Question: Sonyas utility function is given by: U = C .25 L .75 ,MU C = .25C -0.75 L 0.75 , MU L = .75C 0.25

Sonya’s utility function is given by:

U = C^.25L^.75,MU_C= .25C^-0.75L^0.75, MU_L= .75C^0.25L^-0.25

Where C is income and she spends her entire income on consumption, L is the number of hours spent each day in leisure. Assume that her current wage rate is $12 per hour worked, she has no non-work income, and she can work as many hours as she wishes per day (not to exceed 24 hours of course).

How many hours will Sonya choose to work, how many hours will she devote to leisure activities, and how much does she choose to spend on consumption each day? (Note: use the tangency condition and budget constraint to solve).

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