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PS4_Chapter9_solution

# PS4_Chapter9_solution - ECO 100B Problem Set 4 1(a At the...

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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 (d) The consumer°s price goes up from 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 consumer°s share is 20 21 and the producer°s share is 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 µ (1) = 50 21 2. (a) The Long Run Supply curve is horizontal at P = 33 7 . (b) From the consumer°s perspective, the new Long-run supply curve will be 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 µ = 6600 7 (c) The entire burden of the tax is on the consumers since the amount that producers receive
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