10fB_ps05 - Microeconomics ECON 100A Problem Set 5 Due...

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Microeconomics ECON 100A Problem Set 5 Due October 26, 2010 (Solutions Posted October 29, 2010) 1. Consider the expenditure minimization problem subject to achieving a given level of utility 5 . 1 5 . 0 8 z x U = a. Illustrate the consumer’s problem b. Write down the first order conditions for this constrained optimization problem . c. Solve for the optimal consumption bundle, X h and Z h , as a function of x p , z p , and U . d. Solve for minimum expenditures as a function of x p , z p , and U e. OK, now you will need to get a calculator. Let Px=$2.50 and Pz=$3.33 and U =432. What are the numerical values of X h , Z h and E? Put these values on your graph. f. What is the numerical value of λ h ? Use words to interpret this number. You did the utility maximization subject to a budget constraint question with this utility function (and derived Marshallian demand curves) on an earlier problem set. Compare the value of λ h you get here to the value of λ * from that earlier question. How are these two different Lagrange
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10fB_ps05 - Microeconomics ECON 100A Problem Set 5 Due...

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