May's Utility Function Is U = C + 14D^1/22

question 50

Essay

May's utility function is U = C + 14D^1/22.5(H +J)², where C is dollars spent on goods other than housecleaning, D is the number of hours per day that somebody spends cleaning her house, H is the number of hours per day May spends cleaning her house, and J is the number of hours per day May spends working at her job.All May's income comes from her job.She can work as many hours a day as she wishes at a wage of $7 an hour.
a.If she cannot hire anyone to do her housecleaning, how many hours will she spend on the job and how many hours will she spend housecleaning?
b.If she can hire a housecleaner at $5 an hour, how many hours will she work on her job, how many hours of housecleaning will she hire, and how many hours will she clean house?

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Definitions:

Output

The total amount of goods and services produced by an economy over a specific period.

Levels

Levels refer to the different positions or stages in a hierarchical structure or process, indicating varying degrees of magnitude, importance, or progress.

Efficient Scale

The level of production that minimizes long-term average total costs, resulting from economies of scale without incurring diseconomies of scale.

Marginal Cost

The supplementary cost attached to the output of an additional product or service unit.