10fB_ps07solutions

# 10fB_ps07solutions - Microeconomics ECON 100A Problem Set 7...

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Microeconomics ECON 100A Problem Set 7 Due November 9, 2010 (Solutions Posted November 12, 2010) 1. From problem set 4 question 3 you already have seen the following utility function: z x z x U 2 ) , ( + = a. Solve for the optimal consumption bundle, x* and z*, as a function of x p , z p , and Y. z*(p x , p z , Y)= 2 ) ( z x p p , x*(p x , p z , Y)= x z x p p p Y 2 ) ( - [If 2 ) ( z x p p Y - <0 then x*=0, z*= z p Y ] b. What are x*, and z* if Y=100, 2 = x p 1 = z p x*=48, z*=4 c. What is the level of utility given x* and z*? U=52 d. Solve for the Hicksian demand functions X h (p x , p z , U ) and Z h (p x , p z , U ). ) ( 2 pz p U x x h - = , 2 ) ( z x h p p z = e. NOW, Suppose P x falls to \$1. At this new, lower price of X, what are the ordinary demands, X* and Z*, and the consumer’s maximum achievable utility? x*=99, z*=1, U=101 f. What are the values of X h (p x , p z , U ) and Z h (p x , p z , U ) if U is equal to value you solved for in part c, and 1 = x p 1 = z p 50 = h x , 1 = h z

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g. What are the income and substitution effects of this lower price of X? Please draw a picture and label it with the values you solve for. Total Effect is move from x*=48 to x*=99; TE = 51 Subst effect is move from 48 to 50, SE = 2 Income effect is move from 50 to 99, IE = 49 2. From problem set 5 question 3 you already have seen the following utility function: U=Z+4X a. Solve for the optimal consumption bundle, x* and z*, as a function of x p , z p , and Y. If p x < 4p z : X * = Y/ p x and Z * = 0 If p x > 4p z : X * =0 and Z * = Y/ p z b. What are x*, and z* if Y=100, 2 = x p 1 = z p Because (\$2) < 4(\$1): X * =50 and Z * = 0 c. What is the level of utility given x* and z*? U = 200 d. Solve for the Hicksian demand functions X h (p x , p z , U ) and Z h (p x , p z , U ). If p x < 4p z : X h (Px, Pz, U ) = U /4 and Z h (Px, Pz, U ) = 0
x > 4p z : X h (Px, Pz, U ) = 0 and Z h (Px, Pz, U ) = U e. NOW, Suppose P x rises to \$5. At this new, higher price of X, what are the ordinary demands, X* and Z*, and the consumer’s maximum achievable utility? Because (\$5) > 4(\$1): X * =0 and Z * = 100 U=100 f. What are the values of X h (p x , p z , U ) and Z h (p x , p z , U ) if U is equal to value you solved for in part c, and 5 = x p 1 = z p Because (\$5) > 4(\$1): X h (Px, Pz, U ) = 0 and Z h (Px, Pz, U ) = 200 g. What are the income and substitution effects of this lower price of X? Please draw a picture and label it with the values you solve for. Total Effect is move from x*=50 to x*=0; TE = -50 Subst effect is move from 50 to 0, SE = -50 Income effect is move from 0 to 0, IE = 0 3. True or false. Explain fully. (Hint: the answer if false.) a. A Hicksian demand curve has a positive slope if the substitution effect is less than the income effect and both effects work in the same direction. Hicksians consider the substitution effect only and always have negative slopes (or zero or

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## This note was uploaded on 11/30/2011 for the course ECON 311 taught by Professor Zambrano during the Fall '08 term at Cal Poly.

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10fB_ps07solutions - Microeconomics ECON 100A Problem Set 7...

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