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Midterm

2GG3_2009_Fall_Test_2_Answers.pdf

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Department
Economics
Course
ECON 2GG3
Professor
Douglas Bruce
Semester
Fall

Description
Answers to Test 2 Econ 2GG3 Fall 2009 1. With good Y on the vertical axis and good X on the horizontal axis, illustrate a consumer's income and substitution effects for good X when its price increases (while the price of good Y and income are unchanged) and both goods are normal. 1 1 2 2 2. A consumer has preferences Ux=x +1 2 . Initially, the price of good 1 is $1 per unit, the price of good 2 is $2 per unit, and the consumer's income is $6. If the price of good 2 drops to $1, what are the income and substitution effects for good 2? First get the ordinary demands and the compensated demand for good 2. 1 1 −2 1 1 ⎫ MU 1 1 2 1 1 P 2 2 P2 ⎪ =⇒ =⇒ = −1 x1 2 ⎪ P 1 1 MU 2 2 P 1 x 2 P2 1 ⎬⇒=Ux x + 2 2 22 2 2 ⎪ P1 1 1 Ux=+x 2 2 ⎪ 1 2 ⎭ 2 * ⎛ ⎞ P1 h2 1 2, = ⎜ ⎟ ⎝ ⎠1 2 1 1 ⎛⎞ 2 ⎫ 2 MU 1 =⇒ = x x xP2 x P2 ⎪ ⎛⎞P MU P 1 2 P1 2 ⎜⎟P ⎬⇒x2P 12 22 = m 2 2 1 ⎝⎠ 1 ⎪ ⎝⎠P1 Px +=Px m 11 2 2 ⎭ P m xP( ), = 1 2 1 2 1 22PP P m ⎫ xP ( ), = 1 2 1 2 P1 22 ⎪ 2 ⎪ ⇒= x ⎛⎞P2 1 m ⎛P 2 ⎬ 1 ⎜⎟PPPP + x x= 2 ⎪ ⎝⎠ 1 1 22 1 2 ⎜P ⎪ ⎝⎠1 ⎭ xP( ), = P2 m 1 1 2 PP + 1 21 26 16 Initially we havex1() 2, 6 = = 4 and x2() 2, 6 = =1 so 12+ 12+ 1 11 1 2 2 22 2 * ⎛ ⎞ 9 Ux=+x 1 2= 41 3. The imaginary bundle involves h2()1,3 = ⎜ ⎟ 3 = . ⎝ ⎠ 4 The substitution effecth x() ( )− 1, 2, 6= 5 1 . 2 2 4 4 93 The income effect isx2(2 ( )− = 1,1,3 3 = . 44 3. Rob consumes only two goods—vodka and gatorade. He combines these into a toxic swill called vadorade that is three parts gatorade and one part vodka resulting in his utility functionx= min { V Gx }. Initially, a litre of vodka costs Rob $60, a litre of gatorade costs him $5, and his income is $450. Then one year, due to a poor gator harvest, the price of gatorade jumps to $10 per litre. What is the compensating variation to Rob of this price change? 3xV G ⎫ * m ⎬⇒ +Px⇒VV=PG V) m x V PVV +G G m ⎭ 3PG V 3xx= V G ⎪ 3m m ⎬ ⇒= x G xV= ⎪ 3PPG V 3PG V ⎭ x Un3x,m=n3{} , ⎧ ⎫ m m m3 3 = V G ⎨ 3P3P PP3 PP ⎩ ⎭ G VG V G V ⎡ ⎡ ⎤ m − CV ⎤ ⎢ ⎢ ⎥ = ⎥ ⎣ ⎣ ⎦nitial prices new prices⎦ 3( )− 3m =
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