Most developed countries prohibit employers from paying wages below some minimum level w. This is an example of a price floor in the labor market — and the policy has an impact in a labor market so long as w > w∗ (where w∗ is the equilibrium wage in the absence of policy-induced wage distortions.)
A. Suppose w is indeed set above w∗, and suppose that labor supply slopes up.
(a) Illustrate this labor market—and the impact of the minimum wage law on employment.
(b) Suppose that the disequilibrium unemployment caused by the minimum wage gives rise to more intense effort on the part of workers to find employment. Can you illustrate in your graph the equilibrium cost of the additional effort workers expend in securing employment?
(c) If leisure were quasilinear (and you could therefore measure worker surplus on the labor supply curve), what’s the largest that deadweight loss from the minimum wage might become?
(d) How is the decrease in employment caused by the minimum wage (relative to the non-minimum wage employment level) related to the wage elasticity of labor demand? How is it related to the wage elasticity of labor supply?
(e) Define unemployment as the difference between the number of people willing to work at a given wage and the number of people who can find work at that wage. How is the size of unemployment at the minimum wage affected by the wage elasticities of labor supply and demand?
(f) How is the equilibrium cost of effort exerted by workers to secure employment affected by the wage elasticities of labor demand and supply?
B. Suppose that labor demand is given by ℓD = (A/w)α and labor supply is given by ℓS = (Bw)β.
(a)What is the wage elasticity of labor demand and labor supply?
(b)What is the equilibrium wage in the absence of any distortions?
(c) What is the equilibrium labor employment in the absence of any distortions?
(d) Suppose A = 24,500, B = 500 and α = β = 1. Determine the equilibrium wage w∗ and labor employment ℓ∗.
(e) Suppose that a minimum wage of $10 is imposed. What is the new employment level ℓA — and the size of the drop in employment (ℓ∗ −ℓA)?
(f ) How large is unemployment under this minimum wage — with unemployment U defined as the difference between the labor that seeks employment and the labor that is actually employed at the minimum wage?
(g) If the new equilibrium is reached through workers expending increased effort in securing employment, what is the equilibrium effort cost c∗?
(h) Create a table with w∗, ℓ∗, ℓA, (ℓ∗−ℓA),U and c∗ along the top. Then fill in the first row for the case you have just calculated—i.e. the case where A = 24,500, B = 500 and α = β= 1.
(i) Next consider the case where A = 11,668, B = 500, α = 1.1 and β = 1. Fill in the second row of the table for this case — and explain what is happening in terms of the change in wage elasticities.
(j) Finally, consider the case where A = 24,500, B = 238.1, α = 1 and β = 1.1. Fill in the third row of the table for this case — and again explain what is happening in terms of the change in wage elasticities.