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:

Economic Value

The total value that an asset generates, encompassing both current and future benefits.

Useful Life

The estimated duration over which an asset is expected to be functional and economically useful.

Value-Based Pricing

A pricing strategy that sets product or service prices based on the perceived value to the customer rather than on the cost of production.

Operating Cost

Expenses associated with running a business's core operations, typically including costs of goods sold, labor, and overhead.