ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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PROBLEM (2) (a) A consumer has utility u(x,y,z)= In(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz =1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? %3D 1 2 3 (HINT: MUx = , MUY =, MUz = and remember the "equivalent bang for the buck" condition) y Z (b) Forget about (a). Suppose you have t = 29 hours in total to spend on 3 projects X, Y and Z to make some money. If you spend x hours on project X, you make 2vx dollars; you spend y hours on project Y, you make 3vy dollars; If you spend z hours on project Z, you make 4vz dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x ? on y? on z ? If
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Transcribed Image Text:PROBLEM (2) (a) A consumer has utility u(x,y,z)= In(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz =1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? %3D 1 2 3 (HINT: MUx = , MUY =, MUz = and remember the "equivalent bang for the buck" condition) y Z (b) Forget about (a). Suppose you have t = 29 hours in total to spend on 3 projects X, Y and Z to make some money. If you spend x hours on project X, you make 2vx dollars; you spend y hours on project Y, you make 3vy dollars; If you spend z hours on project Z, you make 4vz dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x ? on y? on z ? If
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