econ101_ps7_sol - METU Department of Economics Econ 101...

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1 METU Department of Economics Econ 101: Introduction to Economics I All sections (01-02-03) Fall 2010 PROBLEM SET 7 (With Answers) PART A- PROBLEMS 1. A monopoly’s cost and revenue structure is given below: Q P = AR TR MR TC MC PROFIT 0 31 0 3 -3 1 28 28 28 21 18 7 2 25 50 22 38 17 12 3 22 66 16 54 16 12 4 19 76 10 71 17 5 5 16 80 4 90 19 -10 6 13 78 -2 110 20 -32 7 10 70 -8 132 22 -62 8 7 56 -14 157 25 -101 9 4 36 -20 185 28 -149 10 1 10 -26 215 30 -205 a) Fill the blank cells. b) Monopoly’s equilibrium price is 22. c) Monopoly’s equilibrium quantity is 3. d) Profit/Loss at equilibrium is 12.
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2 2. The diagram below shows the demand and unit cost situation of a monopolist. a) In order to maximize profits or minimize losses how much should this firm produce and at which price? Q = 0E, P = 0A b) In equilibrium how much total revenue will the firm collect? 0AJE c) In equilibrium how much total cost will the firm incur? 0BHE d) State whether the firm faces a profit or a loss in the equilibrium. Profit by AJBH 3. The monopolist will allocate production so that MC = MR in each market. MC = MR 1 =MR 2 TC – 20Q – 20 =0 or TC = 20Q + 20, then MC is constant at 20. In market 1, Q 1 = 16 – 0.2P 1 or P 1 = 80 – 5Q 1 TR 1 = P 1 Q 1 = (80 – 5Q 1 )*Q 1 = 80Q 1 - 5Q 1 2 MR 1 = 80 – 10Q 1 Then 80 – 10Q 1 = 20 and Q 1 =6, P 1 =50 In market 2 Q 2 =4 and P 2 =100 a) Profits with price discrimination: S=(TR 1 + TR 2 ) – TC = 480 Quantity Price and Cost per unit A B C MC ATC MR Demand H N J L E G 0
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3 4. a) Marginal cost = $5. Total cost = 2,000 + 5 q. Let us rearrange the demand equation as: p = 20 – q/100. So total revenue = p*q = 20 q – q 2 /100. b) Marginal revenue = 20 – q/50. c) In the monopoly equilibrium MR = MC, which implies, using our expressions, 20 – q/50 = 5. From this we can solve for the equilibrium quantity as q * = 750. Plugging that into the demand equation we solve for equilibrium price as p * = 12.5. d) Maki’s profit = total revenue – total cost = (12.5 × 750) – (2,000 + 5 × 750) = 3625. e) Consumer surplus = ½ [750 × (20 – 12.5)] = 2812.5. f)
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This note was uploaded on 01/05/2012 for the course ECON 101 taught by Professor Gulipektunc during the Spring '11 term at Middle East Technical University.

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econ101_ps7_sol - METU Department of Economics Econ 101...

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