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10fB_ps07 - Microeconomics ECON 100A Problem Set 7 Due...

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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. b. What are x*, and z* if Y=100, 2 = x p 1 = z p c. What is the level of utility given x* and z*? d. Solve for the Hicksian demand functions X h (p x , p z , U ) and Z h (p x , p z , U ). 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? 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 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. 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. b. What are x*, and z* if Y=100, 2 = x p 1 = z p c. What is the level of utility given x* and z*? d. Solve for the Hicksian demand functions X h (p x , p z , U ) and Z h (p x , p z , U ). e. NOW, Suppose P x rises to $5. At this new, lower price of X, what are the ordinary demands, X* and Z*, and the consumer’s maximum achievable utility? 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 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.
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3. True or false. Explain fully. (Hint: the answer if false.)
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