Question A:
Tatum is a mother of Anny (1 year old). Tatum derives utility from income Y (i.e. a disposable income that she can spend on consumption goods other than childcare) and leisure L according to the utility function U(Y,L)=Y*L . She has non-labour income of $200 per day. Her time endowment is 16 hours per day that can be spent either on Leisure (which mostly consists of caring for Anny) or labour market work. If Tatum works she has to leave Anny in the child care. Tatum’s wage is $20 per hour, while the childcare cost $5 per hour. Tatum only uses childcare when she works.

What is Tatum’s reservation wage? Round your answer to the first decimal point.

Question B:

Staying with the scenario in QA.  Compute how many hours Tatum will work under these circumstances. Round your answer to the first decimal point.

Question C:

Stay with the scenario in QA .  Now suppose the government introduces the childcare subsidy that covers 100% of childcare costs of working parents. How many hours will Tatum work under the new policy? Round your answer to the first decimal point

a)In labor economics, the reservation wage is the lowest wage rate at which a worker would be willing to accept a particular type of job. An individual's reservation wage may change over time depending on a number of factors, like changes in the individual's overall wealth, changes in marital status or living arrangements, length of unemployment, and health and disability issues.

Reservation wage is solved by evaluating the MRS at the endowment point if the person is not working.

Here MRS= Y/L = 200/16 = 12.5

Here Tatum would have to spend $5 on child care per hour is she works therefore her reservation wage would be $12.5 + $5= $17.5

b) 16= Y + L (her time constraint)

Budget constraint here would be C= 20Y+200(NLY)-5Y

=15Y+200

Y-hours worked

NLY- non-labour income

The slope of the budget constraint will be -15

and as per the utility function U=Y*L

MU_L/MU_Y = Y/L

At optimum point Y/L = 15 which makes Y=15L

Putting this value in time constraint we'll get L=16/16= 1 hr

the remaining 15 hrs would be spent on work

c) Now since the government has subsidized the child care by 100% the budget constraint here would be

Budget constraint : C= 20Y+NLY

This would make the slope equal to -20

and Y= 20L

putting this value in 16=Y+L

would give 16=21L:

L=0.8 hrs

and the reaming hrs that is 15.2 would go in working.