Consider an economy with production function given by Y = AK0:5L0:5 where A is the total factor productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is xed and equal to 1. Assume A=100. a. Write the rm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage. b. Assume labor supply is inelastic and xed at L = 100. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph. c. Suppose the economy faces a positive productivity shock and TFP is now A=200. Display graphically the new labor demand function. What are the equilibrium values of employment and the real wage? d. Compute the total output when A=100 and when A=200. What is the output's growth rate? Compare that growth rate with the growth rate in A. How does the growth rate of output per capita compares to the growth rate in A? Explain carefully. e. Now, suppose that Congress, concerned about the welfare of the working class, passes a law setting the minimum wage that is 10 percent above the equilibrium wage you just derived (in the case where A = 100). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the e ects of this law? Speci cally, calculate what happens to the real wage, the employment, the output, and the total amount earned by workers. f. Does Congress succeed in its goal of helping the working class? Explain. g. Do you think the analysis provides a good way of thinking about a minimum-wage low? Why or
Consider an economy with production function given by Y = AK0:5L0:5 where A is the total factor
productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is
xed and equal to 1. Assume A=100.
a. Write the rm's problem of choosing labor
of the real wage.
b. Assume labor supply is inelastic and xed at L
= 100. Find the equilibrium values of the wage
and the employment level for this economy. Display graphically the labor supply and the labor
demand
c. Suppose the economy faces a positive productivity shock and TFP is now A=200. Display
graphically the new labor demand function. What are the equilibrium values of employment and
the real wage?
d. Compute the total output when A=100 and when A=200. What is the output's growth rate?
Compare that growth rate with the growth rate in A. How does the growth rate of output per
capita compares to the growth rate in A? Explain carefully.
e. Now, suppose that Congress, concerned about the welfare of the working class, passes a law
setting the minimum wage that is 10 percent above the equilibrium wage you just derived (in
the case where A = 100). Assuming that Congress cannot dictate how many workers are hired
at the mandated wage, what are the e ects of this law? Speci cally, calculate what happens to
the real wage, the employment, the output, and the total amount earned by workers.
f. Does Congress succeed in its goal of helping the working class? Explain.
g. Do you think the analysis provides a good way of thinking about a minimum-wage low? Why or
why not?
Production function : Y = A K0.5L0.5
Where , A = 100
Optimal labor demand is at the point where the value of the marginal product of labor is equal to the wage rate.
VMP(L) = Output Price * Marginal Product of Labor
Let the output price be 'p'.
Real wage(w)=W/P
So at optimum labor demand
MPPL=W/P
MPPL=w
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