Labor Economics: Theory

questions
abor income is a function of the year of schooling and following econometric model estimated:
lnYM = 10.5 + SM
lnYF = 9.4 + 0.7SF
where ln is the natural log, Y is income, S is the average year of the schoolings, and subscripts, M and F are
Male and Female respectively.
a. What is the coefficient of SM? And explain the economic meaning of the coefficient of SM.

b. Assume that the average years of schooling is 10 years for both men and women. With the given
information, analyze if there is any discrimination between men and women. Graphically show the two
equations and indicate the portion of discrimination
q2
Suppose that the production function is given as a function of two inputs, L and K, where L is the quantity of
labor and K is the quantity of capital, and expressed as below:
Q=65L-4L2 + 32K-2K2
The price of output is $10 per unit, the price of labor is $40 per unit, and the price of capital is $80 per unit
(note, P = 10, w = 40 and r = 80). Answer the followings.
a. Derive the equations for MPL and MPK.
b. Identify the equation of equality for cost minimization in this given example.
c. If 4 units of capital are hired, how many units of labor is to be hired to meet the condition of cost
minimization?
d. If 7 units of labor are hired, how many units of capital is to be hired to meet the condition of cost
minimization?
q3
Suppose that labor is the only input in a monopsony firm, and total factor cost, TFC and the production function
are given that:
TFC = 4L + 2L2 and Q = 32L – L2
Note that the output market is under a perfect competition and the price is $2 per unit and labor supply curve is
the average factor curve, AFC.
a. Derive the equations for labor demand and labor supply curves.
b. Derive the marginal factor cost curves.
c. Graphically show the curves you derived from #a and #b above.
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d. What are the employment level and wage rate at the profit maximization?
e. If the government imposes the minimum wage of $12, what will be the employment level?

Sample Solution

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