This study source was downloaded by 100000842097825 from CourseHero com on 02 23 2022 10 01 36 GMT 06 00 https www coursehero com file 88830328 EF4480 Problem Set 1 Solutionpdf 1 City University of Hong Kong Semester B 2020 21 EF4480 Industrial Organization Problem Set 1 Solutions 1 True or False Price discrimination always increases economic efficiency relative to what would be achieved by a single uniform monopoly price False If the aggregate quantity does not increase then efficiency of the firm does not increase Likewise if the aggregate quantity does not increase or if additional markets are not served social welfare is not increased 2 Suppose that a monopolist faces a demand curve given by where e 1 Assume the monopolist has a constant marginal cost equal to c A Show that if there were perfect competition total social welfare would equal 1 1 B How much welfare is lost due to monopoly Note the algebra here can get very tedious Do not worry about getting it exactly right Instead it is important you set up the problem correctly and are clear that you are measuring the correct object a Under perfect competition we have price marginal revenue equal to marginal cost so that P c Therefore total social welfare is equal to TS 11 1 11 0 1 1 1 b A profit maximizing monopolist will set quantity at the point where MR MC 1 1 1 1 1 Which yields a price of 1 1 Therefore the loss of welfare equals DWL 11 1 11 1 1 1 1 1 1 c 1 1 1 1 1 1 1 1 This study source was downloaded by 100000842097825 from CourseHero com on 02 23 2022 10 01 36 GMT 06 00 https www coursehero com file 88830328 EF4480 Problem Set 1 Solutionpdf 2 Remember that e 1 Thus the first term 1 1 is positive The whole expression is positive then if 1 1 1 1 1 1 1 1 1 1 1 2 1 We have 0 1 1 1 and 1 2 1 1 Thus the term in the parentheses is negative and the whole expression is less than 1 Therefore DWL 0 so there is in fact a loss in total welfare 3 You are a produce grocer who sells two products apples and bananas you sell them in bushels but we ll just consider a bushel to be one unit of fruit Each costs you 1 per bushel wholesale which is your only cost You can prevent resale among your customers of which there are three each with unit inelastic demand Consumer 1 has a willingness to pay of 2 per apple bushel and 8 per banana bushel For Consumer 2 the willingness to pay is 4 for apples and 6 for bananas Consumer 3 would pay up to 9 for apples but only 1 for bananas A Suppose you price apples and bananas separately What is the profit maximizing price for each B What is the profit maximizing price if you sell the two fruit as a pure bundle C What leads to higher profits selling separately or offering a pure bundle Explain how this answer relates to the correlation in consumers willingness to pay across apples and bananas a You would never sell apples for less than 2 or more than 9 or bananas for less than 1 or more than 8 For apples if you set the price of an apple to 2 you sell 3 units at a margin of 1 each so the profit is 3 With a price at 4 you sell 2 units at 3 margin so the profit is 6 With price at 9 you sell 1 unit at 8 margin so the profit is 8 For bananas if you set the price of a banana at 1 you sell 3 units at a margin of 0 each so profit is 0 With price at 6 you sell 2 units at 5 margin so the profit is 10 With price at 8 you sell 1 unit at 7 margin so the profit is 7 Therefore it is profit maximizing to set the price of an apple at 9 and the price of a banana at 6 Profits are 8 10 18 b Each consumer has a total valuation of 10 so charge that and sell three bundles at 10 Revenues are 30 costs are 6 and profits are 24 c Offering the pure bundle leads to higher profits see answers above This is because consumers willingness to pay is negatively correlated across apples and bananas 4 The inverse market demand for fax paper is given by P 400 2Q There are two firms who produce fax paper Each firm has a unit cost of production equal to 40 and they This study source was downloaded by 100000842097825 from CourseHero com on 02 23 2022 10 01 36 GMT 06 00 https www coursehero com file 88830328 EF4480 Problem Set 1 Solutionpdf 3 compete in the market in quantities That is they can choose any quantity to produce and they make their quantity choices simultaneously A Show how to derive the Nash equilibrium to this game What are firms profit in equilibrium B What is the monopoly output i e the one that maximizes total industry profit Why isn t producing one half the monopoly output a Nash equilibrium outcome a To determine firm 1 s best response function equate its marginal revenue with marginal cost 400 4 1 2 2 40 1 14 360 2 2 Since the firms are identical 1 2 14 360 2 60 160 Firm 1 s profit is 1 160 40 60 7200 b The monopoly output is 14 360 90 45 45 is a not a solution because if one firm produces 45 then the other produces 14 360 2 45 67 5 to maximize its profit 5 Consider a Stackelberg game of quantity competition between two firms Firm 1 is the leader and firm 2 is the follower Market demand is described by the inverse demand P 1000 4Q Each firm has a constant unit cost of production equal to 20 A Solve for the Subgame perfect equilibrium B Suppose firm 2 s unit cost of production is c 20 Is it possible that in equilibrium the two firms had the same market share a Firm 2 chooses its quantity to maximize 2 2 1000 4 1 4 2 20 2 2 2 1000 4 1 8 2 20 0 2 18 980 4 1 Now Firm 1 chooses its quantity to maximize 1 1 1000 4 1 4 2 20 1 1 980 4 1 12 980 4 1 12 1 980 4 1 1 1 980 8 1 0 1 9808 122 5 2 61 25 This study source was downloaded by 100000842097825 from CourseHero com on 02 23 2022 10 01 36 GMT 06 00 https www coursehero com file 88830328 EF4480 Problem Set 1 Solutionpdf Powered by TCPDF www tcpdf org 4 b There is no non negative c such that the leader and the follower have the same market share To see consider …