Question

Simon, who lives in Little Rock, AR, contemplates moving to Chicago, IL.

(a) Suppose that the discrimination factor in Little Rock is d = 0.25. How much does Simon earn if the value of his marginal product of labor is $10?

(b) Assume that the moving cost is $50,000 and the discount rate is 10%. How much should Simon earn in Chicago per hour in order to move? For simplicity, Assume that he works 8 hours a day, 22 days a week, and for 12 months, and lives forever.

(c) Suppose that Simon is paid at his marginal product of labor in Chicago. Will he move? Find the nepotism factor where he moves.

Answer 1

a)

Discrimination factor = d = 0.25

Value of marginal product = VMPL = $10

We know that w/*(1+d) = DVMPL

w*(1+0.25) = 10

w = $8

Simon's wage is $8/hour

b)

Moving cost = M = $450000

Discount rate = i = 10%

Working hours = 8*22*12 = 2112

If the wage is x

Savings in wage/year = (x-8)*2212

PW of salaries earned per year in perpetuity would be equivalent to M.

PW of perpetuity = [(x-8)*2212]/10% = 50000

(x-8)*2212 = 5000

x-8=2.260398

x=10.260398

Minimum wage that Simon would accept = $10.26/hour

c)
If a wage of $10 (i.e. VMPL) is offered, the offer would not be approved because it is less than the minimum appropriate wage measured in part b.
If nepotism factor is n,

Then x* (1-n) = 10

Or, 10.26(1-n) = 10

Or, n = 0.025

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