10fB_ps05solutions_v2

# 10fB_ps05solutions_v2 - Microeconomics ECON 100A Problem...

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Microeconomics ECON 100A Problem Set 5 Solutions 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 Here’s an example. The numbers are the optimal consumption point for taken from an earlier utility maximization problem, using px = 2.50 and pz = 3.33 and Y = 40. Z 9 U=432 4 X b. Write down the first order conditions for this constrained optimization problem . 0 8 ) 3 ( 0 12 ) 2 ( 0 4 ) 1 ( . . . ) 8 ( 5 . 1 5 . 0 5 . 0 5 . 0 5 . 1 5 . 0 5 . 1 5 . 0 = - = = - = = - = - - + = - U z x L z x p z L z x p x L C O F U z x z p x p L z x z x λ c. Solve for the optimal consumption bundle, X h and Z h , as a function of x p , z p , and U . X h (Px, Pz, U ) = ( U /8) 1/2 (p z /3p x ) 3/4 Z h (Px, Pz, U ) = ( U /8) 1/2 (3p x /p z ) 1/4

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d. Solve for minimum expenditures as a function of x p , z p , and U E (Px, Pz, U ) = p x ( U /8) 1/2 (p z /3p x ) 3/4 + p z ( U /8) 1/2 (3p x /p z ) 1/4 (…can you simplify this further?) 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. Z
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10fB_ps05solutions_v2 - Microeconomics ECON 100A Problem...

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