi-∑qjj≠i-c)qi for i = 1, 2, 3. So maximizing profits gives the first order condition: 1 − 2qi− ∑qjj≠i− 𝑐=0 Thus, we have the following best-response functions: qi=1-∑qjj≠i-c2 Since these firms are identical, we assume q1=q2=q3, which gives: qi=1-2qi-c2 So, we have q1=q2=q3=(1-c)/4. Therefore, the aggregate quantity traded in the market is Q=3(1-c)/4. The market price is P=1-Q=(1+3c)/4. Each firm’s profit is therefore 𝜋𝑖=(P-c)qi=(1-c)2/16. B. For a monopolist, the problem is: maxQ (1-Q)Q-cQ The equilibrium is: Q=(1-c)/2, P=1-Q=(1+c)/2, and profit is (1-c)2/4. The total Cournot profits are 3(1-c)2/16, which is less than the monopoly profits. Thus, the three firms will want to merge into a monopoly. C. If the two firms merge into