Econ 412 – Fall 2015

Problem Set 5 (Total 100 points)

2. (20 points, Do this in Excel) Is it worth going to college? Let’s suppose that a typical

college educated professional makes 85,000 dollars per year and a high school graduate

makes 45,000 dollars per year. The direct costs of college (tuition, books, and so on)

are 16,000 dollars a year (notice that a typical college degree would take 4 years). For

the purpose of this exercise, consider that the earnings are constant until the age of

64; and thereafter, the earnings are zero.

(a) Suppose that John is now eighteen, and he is contemplating on the possibility

of going to college, should he go? Use a discount rate of 10 percent for your

calculations. You should have 47 terms in the sum of the present value, one term

for each year that elapses between ages of 18 and 64.

(b) What is the internal rate of return ? Hint: Remember that the IRR is the rate

at which the net present value is zero, you may not be able to get the difference

(or error) to be exactly zero due “rounding error issues” in Excel. It is sufficient

to show that the net present value is close to a 1000 dollars.

(c) Now suppose that he is also a great football player. However, it is a risky sport,

and at most he can play until the age of 30. The contract that he can get is a

million dollars a year. What should he do? Show your calculations

3. (20 points, Oaxaca Decomposition ) Consider two earning functions, one for females

and another for males, of the following form: wm = ?m + ?msm and wf = ?f + ?f sf ,

where sg denotes the years of schooling of the gender g, and wg corresponds to the

earning of that gender.

Let’s denote the wage gap between females and males by ? ¯w so that ? ¯w = ¯wm ? w¯f .

Follow the steps from the lecture notes, and decompose the wage differential ? ¯w into

a portion that arises because these two groups have different skills, and a portion

attributable to labor market discrimination.

4. (20 points, A signaling model) Consider the model we learned in class where workers

can invest in education as a signal. There is a ? ? (0, 1) fraction of ’good guys’ with

high productivity xh, and (1??) of ’bad ones’ with low productivity xl

, where xh > xl

.

The total cost of acquiring an education level y is cly and chy (depending on the type

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of worker). Education serves as an education device, but it costs utility. In particular,

it is more expensive for the ’bad ones’ (ch < cl). The utility for a worker is given by

Ui = w ? ciy ?i ? H, L, where w is the wage.

We assume that the firm’s production function is linear in workers’ productivity. The

profit function is given by ?(x, w) = x ? w, where x is the productivity of the worker,

and w the wage.

(a) Draw a typical indifference curve for the ’bad’ guys and for the ’good’ guys.

(b) What wage will the firm offer if signaling is NOT possible?

(c) Suppose now that the workers can signal, under what conditions a pooling equilibrium

exist? What are the offered wages in a pooling equilibrium?

(d) Suppose now that the workers can signal, under what conditions a separating

equilibrium exist? What are the offered wages in a separating?

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