# Economics 151 – The aggregate demand for labor curve

Subject: Economics    / General Economics
Question

Economics 151A

Problem Set 3

1. The aggregate demand for labor curve is , where w is the wage and a > 0 and b < 0. The aggregate labor supply curve by , where c > 0, d > 0, and a > c. Labor supply and demand are measured in hours.

a. Graph the labor market equilibrium, and solve for the equilibrium wage and number of hours, as functions of a, b, c, and d.

b. Congress is considering raising taxes to finance public health insurance. Under the Republican plan, workers would be taxed an amount t per hour worked. Democrats object to taxing workers, and instead propose taxing employers an amount t for each hour worked by an employee. Using graphs, show the effects of these alternative tax plans on wages and on employment.

c. Solve for the equilibrium wage and number of hours under each plan.

d. Which plan is better for workers? Show this explicitly.

e. If a = 10, b = -1, c = 0, and d = 1, calculate the deadweight loss from a payroll tax of 0.2.

2. A few years ago, the city of Santa Monica was considering enacting a living wage for hotel workers. Opponents argued that mandating a wage above the equilibrium wage level would increase hotel prices, lower demand for hotel rooms, and hence reduce employment of hotel workers. Proponents, however, introduced evidence that during the 1990’s, prices for hotel rooms increased and wages of hotel workers increased, yet over the same period the quantity of hotel rooms “sold” increased and hotel worker employment increased. They argued, based on this evidence, that the living wage law, even if did increase hotel prices, would not reduce hotel employment and would in fact be more likely to increase it. Evaluate the argument of the living wage proponents.

3. A labor economist estimates a regression of log earnings on schooling (S), experience (E), ability (A, as measured by IQ), and interactions between schooling and experience, and ability and experience, and obtains the following estimates (assume all estimates are statistically significant):

ln(Y) = 9.90 + .07?S + .03?E + .04?A ?.005?S?E + .008?A?E

Is this evidence more consistent with the human capital model, or the signaling model? Explain your answer.

4. A high school graduate is considering whether to attend college. He predicts that his earnings if she doesn’t attend college will be \$25,000 per year (real). He predicts that his earnings after four years of college will be \$37,000. Tuition costs are \$5,000 per year. Assume that college begins at age 18, and ends at age 22, and that he will work until age 65. (You will find it useful to use a spreadsheet program to solve this problem.)

a. Write out the equation used to evaluate the net benefit of a college education, for discount rate r.

b. If the discount rate is 5%, what is the value of the net benefit (which could be positive or negative) of a college education?

c. How does your answer change if the discount rate is 10%? Why?

d. Suppose the high school graduate estimates that his probability of dying in any year is .01 (so his probability of surviving is .99). How should the equation in part a be modified to account for this?

e. Recalculate the present value of the net benefit of a college education with the mortality risk assumed in part d.

f. Returning to parts a and b, suppose we assume that instead of working until age 65, the individual works forever. How can we calculate the net benefit of a college education? Do the calculation.

5. A high school student deciding about attending college predicts that his earnings without a college education will be \$30,000 per year (real). To decide whether college will be a good investment, he asks a number of his older brother’s friends, who have just complete college, how much they earn. He finds that, on average, their salaries are also \$30,000 per year, and based on this decides that it doesn’t make sense for him to invest in a college education.

a. Even if he and his brother’s friends are equal ability, explain why this may not be a good basis for making his educational investment decision. Does he likely overstate or understate the returns on investing in a college education?

b. What would be a better (if more complicated) strategy for figuring out whether a college education is a good investment?

6. Suppose that real earnings throughout the career are Ys for years of schooling s, and that workers work for n years after leaving school. If we use continuous compounding of interest, rather than annual, then the present value Vs of income with years of schooling s is

.

Similarly, with no schooling, earnings are Y0 and

.

a. Explain why we should expect Vs = V0.

b. Assuming Vs = V0, show that the following equation holds:

.

c. According to this model, if we estimate a regression of log earnings on years of schooling, what is the interpretation of the coefficient on years of schooling?