This study source was downloaded by 100000842097825 from CourseHero com on 02 24 2022 02 30 15 GMT 06 00 https www coursehero com file 88830122 EF4480 Midterm Solutionpdf 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 00 https www coursehero com file 88830122 EF4480 Midterm Solutionpdf 2 QH QL 100QH 100 2000 otherwise 250 1 5P 100200 P 100 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 5 p 40 First order condition of the problem implies 1 5 40 250 1 5 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 40 First order condition of the problem implies 1 40 200 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 5 p 40 First order condition of the problem implies 0 5 40 50 0 5 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 00 https 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 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 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 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 a single firm the market becomes a duopoly Then by similar analysis as in Part A we get qi 1 qi c2 So we have q1 q2 1 c 3 Therefore the aggregate quantity traded in the market is Q 2 1 c 3 The market …