Question

Consider the following two scenarios
Original Scenario:
T = 80 hours
Wage = $20
Payroll tax = 20%
Under this original scenario, the worker maximizes their utility by choosing to leisure 30 hours a week (i.e. work 50 hours).

The government then proposes a new plan where everyone is given $300 each week as a supplement to their income. However, to pay for this $300 cash grant they increase the payroll tax to 50%. Thus...
Negative Income Tax Scenario:
T = 80 hours

Wage = $20

Payroll tax = 50%

Cash Grant = $300

(a) Graph the workers two scenarios on ONE graph. You will need to solve for and include the following values in your graph:

• Cmax under the original scenario AND the negative income tax scenario

• The true slope of the budget line in both the original AND negative income tax scenarios.

• In BOTH scenarios: The value of C if the worker leisures for 30 hours

• Finally, since you are TOLD that the optimal C-L bundle under the original scenario occurs at leisure =

  30 hours, correctly draw the indifference curve at that point.

Answer 1

The maximum consumption with the original line will be 80 hours*20$*80%= 80*20*0.8= 80*16=1280

The original budget line being(RED) y=1280-16*x (Consumption reduces by 16$ from maximum of 1280 with each increase in leisure or x axis)

Similarly for the new budget line, hourly rate after tax is 20$*50%=10$

so maximum= 300$+10$*80 hours= 1100$

Budget line(Blue) y=1100-10x but only uptil T=80 (It cannot go all the way to x-axis as total time T is 80 and leisure can't go past that)

Indifference curve will be a curve of which the red the original budget line is a tangent at the point (30,50*16) or (30,800)

Hope it helps, do ask for any clarifications