Homework Assignment 3
Due Tuesday, November 1, 2011
As always, points will be deducted if handed out late (7 points per day)
1. What follows is a slightly simplified version of the earned income tax credit (EITC) which
has become the largest income transfer program in the U.S. You will be asked to draw budget
constraints for an individual (with two children) with and without EITC.
Consider an individual whose only sources of income are labor and EITC. The market wage rate
for a person with this individual’s skills is $8.00 per hour. The individual is not subject to any
income or social security tax. The individual has 5,000 hours a year that could conceivably be
spent on wage earning activities (approximately the hours of an investment banker). If this
person’s annual wage income is less than $9,700, he (she) receives a subsidy of 40% of wage
income in the form of a tax credit from the federal government. If income is between $9,700 and
$12,700, the subsidy is $3880. For every dollar of wage income earned in excess of $12,700, the
tax credit is reduced by 20 cents.
a. Carefully draw a diagram that depicts this individual’s budget constraint between leisure and
after-tax annual income with and without the EITC. It is better to use graph paper to do this,
also draw a large graph.
b. What is opportunity cost of leisure in the absence of EITC program? Explain what happen to
the opportunity costs of leisure as you move along the EITC budget line and compare the
opportunity cost of leisure without the program to the opportunity costs of leisure with the
c. How would the income and substitution effects be different on each segment of the EITC?
d. Is the following statement true or not? Explain. The impact on hours worked of the EITC
program would depend in part on whether people consider leisure to be a normal or an
2. Suppose a country does not have a payroll tax and is considering imposing one, perhaps to
finance pensions of retirees.
a. Using isoquants and isocosts, explain what will happen to the mix of inputs used by
firms. Also explain what will happen to the demand for labor. (Assume that capital and
labor are neither perfect complements nor perfect substitutes).
b. Making use of isoquants and isocosts, explain what would happen to average and
3. Suppose the production function for a firm is Q =30*K*L. The Marginal Product of Labor is
30K, while the MP of capital is 30L..
a. If the wage rate is $10 per unit of labor and the rental rate of capital is $5 per unit of capital,
how much capital and labor should the firm employ in the long run to minimize the cost of
producing 37500 units?
b. Using the input prices described in b, what would the Fixed Cost, Total Cost, and Average
Total Cost of producing 37,500?
4. The domestic demand and supply for a good are Qd= 1450-100P and Qs= -125+125P.
a. Find consumption and production levels of equilibrium
b. Suppose the government though a production subsidy or allowing more imports brings the
price of the product down to $5 without causing a shortage. Estimate how much better off