wk3 practice questions ans

wk3 practice questions ans - The Colorado College...

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1 The Colorado College Department of Economics and Business Block 7 Econ 207 Practice Question set 3 ans. 1. (a) The monopolists’ profit is set-up as: π = TR –TC = P.Q – TC = (304 – 2Q)Q – 500 -4Q – 8Q 2 = 304Q – 2Q 2 – 500 – 4Q – 8Q 2 Setting MC MR dQ d = = 0 π 304 - 4Q = 4 + 16Q 300 = 20Q Q* = 15 . P* = 304 – 2(15) = 304 – 30 = $274 π = TR –TC = 274(15) – 500 - 4(15) – 8(15) 2 = 4110 – 2360 = 1750 (b) With the imposition of the unit tax the new profit expression for the monopolist is; π = TR –TC – tQ = 304Q – 2Q 2 – 500 – 4Q – 8Q 2 – 10q Setting 0 = dQ d => 304 - 4Q – 4 - 16Q – 10 = 0 300 – 10 = 20q Q* = 290/20 = 14.5 P* = 304 – 2(14.5) = 304 - 29 = $275 New π = TR –TC = 275(14.5) – 500 - 4(14.5) – 8(14.5) 2 = 3987.5 – 2240 = 1747.5
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2 (c) Total Revenue(TR) for the monopolist = P.Q.= 304Q – 4Q 2 When the monopolist maximizes total revenue , the optimal condition is given by: 0 ) ( = dQ TR d => 304 – 8Q = 0 Q* = 304/8 = 38 . P* = 304 – 2(38) = 304 – 76 = $228 . Profits = TR –TC = 228(38) – 500 – 4(38) – 8(38) 2 = 8664 – 12204 = - 3540 . [Note: the monopolist has negative profits because its objective here is to maximize revenue, not profits. If total cost of production was zero, then the objective of profit maximization and revenue maximization boils down to the same thing. As in the basic Cournot model] 2. (a) When AC is constant it equals MC i.e. AC = MC.
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This note was uploaded on 04/19/2008 for the course EC 207 taught by Professor Ghosh during the Spring '08 term at Colorado College.

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wk3 practice questions ans - The Colorado College...

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