Attached 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 sheconsumes 30 units of z. What is her income? How much money does she spend on x?%3D123(HINT: MUx = , MUY =, MUz =and remember the "equivalent bang for the buck" condition)yZ(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 isthe optimal amount of time to spend on x ? on y? on z ?If

since you have asked multiple questions and according to our policy we can only solve the first part…

(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? (HINT: MUx =, MUY =, MUz = and remember the "equivalent bang for the buck" condition)

(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? (HINT: MUx =, MUY =, MUz = and remember the "equivalent bang for the buck" condition)

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Attached

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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