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Unformatted text preview: ANSWERS to Questions 35/ Discussion 4 Answer to Q.3 a) If MRS is higher than the price ratio P1 , then Kate will only spend her money on good 1. If P2 MRS1, 2 < P1 P , than she spends her money only on good 2. If MRS = 1 , then any bundle on the P2 P2 budget line is optimal. Kate's MRS equals 2. Hence the demand functions are: m m p1 p1 p , _ if p > 2 p , _ if p < 2 2 2 2 1 m m p p x1 = [0, ], _ if 1 = 2, x2 = [0, ], _ if 1 = 2, p2 p2 p1 p2 p1 p1 >2 <2 0, _ if 0, _ if p2 p2 b) p2=1, m=10 At any price higher than 2 (p1>2), Kate only buys good 2. Hence for x1=0, x2=10. Fo p1=2, the budget line has the same slope as the indifference curves, so any point on the budget line will be optimal: x2 = 10 - 2 x1 (the BL, for p1=2). For p1<2, Kate only buys good 1. Hence for x1>5, x2=0. The price offer curve is: 10 - 2 x1 , _ if _ x1 < 5 x2 = , 0, _ if _ x1 5
To find the demand curve, we plug p2 and m into the demand functions from part (a): 10 p , _ if _ p1 < 2 1 10 x1 = [0, ], _ if _ p1 = 2, p1 0, _ if _ p1 > 2 c) Commodity 1 is an ordinary good, since it is (weakly) decreasing in its own price. d) Both goods are normal, since they are (weakly) increasing in m. e) We have Answer to Q.4 The magic formulas for CobbDouglas demands are dx1 dx > 0, _ and _ 2 > 0 , so they are substitutes. dp2 dp1 x1 =
a) a m 4m b m m = , x2 = = a + b p1 5 p1 a + b p2 5 p1 START (p1=10, p2=1, m=100): x1 = 4m m = 8 , and x 2 = = 20 5 p1 5 p1 END (p1=5, p2=1, m=100): x1 = 4m m = 16 , and x2 = = 20 5 p1 5 p1 The change in consumption of x1 is: x1 = 16 - 8 = 8 . b) They are ordinary goods because the demand increases when price drops (downward slopping demand) c) To find the substitution effect, we need to find the change in demand when prices are different but the consumer can still afford the starting bundle: x1S = x1 ( p ' , m' ) - x1 ( p, m ) . Auxiliary income: m'=p1'x1*+p2x2*=5x8+1x20=60 Hence, the optimal demand with income m'=60 and the new prices is: x1 = This implies that the substitution effect is: SE=9.68=1.6 d) Income effect is the change in demand when prices are kept the same at the new prices, but n purchasing power is different: x1 = x1 ( p ' , m ) - x1 ( p ' , m' ) . So, it is the rest of the change in x1: IE=6.4 4m ' = 9.6 5 p1 ' e) Income effect is positive, which means movie is a normal good (With CobbDouglas preferences, both goods are normal). f) SE IE Answer to Q.5 a) The two conditions for these perfect complements are: 5 x1 = x2 p1 x1 + p2 x2 = m Hence, x1 = m 5m and x2 = p1 + 5 p2 p1 + 5 p2 m 200 5m = = 5 and x 2 = = 25 . p1 + 5 p2 15 + 5 x5 p1 + 5 p2 START (p1=15, p2=5, m=200): x1 = END (p1'=5, p2=5, m=200): x1 = m 200 5m = = 6.67 and x2 = = 33.33 p1 '+5 p2 5 + 5 x5 p1 '+5 p2 The change in consumption of x1 is: x1 = 33.33 - 25 = 8.33 b) m'=150. Substitution effect is zero: SE=0. c) Income effect equals the total change: IE=8.33 ...
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This note was uploaded on 08/08/2008 for the course ECON 301 taught by Professor Hansen during the Spring '08 term at Wisconsin.
- Spring '08