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.

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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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