problem 1: Consider an individual facing a wage rate w. There is a total of 100 hrs available for work or leisure in a week.

a) Represent his budget constraint graphically.
b) Represent the effect of a reduction in the wage rate.
c) Represent the effect of a proportional tax on the labor income.
d) Assume that the individual should pay a 10$ per week in taxes, regardless of how much he works. How does this influence his budget constraint?

problem 2: Assume that the wage rate is w = 1. An agent is working 6 hrs per day and consumes 5 units of goods per day. Assume that the agent claims to be indifferent between his current situation and working one more hour in exchange for two additional units of consumption. Is this agent maximizing is utility? Why? Should he be working more hours? Or fewer?

problem 3: Draw an indifference curve for the consumption and hours of work.

problem 4: Assume, as in the federal income tax code for the United States, that the representative consumer faces a wage income tax with a standard deduction. That is the representative consumer pays no tax on wage income for the first x units of real wage income, and then pays a proportional tax t on each unit of real wage income greater than x.

Thus, the consumer’s budget constraint is given by c = w(h - 1 + (Pie) if w(h - 1) ≤ x, or c = (1-t) w(h-1) + tx +(pie) if w(h-1) ≥ x. Now, assume that the government decreases the tax deduction x. By using diagrams, find out the effects of this tax change on the consumer and elucidate your results in terms of income and substitution effects. Make sure that you consider two cases. In the first case the consumer doesn’t pay any tax before is x reduced, and in the second case the consumer pays a positive tax before x is reduced.