Question

The employment of teaching assistants (TAs) by major universities can be characterized as a monopsony. Suppose the demand for TAs is \(W=30,000-125 n\) where \(W\) is the wage (as an annual salary) and \(n\) is the number of TAs hired. The supply of TAs is given by \(W=1000+75 n\) a. If the university takes advantage of its monopsonist position, how many TAs will it hire? What wage will it pay? b. If, instead, the university faced an infinite supply of TAs at the annual wage level of \(\$ 10,000,\) how many TAs would it hire?

Short answer

a. Under monopsony, the university hires 238 TAs and pays each a wage of \$17,950 per year. b. With an infinite supply at \$10,000, the university hires 160 TAs.

Step-by-step solution

Find the quantity and wage under monopsony

Under monopsony, the university hires where marginal cost of labor (MCL) equals the marginal benefit of labor (MBL). The MBL is represented by the demand function for labor, \(W=30,000-125 n\). MCL is derived from the supply function (the wage equals the average cost of labor) by taking the derivative of the supply function \(W=1000+75 n\). The derivative is \(75\). Equating MBL and MCL gives the equation: \(30,000 - 125n = 75\)

Solve for the number of TAs hired under monopsony

Solving the equation \(30,000 - 125n = 75\) for \(n\) gives the number of TAs the university hires from the market. The solution is \(n = 238\).

Find the wage paid under monopsony

Substitute \(n\) back into the supply equation to find the wage the university pays under the monopsony condition. The solution is \(W = 1000+ 75*238 = \$17950\).

Calculate the number of TAs hired under an infinite supply

Under a condition of infinite supply at a wage of \$10,000, the university hires until the wage equals the marginal benefit of labor. Solving the equation \(30,000 - 125n = 10,000\) yields the result \(n = 160\).

Key concepts

Understanding Marginal Cost of Labor

In the context of a monopsony, the marginal cost of labor (MCL) plays a crucial role. A monopsony is a market condition where there is only one buyer for a particular type of labor. The university in this exercise is the monopsonist hiring teaching assistants (TAs). The MCL represents the additional cost the university incurs when hiring an additional TA.

In this instance, the supply function, which is given as \(W = 1000 + 75n\), informs us of the wage necessary to attract \(n\) number of TAs. By taking the derivative of this supply function with respect to \(n\), we determine that the MCL is \(75\). This derivative indicates that for each additional TA the university hires, the wage it effectively pays increases by \($75\).

Understanding this principle helps us realize why the university does not simply hire as many TAs as possible under monopsony conditions. Instead, it balances the costs and benefits by setting MCL equal to the marginal benefit of labor (MBL). This ensures that hiring additional workers doesn't cost more than the benefit they bring.

Exploring Marginal Benefit of Labor

In a monopsony scenario, the marginal benefit of labor (MBL) is derived from the demand function for labor. Here, it is represented by the formula \(W = 30000 - 125n\). This equation demonstrates how much an employer, like the university, values the added productivity brought by each additional TA.

The important task for a monopsonistic employer is to find the point where MCL equals MBL. This equilibrium indicates the most efficient number of TAs to hire that maximizes the university's benefit without incurring unnecessary costs. In the exercise, setting the MCL (found by taking the derivative of the supply function to be 75) equal to the MBL equation \(30000 - 125n\) allows the university to determine that it should hire 238 TAs.

Understanding the MBL helps students grasp how demand affects wages and employment decisions in a monopsony. It highlights how an employer assesses each worker's contribution relative to their cost.

Supply and Demand in Monopsony

The traditional laws of supply and demand take on unique characteristics in a monopsony. In most markets, multiple employers vie for workers, balancing supply and demand. However, in a monopsony, a single employer significantly influences both aspects.

The supply curve for labor is offered by the equation \(W = 1000 + 75n\), showing the wage required to attract a certain number of TAs. Conversely, the demand curve reflects the university's willingness to pay based on its perceived necessity of labor, \(W = 30000 - 125n\).

In a competitive market, equilibrium is where the supply and demand functions intersect, determining employment levels and wage rates. In a monopsony, however, the employer manipulates this equilibrium by hiring fewer workers at lower wages. This is visible when comparing the monopsony's hiring decisions with an infinite supply scenario, where the university hires only up to the point where the wage equates to its perceived marginal benefit of labor.

By examining supply and demand from a monopsony perspective, students can see how monopsonies strategically set wages and labor levels to their advantage, contrasting sharply with perfectly competitive markets.