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Intermediate Microeconomics Due: March 24, 2004 March 31, 2004 Prof. Li-Chen Hsu Answer Key to Problem Set #6 1. (a) False. dq p p 3mp 2 1 which is a constant. As the result, absolute dp q 3m / p value of the price elasticity of demand is unchanged as price increases. 1 1 (b) False. q 20 2 p p 10 q R pq 10q q 2 2 2 MR 10 q 10 20 2 p 10 2 p MR / p 10 2 . As the result, the p ratio of marginal revenue to price increases as price increases. (c) False. consumer 1: 11 20 3x x1 3 consumer 2: 11 16 x x2 5 . The total quantity demanded by the two consumers is 8 when the price is 11. (d) False. If a good has an elasticity of demand greater than 1 in absolute value we say that it has an elastic demand. We cannot know the elasticity of demand according to the questions, so we cannot conclude that the demand for cucumbers is elastic. (e) True. The weighted average of the income elasticities must be 1, so if one good has a negative income elasticity, the other good must have an elasticity greater than 1 to get the average to be 1. 2. (a) q( p) 130 p / 5 p / 5 130 q p(q) 650 5q . (b) R(q) pq 650q 5q 2 dR(q) max R 0 650 10q 0 q* 65 p* 650 5 65 325 . dq (c) 3. dq p 1 325 1 . dp q 5 65 Q Qs Qa Qh (520 230 200) (13 1 5) P 950 19P . dq p P 19 1 38P 950 P 25 . dp q 950 19 P 4. (a) 48 518 5q q 94 dq p 1 48 48 . dp q 5 94 470 20036sol-1 . 5. (b) dq p p 2.5 1000 p 3.5 m2 2.5(m 60, p 45) . dp q 1000 p 2.5 m2 (c) dq p p 2 p 38 2( p 1)3 1.9 . 2 dp q ( p 1) ( p 1) 20 (d) dq p 20 1000 (undefined ) . dp q 0 Q 2500 400 p R pQ 2.5Q MR 2.5 m m 15000 1 400 p 2500 Q 2500 Q p 2.5 Q 10 10 10 400 1 2 1 15000 Q MR 2.5 Q and Q 2500 400(1.5) 400 400 200 10 1 400 0.5 . 200 6. (a) PD (qt* ) t PS (qt* ) 305 5qt* 54 8 4qt* qt* 27 . (b) PD (q* ) PS (q* ) 305 5q* 8 4q* q* 33 , PDt 305 5 qt* 305 135 170 PSt 8 4qt* 8 108 116 , DWL (170 116) (33 27) 162 . 2 7. qD 960 7 40 680, qS 160 3 40 280 excess demand 680 280 400 . 8. qD 200 140 60, qS 50 0.5 140 120 excess supply 120 60 60 , so the government costs 60 $140 $8400 to buy the corn. 20036sol-2