Question

Suppose that Marta's hourly wage is $20 per hour, her rental property yields $100 per day, and she has 16 hours in a day to allocate between leisure and work.

a. What is her daily budget constraint? Draw it in a diagram.

b. How much can Marta consume if she enjoys 16 hours of leisure?

c. Suppose that the government imposes a 25% income tax. What is her budget constraint now? n the same diagram, using a dashed line, draw the new budget constraint.

d. What happens if the government sets the tax rate to zero on unearned income and on the first $120 of her earnings, but imposes a 25% tax for each dollar earned more than $120? In a new diagram, draw her original (from part (a)) and her new budget constraint.

Answer 1

a)

Rental Income(R) = $100

Hourly wages(w) = $20

Total Time(T) = 16

Maximum labor income that can be earned = 16*$20 = $320

Total Income = $320 + $100 = $420

Let consumption = c and leisure = l

Hence c = w*(T-l) + R, This implies that consumption is equal to labor income plus rental income

c + wl = wT+R. This implies that price of leisure is w.

On the horizontal axis we measure leisure( the maximum of which can be 16) and on the vertical axis we measure consumption (the maximum of which can be $420)

Her budget line is given by ABC

b)

If she enjoys 16 hours of leisure, it means that she works for 0 hours. Hence wage income equals 0. Total Income is 0+rental Income = $100. Hence consumption = $100

c)

If 25% income tax is imposed.

Her rental Income(R) now is 100 - 25% of 100 = $75

Her wage income will also be taxed at 25%. So if she works for 16 hours. Her wage income is 16*20 = $320. After tax wage income is $320 - 25% of 320 = $240

Total Income after tax = $240+$75 = $315. Which gives us the new vertical intercept.

Thus new budget line is DEC (shown in diagram in part a)

d)

Rental Income is untaxed and is $100

She will get earning of $120 if she works for 6 hours (and thus consumes leisure for 10 hours). It will also be untaxed. Hence till 6 work hours, her new budget line will coincide will the old budget line.

After 6 work hours, her earning will be taxed at 25%. So if she decides to work for 16 hours.

Her wage earning: for first six hours = 6*20 = $120. For next 10 hours = 10*20 = $200. It will be taxed at 25%. Hence net earning for next 10 hours $200-25% of $200 = $150. Total wage earning = $120+$150 = $270

Total Income = $270+$100 = $370. Which is the new vertical intercept.

Her new budget line will be EDBC.

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