Martina Has the Following Utility Function: U(C, L)= (CL)^1/2 where

question 44

Essay

Martina has the following utility function: U(C, L)= (CL)^1/2 where C is the quantity of goods consumed and L is the number of hours of leisure. Martina requires eight hours of rest each day. Therefore she has 16 hours available for work. Let H be the number of hours employed such that H = 16 - L. Let P be the price of C and W be the hourly wage.
i)Assume she is required to pay an income tax of T = 0.3( Y - 60)where Y is her pretax income. How many hours per day will she work at P = $1 and W = $10?
ii)Assume there is no income tax but her terms of employment change. She is now paid time and a half for work in excess of 6 hours per day. How many hours per day will she choose to work at P = $1, W = $10, and overtime of W' = $15?

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Definitions:

Shift Right

In economic terms, a shift to the right of a demand or supply curve represents an increase in demand or supply.

Remaining Firms

The number of businesses that continue to operate in a market after others have exited, often in response to economic conditions or competitive pressures.

Demand Curve

A graphical representation showing the relationship between the price of a good and the quantity demanded by consumers at those prices.

Long-Run Equilibrium

A state in a market where all firms are making zero economic profit, input factors are fully adjustable, and no firm has an incentive to enter or exit the market.