Econ 190 / Wednesday, April 26, 2006
1. Consider a labor market where the labor demand and supply curves are given by the equations:
Demand: wD = 30 - 0.04E
Supply: wS = 0.05E - 15
a. Calculate the equilibrium wage, employment level, and unemployment rate.
To calculate the equilibrium wage and employment level, the quantity of labor supplied must be equal to the quantity of labor demanded. In other words,
The equilibrium employment level E* = 500. To solve for the equilibrium wage rate, E* = 500 can be substituted into either the labor demand or labor supply equation.
Therefore, the equilibrium wage rate is w* = $10. By definition, since ES = ED, there exists no unemployment. The other way to determine the unemployment rate is by using the following formula:
b. Suppose the government imposes a payroll tax of $9 per labor unit on the employer. Calculate the new equilibrium wage and employment level. What is the new per-unit cost of labor to the firm? What percentage of the tax is ultimately paid by the workers? What percentage is paid by the firm? Would the result have been different if the tax were instead imposed on the employee? If so, how?
If the government imposes a payroll tax, the demand curve for labor will shift left. The easiest way to think of how this influences the problem mathematically is that the original vertical intercept of 30 shifts down by the amount of the tax, or 9 units. Thus, the new labor demand equation is:
wD = 30 - 0.04E – 9 = 21 – 0.04E
Equilibrium is determined in the same manner as before:
The new employment level is solved by substituting E = 400 into either the demand or supply equation:
The firm pays $5 to the worker and an additional $9 to the government in the form of a tax, which implies the cost of one unit of labor is now $14.
Of the original $9 tax, 5/9 = 55.56% is paid by the worker in the form of lower wages (wages decreased by $5 from $10 to $5), and 4/9 = 44.44% is paid by the firm in the form of higher per-unit labor costs (the cost of labor increased by $4 from $10 to $14).
If the tax were instead imposed on the worker, the result of sharing the tax burden 55.56% (for the worker) and 44.44% (for the firm) would have been identical.
c. Using the original labor supply and demand functions, calculate the unemployment rate (in the absence of the tax from part (b)) if the government were to impose a minimum wage of $12.
If the government implements a minimum wage of $12, wS = 12 = 0.05E-15 à 27 = 0.05E à ES = 540. On the demand side of the market, wD = 12 = 30 – 0.04E à 0.04E = 18 à ED = 450. The unemployment rate is then:
In other words, 16.67%, or 90 of the 540 workers seeking jobs, will be unable to find one at the minimum wage of $12.
2. Suppose a firm is a perfectly discriminating monopsonist. The government imposes a minimum wage on this market. What happens to wages and employment (Chapter 5, Problem 5)?
w Smin w
w*
D
ED E* ES E
Recall that a perfectly-discriminating monopsonist hires up to the point where quantity of labor supplied is equal to the quantity of labor demanded, or at the intersection of the labor supply and demand curves. It hires the same number of employees as a perfectly competitive firm, E*, but it pays only the last worker hired the same wage as a perfectly competitive firm, w*. All other workers are paid their reservation wage, w < w*. In the absence of a minimum wage, there is no unemployment.
If the government imposes a minimum wage on a perfectly-discriminating monopsonist, the number of workers the firm is willing to hire, ED, is less than the number of workers willing to work at the minimum wage, wS. Thus, unemployment will exist. Workers who are able to secure jobs will enjoy a wage increase from their minimum wage to the minimum wage. Unlike in the absence of a minimum wage, all workers are paid the same rate now.
The only difference between this scenario and a perfectly competitive firm is that prior to the imposition of the minimum wage, only the E*th worker hired by this firm is paid the perfectly competitive wage, w*. The minimum wage outcome is identical for this firm and in a perfectly competitive framework.
3. What happens to wages and employment if the government imposes a payroll tax on a non-discriminating monopsonist? Compare the responses in the monopsonistic market to the responses that would have been observed if the market were competitive (Chapter 5, Problem 6).
w MCS
wPC1
wPC2
wM1
wM2
D’ D
EM2EM1EC2EC1 E
A non-discriminating monopsonist faces a marginal cost (of employment) curve that is not equal to its labor supply curve. More specifically, MC > S. The profit-maximization strategy for a non-discriminating monopsonist is to continue hiring workers until MCE = VMPE, producing an outcome of (EM1,wM1), where wM1 is determined from the supply curve, not MCE. Note that originally, EM1 < EC1 and wM1 < wC1, where subscript “C” represents the perfectly competitive outcomes.
A monopsonist originally paying wM1 for EM1 workers will now be willing to pay a lesser wage so as to absorb the cost of the tax, as well as the employment costs, and not be worse off than before the tax was imposed. This causes a leftward shift of the demand curve. The new intersection of demand and either the supply or marginal cost curve suggests that both the monopsonist and a perfectly competitive firm will demand fewer workers. Both will also pay less. Note here that the new perfectly competitive outcome (in the presence of the tax) is still better than the monopolistic outcome, where EM2 < EC2 and wM2 < wC2.