Question

2. There are two individuals: John and Zak. Use the information below to answer (a) – (b): Wage function for both is given by W = A²ln(E) where E is education and A is ability. John's ability is 1000 and Zak’s is 2000. Additionally, they face the same cost function given by C = 500EA.

   1. a) What is E* and W* for John and Zak?

   2. b) Why will John not get more E than E*? Explain by comparing MB_E and MC_E

Answer 1

a)

We are given that

W=A²ln(E)

MBE=dW/dE=A²/E

C=500*E*A

MCE=dC/dE=500*A

Now take the case of John, A=1000

MBE=1000^2/E=1000000/E

MCE=500*A=500*1000=500000

Set MBE=MCE for optimal level of E

1000000/E=500000

E*=2

W*=A²ln(E)=1000^2*ln(2)=$693,147.18

Now take the case of Zak, A=2000

MBE=2000^2/E=4000000/E

MCE=500*A=500*2000=1000000

Set MBE=MCE for optimal level of E

4000000/E=1000000

E*=4

W*=A²ln(E)=2000^2*ln(4)=$5,545,177.44

b)

If John gets more E than E* say 3.

MBE=1000000/3=333333.33

MCE=500000

We observe that MBE<MCE at a higher level of E.It means that there is a negative addition to net benefit. So, John will not try to get E which is more than E*(optimal level of E)