Question

While having lunch with his friend Mr. Howard Joel Wolowitz (Howie), Dr. Sheldon Cooper decided to explain to him that he makes more money not only because he has a PhD. but also because he is a “master.” Sheldon estimates that wages at the university can be approximated by W = Aln(E), where E is years of education and A is ability. Sheldon’s ability is 4,200 and Howie’s ability is 3,600. Furthermore, Sheldon calculates that the cost of obtaining schooling level E is given by C = 200E. Assuming that Sheldon’s estimation of the cost and benefitfunctions are correct, answer the following questions:

a. Calculate Sheldon’s and Howie’s years of education assuming Sheldon and Howie choose the level of education that makes them best off. (HINT1: Optimal schooling takes place where marginal benefit and marginal cost intersect.) (HINT2: The marginal benefit for the function form W = Aln(E), is A/E)

b. Calculate Sheldon’s and Howie’s wages when they obtain the level of education found in part a.

c. Calculate Sheldon’s wage if he had Howie’s education.

d. Explain why it is not optimal for Howie to get more education than he did.

e. Is it incorrect to interpret the difference in Howie’s and Sheldon’s wages as the return to education?

Answer 1

Cost function is given by

C=200E

Marginal Cost=dC/dE=200

So, W=A ln(E)

Marginal benefit of education=dW/dE=A/E

a)

In case of Sheldon

A=4200

Marginal benefit of education=dW/dE=4200/E

Set Marginal benefit=Marginal Cost

4200/E=200

E=21

Sheldon's optimal level of schooling is 21 years

In case of  Howie

A=3600

Marginal benefit of education=dW/dE=3600/E

Set Marginal benefit=Marginal Cost

3600/E=200

E=18

Howie's optimal level of schooling is 18 years

b)

W=A ln(E)

In case of Sheldon, E=21 and A=4200

W=A ln(E)=4200*Ln(21)=12786.99

In case of Howie, E=18 and A=3600

W=A ln(E)=3600*Ln(18)=10405.34

c)

In this case, E=18 and A=4200

W=A ln(E)=4200*Ln(18)=12139.56

d)

In case Howie goes for more education, Marginal benefit will be less than the marginal cost. Net marginal benefit will be negative.

e)

In this case, wage rate depends upon ability and years of schooling both. So, difference in both wage rates is due to combined effects of ability and schooling period. So, it is incorrect to interpret the difference in both wages as return to education.