Question

Emma has a utility function of u(c, l) = 9c1/3l 2/3 . She works as a...

Emma has a utility function of u(c, l) = 9c1/3l 2/3 . She works as a policewoman at a wage of 30 dollars an hour. She doesn’t have any income outside of her work. Calculate the optimal hours of work she would pick and her optimal consumption.

Homework Answers

Answer #1

Utility function = 9c^1/3 l^2/3. From utility function, MRS = -MUc/MUl = -9 * 1/3 *c^-2/3 * l^2/3 divided by 9 * 2/3 *c^1/3 * l^-2/3 = -l/2c

Consumption = income = (24 - l)*30

c = 720 - 30l

c + 30l = 720

Slope of budget = -1/30

At the optimum level MRS = slope of budget

-l/2c = -1/30

This gives c= 15l

Use the value in budget equation

15l + 30l = 720

l = 720/45 = 16

Hence the optimal hours of work she would pick is (24 - 16) = 8 hours and consumption = 8*30 = $240.

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