Problem 1

Consider the model of labor supply. This problem examines the effects of unemployment benefits, which give an individual an amount b if he does not work (leisure l = h, labor N = 0), but nothing if he works any number of hours (b = 0 if N >0). Suppose that workers in the population have different preferences for consumption and leisure (varying MRS’s), and analyze the following using a static model.

1. Show graphically the budget constraint of workers
2. Show that depending on MRS’s some workers are not affected by unemployment benefits while some workers might decide not to work
3. Show graphically how suppressing unemployment benefits (b = 0)

1. affects the consumption/leisure decision of individuals with different preferences (MRS’s).
2. impacts on aggregate labor supply (think about the extensive margin and the intensive margin)

Problem 2

This problem examines the effect of consumption taxes on labor supply. Consider a consumer with utility function:

We assume there are no lump-sum taxes and no dividend income: \(\pi \) = T = 0. We assume h = 1 and the wage rate w = 1. There is a consumption tax such that for each purchased unit of consumption, the consumer needs to pay 1 + t units where t goes to the government. The consumer budget constraint is:

1. What is the opportunity cost of leisure? Precisely, if leisure increases by 1 unit, by how much must consumption decrease to satisfy the budget constraint of the consumer?
2. What is the optimality condition of the consumer? Hint: the optimality condition seen in lecture needs to take into account the consumption tax (there should be a t somewhere).
3. Calculate consumption c, leisure l and labor supply N ^s of the consumer as a function of t.
4. What is tax revenue?
5. In the US, the average tax rate (cf. lecture) is about 40%. Assume the government decides to increase taxes to 50%. What would be the effect of this reform on tax revenue?
6. The government increases taxes to 80%. What is the effect of this reform on tax revenue?
7. Give a brief interpretation of the difference between 5 and 6.

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Solution: The downloadable solution consists of 9 pages, 752 words and 4 charts.
Deliverable: Word Document