Suppose you have 60 hours of leisure that you could devote to work per week, and suppose that you can earn an hourly wage of $25.
A: Suppose the government imposes a 20% tax on all wage income.
(a) Illustrate your weekly budget constraint before and after the tax on a graph with weekly leisure hours on the horizontal and weekly consumption (measured in dollars) on the vertical axis. Carefully label all intercepts and slopes.
(b) Suppose you decide to work 40 hours per week after the tax is imposed. How much wage tax do you pay per week? Can you illustrate this as a vertical distance in your graph?
(c) Suppose that instead of leisure hours on the horizontal axis, you put labor hours on this axis. Illustrate your budget constraints that have the same information as the ones you drew in (a).
Assume again that the leisure endowment is 60 per week.
B: Suppose the government imposes a tax rate t (expressed as a rate between 0 and 1) on all wage income.
(a) Write down the mathematical equations for the budget constraints and describe how they relate to the constraints you drew in A(a).
(b) Use your equation to verify your answer to part A(b).
(c) Write down the mathematical equations for the budget constraints you derived in B(a) but now make consumption a function of labor, not leisure hours. Relate this to your graph in A(c).