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ECMC02-PS3A(1) - UNIVERSITY OF TORONTO SCARBOROUGH...

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UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF MANAGEMENT ECMC02: Topics in Price Theory (Intermediate Microeconomics II) Problem Set-3 (Solutions) 1. Short questions: a) False. If the aggregate quantity does not increase, then third degree price discrimination lowers welfare. b) True. A monopolist has an incentive to restrict output in order to increase price. If the government mandates a price ceiling, this motive dissipates, and thus the monopolist will produce more. 2. a) This is a classic two-part tariff. Differential fixed entry fee for different types, and then constant marginal cost per unit (=0). b) This is 2 nd degree price discrimination. The phone company offers a range of different price/quantity combinations, knowing that different types of users will self-select into different categories. c) This is a bundling technique. There is nothing here that necessarily suggests there is any price discrimination going on. d) The $8 price difference may well represent the costs of transporting oil from Europe to the US, so this is probably not price discrimination at all. Also, international commodity markets are very competitive, so price discrimination is unlikely to be possible. e) This may well represent local supply shortages and so higher costs; there is much less fuel to go around in Texas, so the cost of providing it is higher. This is based on supply issues, not any difference in customer demand, so this is not price discrimination. 3. a) C C P Q 2 200 - = C C Q P 2 1 100 - = C C Q MR - = 100 Now, equate marginal revenue for a cold day with marginal cost.
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20 100 = - C Q 80 = C Q 60 ) 80 ( 2 1 100 = - = C P H H P Q 2 300 - = H H Q P 2 1 150 - = H H Q MR - = 150 Now, equate marginal revenue for a hot day with marginal cost. 20 150 = - H Q 130 = H Q 85 ) 130 ( 2 1 150 = - = H P Coca-Cola will charge 60 cents on a cold day and 85 cents on a hot day. b) If half of the days are hot and other half are cold, then the expected aggregate demand faced by the Coca-Cola is P P P Q A 2 250 ) 2 200 ( 2 1 ) 2 300 ( 2 1 - = - + - = Hence, the expected marginal revenue is A A Q MR - = 125 Now, equate expected marginal revenue with marginal cost. 20 125 = - A Q 105 = A Q 5 . 72 = A P c) Profits with price discrimination = 5825 )] 80 )( 20 60 ( ) 130 )( 20 85 [( 2 1 = - + - Profits without price discrimination = 5 . 5512 ) 105 )( 20 5 . 72 ( = - Hence, profit is higher with discrimination. Efficiency is the same (since 80 = C Q and 130 = H Q but these occur ½ the time aggregate quantity is 105 with or without price discrimination. 4. P a = 200-5Q a barb4right MR a = 200-10Q a MC = Δ TC/ Δ Q = 20 bright Set MC = MR and solve for Q. bright (Q a = 18). Plug your Q back into the demand curve. (P a = 110)
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Adult Ridership 0 50 100 150 200 0 10 20 30 40 50 Quantity Dollars b) E D = -(110/18)(-1/5) = 1.22 Demand is elastic. A price reduction of 1% will increase ridership by 1.22%.
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