Human Capital Externalities

Consider the 2-period model of educational choices

discussed in class. Consider the case in which there are

no credit constraints

and use

exactly the same notation as in the notes. Assume that the educational production

function is

f

(

S

) = 1 + ln (

S

)

and that the cost function is

C

(

S

) =

c

S

. Under the

assumption that individuals use schooling choices to maximize the present value of

their "cash-on-hand", answer the following questions:

(a) Derive mathematically the marginal-cost and marginal-benefit curves of educa-

tion, then draw them in a clearly labeled figure and show

graphically

the optimal

level of schooling.

(b) Derive

mathematically

the optimal level of schooling and discuss the factors that

influence its level.

(c) Now suppose that a policy maker realizes that

individual

schooling choices have

an effect on

societal

outcomes, such as aggregate productivity or aggregate health

outcomes. Economists call such effects "Externalities". Let the societal benefit

of the individual choice of schooling

S

be captured by the function

B

(

S

) =

b

S

for some positive constant

b

. (you may think of

B

as a measure of aggregate

productivity, and the function

B

(

S

)

be a schedule of how individual choices aect

this measure). Assume that the objective of the policy maker is that individuals

choose a level of schooling that maximizes the individual cash-on-hand (as in parts

(a) and (b))

plus

the discounted value of the benefit

B

(

S

)

that materializes in

the second period.

1. Write down a mathematical expression for this sum.

2. Repeat part (a), but now using the objective of the policy maker, which

includes the schooling externality in period 2.

3. Repeat part (b), but now using the objective of the policy maker, which

includes the schooling externality in period 2.

4. Compare the optimal level of schooling derived in (b) with the optimal level

of schooling derived in (c)-(iii). Is the schooling level preferred by the pol-

icy maker smaller, larger or identical to the schooling level preferred by the

individual?

5. Can you think of a policy that aligns the interests of the policy maker in terms

of optimal schooling levels with the interests of the individual? Be specific.