aps3x313_s06 - 2 /4Px 2 and Y*=I/Py (Py/4Px). Now you just...

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0 2 4 6 8 10 12 14 16 18 20 22 0 10 20 30 40 50 60 X Px d mkt d hicks A B C 1. Assume Bree has the utility function: u=min{X, Y}. a) To graph Bree’s market demand for X you must first solve for X*(.) i.e., the demand function for X. With this utility function, you can’t set MRS equal to ERS, so you look at the indifference curve/budget line graph and notice that at an optimal bundle it must be true that X=Y. Now use the budget line to get: PxX+PyY=I and by substitution, PxX+PyX=I so that X*=I/(Px+Py). Now you would just graph the inverse of this function, where you rearrange to have Px on the left hand side of the equation to get: Px=(I/X)-Py. See graph. b) Note, with this utility there is NO substitution effect so “d hicks” is vertical. c) Suppose there is an increase in the price of X from Po=$8 to P 1 =$12 (arbitrarily chosen). i) Dupuit change in Bree’s consumer’s surplus = area PoP 1 CA. ii) Bree’s compensating variation for this price increase = area PoP 1 BA 2. From last time we know that: X*=Py
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Unformatted text preview: 2 /4Px 2 and Y*=I/Py (Py/4Px). Now you just take the appropriate partials: a) (X/Px) M = (-2/4)Py 2 Px-3 b) (X/Py) M = (2/4)PyPx-2 c) (Y/Px) M = (1/4)PyPx-2 d) (Y/Py) M = -IPy-2 (1/4)Px-1 3. Ralph has the following utility function: u(X,Y)=XY. a) This is standard Cobb-Douglas with =1/2, so X*=I/2Px and Y*=I/2Py. b) If I=100 and Px=Py=1, then X*=50 and Y*=50. c) If I=100 and Px=2 and Py=1, then X*=25 and Y*=50. d) Revenue = $25, so now if there is a lump sum tax, Ralph has I=75 and with Px=Py=1 you get X*=37.5 and Y*=37.5 e) So, with the unit tax, Ralph has u=25*50=1250 utils. If he makes the bribe and gets the income tax passed his income is $72 and Px=Py=1 and his bundle is X*=36 and Y*=36 so that utility = 1296 utils. Since this utility is great than 1250, he should cut the deal with the politician. Econ 313.2 - Wissink Spring 2006 PS#3 XtraQ - ANSWERS...
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