problem) Consider an economy where the consumer has utility function that depends on consumption of apples c and leisure l

                                                                                    U(c l) = log c + A log l

The total time endowment of the consumer is T, this is allocated among leisure and hours worked. The government is taxing consumption of apples at tax rate τ_c, and labor income at tax rate τ_l. Thus to purchase 1 apple consumer has to pay 1 + τ dollars, and each hour of work increases consumer's incomeby (1 - τ_l)w. Suppose that consumer also has nonlabor income Π (dividends received) which are not taxed.

(a) prepare down the formula for total government revenue.

(b) prepare the two version of the budget constraint:one with l on income side, and then the one with l on expenditure side.

(c) prepare down the problem of the consumer, with l on expenditure side of the budget constraint.

(d) Relate the problem from part (b) to the consumer's problem from HW1, problem 1. What is p1, p2,M, A? Then use the formulas from HW1 for c^* ₁ ,c^*₂ to get the expressions for c^*, l^*

(e) Draw the budget constraint for the case Π = 0, τ_l = 0, τ_c = 0; put l on horizontal axis and c on vertical axis.

(f) Add a budget constraint of the consumer if  Π = 0, τ_l = 0,  but τ_c > 0.

(g) Show the substitution and the income effect of τ_c on the choice of c and l in your diagram.

(h) describe in words the substitution effect and income effects of an increase in τ_c.

(i) Suppose that there is a firm in the economy, producing output Y according to the production function Y = _zH^d where H^d is the total amount of hours that the firm demands. prepare down the problem of the firm that is maximizing profits Π (which are in equilibrium equal to dividends that the consumer receives).

(j) Suppose that the government collects taxes because it needs to finance a war on the other side of the world and needs to spend G on it. Define the competitive equilibrium for this economy with consumer, firm and government.

(k) How would you change this definition if instead G was spent on public goods like defense or highways?

(l) How would you change this definition if instead G was spent on Research & Development that makes workers more productive?

problem) Go to the webpage of the Congressional Budget Offce (CBO) www.cbo.gov/publication/42729 and download the xls file under "Data Underlying Select Figures" link. Use the data available there to do the following:

(a) Reproduce Summary from page XIII and from page 3 in the report www.cbo.gov/sites/default/_les/cbo_les/attachments/10-25-HouseholdIncome.pdf

(b) Use the data to create two pie charts similar to the ones we saw in the class, with shares of the five quintiles on total income, documenting income inequality. Do this for the year 2007 and the year 198x, where x is the last digit from your student ID number.

Bonus Problem.

The last problem on each HW was "data/practical" problem, all other problems were more "theoretical".

 (a) Which data/practical problem did you like the most and why?

 (b) Which theoretical problem did you like the most and why?

 (c) Which data/practical problem did you like the least and why?

 (d) Which theoretical problem did you like the least and why?