PS4_Chapter9_solution

PS4_Chapter9_solutio - ECO 100B Problem Set 4 1(a At the equilibrium 1000 10P 10 200P 990 33 P= = 210 7 6670 Q= 7 =(b Observe that demand and

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ECO 100B Problem Set 4 1. (a) At the equilibrium, 1000 10 P = 10 + 200 P P = 990 210 = 33 7 Q = 6670 7 (b) Observe that demand and supply can be re-written as: P = 100 Q D 10 P = Max Q S 10 200 ; 0 ± The consumer surplus at this allocation is 1 2 ± ² 100 33 7 ³ ± 6670 7 . The Producer Surplus is a bit trickier because the supply curve cannot go into negative prices. PS = 1 2 ± 33 7 ± ² 6670 7 + 10 ³ (c) With the $1 tax, marginal costs increase by $1 and hence, so does the supply curve. So: P = Q S 10 200 + 1 = Q S + 190 200 Q S = 200 P 190 At the equilibrium, Q D = Q S so: 200 P 190 = 1000 10 P P = 17 3 Q = 2830 3 33 7 to 17 3 which is an increase of $ 20 21 . The price received by producers goes down from 33 7 to ² 17 3 1 ³ which is a decrease of 1 21 . The 20 21 1 21 . (e) Given that demand and supply are linear, the DWL will be the area of the triangle, 1
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which is 1 2 ( tax ) ( Change in Q ) . So DWL in SR = 1 2 6670 7 2830 3 ± (1) = 50 21 2. (a) The Long Run Supply curve is horizontal at P = 33 7 . P = 33 7 + 1 = 40 7 The long-run price will be P = 40 7 . Using the demand curve, the long-run quantity will be Q = 1000 10 40 7 ± = 6600 7 (c) The entire burden of the tax is on the consumers since the amount that producers receive
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This note was uploaded on 10/21/2010 for the course ECON 1530 taught by Professor Ohly during the Spring '10 term at Dartmouth.

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PS4_Chapter9_solutio - ECO 100B Problem Set 4 1(a At the equilibrium 1000 10P 10 200P 990 33 P= = 210 7 6670 Q= 7 =(b Observe that demand and

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