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Chapter 10: Problem 14

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

Expert verified
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

01

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: \(30,000 - 125n = 75\)
02

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 \(n = 238\).
03

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 \(W = 1000+ 75*238 = \$17950\).
04

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 \(n = 160\).

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Most popular questions from this chapter

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