A consumer has utility u(x,y,z)= ln(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) (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 2√? dollars; If you spend y hours on project Y, you make ?√? dollars; If you spend z hours on project Z, you make ?√? 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 ?
A consumer has utility u(x,y,z)= ln(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)
(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 2√? dollars;
If you spend y hours on project Y, you make ?√? dollars;
If you spend z hours on project Z, you make ?√? 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 ?
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