Consider an individual whose preferences are: u(c, 1 l) = ln(c) + ln(100 l). First, take 4, say number N. The weight on leisure (the parameter ) is equal to 2+(N/5). Next, consider 44 and add $20, that would be your hourly wage.

(a) What is the optimal labor and consumption in the absence of any taxes or transfers?

(b) Suppose now that the government introduces a progressive tax schedule. The first $500 of income are taxed at 20%, and any additional income above $500 is taxed at (40+N) percent, where N is 4. What is the impact of such a policy on this individual's consumption and hours worked?

(c) What is the total amount of taxes paid by this individual? What are the average and the marginal tax rate that this individual faces?

(d) Compare this policy with a policy where this individual faces a proportional tax equal to the average tax you calculated in part (c).