This problem examines the effect of consumption taxes on labor supply. Consider a consumer with utility function:
U(c, l) = c+ 0.5 logl
We assume there are no lump-sum taxes and no dividend income: ? = 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 +t)c+l = 1
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 Ns 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 e?ect of this reform on tax revenue?
7. Give a brief interpretation of the di?erence between 5. and 6.
Consider the model of labor supply of Chapter 4. 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 a?ected by unemployment bene?ts while some workers might decide not to work
3. Show graphically how suppressing unemployment bene?ts (b = 0)
(a) affects the consumption/leisure decision of individuals with di?erent preferences (MRS's).
(b) impacts on aggregate labor supply (think about the extensive margin and the intensive margin)