Question

Shows information from the supply curve for labor for a monopsonist, that is, the wage rate required at each level of employment. $$\begin{array}{l|l}\hline \text { Labor } & \text { Wage } \\\\\hline 1 & 1 \\\\\hline 2 & 3 \\\\\hline 3 & 5 \\ \hline 4 & 7 \\\\\hline 5 & 8 \\\\\hline 6 & 10 \\\\\hline\end{array}$$ a. What is the monopsonist's marginal cost of labor at each level of employment? b. If each unit of labor's marginal revenue product is \(\$ 13,\) what is the firm's profit maximizing level of employment and wage?

Short answer

The monopsonist's marginal cost of labor for each level of employment is 1, 2, 2, 2, 1, and 2 respectively. To maximize profit, the firm should employ workers until MRP ($13) equals MCL. Comparing the MRP to the calculated MCL values, the profit maximizing level of employment is 5 workers with a wage of $8 per worker.

Step-by-step solution

Interpret the table

The given table shows the number of labor units (workers) employed by the monopsonist and the corresponding wages required for each level of employment. For example, the wage required to employ 2 workers is $3 per worker. #Step 2: Calculate the marginal cost of labor at each level of employment#

Formula for Marginal Cost of Labor

The Marginal Cost of Labor (MCL) is the additional cost incurred by the employer when employing an additional worker. To calculate the MCL for each level of employment, use the following formula: \[ MCL = \frac{\Delta Total \thinspace Cost}{\Delta Labor} \] where \(\Delta\) represents the change in a variable.

Calculate MCL

Calculate the MCL at each level of employment using the given table and the MCL formula: (Notice that for the first worker, MCL = Wage, as there is no previous worker to compare to) 1. \( MCL_1 = 1 \) 2. \( MCL_2 = \frac{(3 - 1)}{(2 - 1)} = 2 \) 3. \( MCL_3 = \frac{(5 - 3)}{(3 - 2)} = 2 \) 4. \( MCL_4 = \frac{(7 - 5)}{(4 - 3)} = 2 \) 5. \( MCL_5 = \frac{(8 - 7)}{(5 - 4)} = 1 \) 6. \( MCL_6 = \frac{(10 - 8)}{(6 - 5)} = 2 \) So, the marginal cost of labor at each level of employment is 1, 2, 2, 2, 1, and 2 respectively. #Step 3: Find the profit maximizing level of employment and wage#

Formula for Profit Maximization

To maximize profit, the firm should continue to employ workers until the marginal revenue product of labor (MRP) equals the marginal cost of labor (MCL). In this case, MRP is given as $13.

Compare MRP and MCL

Compare the MRP to the calculated MCL values: 1. At the 1st worker, MRP ($13) > MCL (1) 2. At the 2nd worker, MRP ($13) > MCL (2) 3. At the 3rd worker, MRP ($13) > MCL (2) 4. At the 4th worker, MRP ($13) > MCL (2) 5. At the 5th worker, MRP ($13) > MCL (1) 6. At the 6th worker, MRP ($13) < MCL (2)

Determine Profit Maximizing Employment and Wage

Since the 6th worker has an MCL of 2, which is higher than the MRP of \(13, the monopsonist would stop employing additional workers at that point. So, the profit maximizing employment level is 5 workers with a wage of \)8 per worker.

Key concepts

Marginal Cost of Labor (MCL)

Understanding the Marginal Cost of Labor (MCL) is crucial in labor economics, particularly for monopsonists who are the sole purchasers of labor in a market. MCL represents the additional cost an employer incurs to hire one more worker.

It's important to differentiate between the wage rate and the marginal cost of labor. The wage rate is the amount paid to each worker, while MCL takes into account not just the wage of the additional worker but also any increases in previous workers' wages that may occur as a result of hiring more labor. This concept is consistent with the law of supply and demand, where increasing demand for workers leads to higher wages.

In the example exercise, we see that the MCL fluctuates with each additional worker hired. For instance, the MCL increases to 2 when hiring the second worker, as the wage jumps from 1 to 3. However, it's worth noting that hiring the fifth worker only increases the total cost by 1, making it an outlier compared to the cost increments for other workers. This could reflect a unique scenario in the labor supply where a certain worker might accept a smaller wage increase.

The calculation of MCL is vital for monopsonists to understand labor costs, particularly when considering the profit-maximizing level of employment. A well-calibrated understanding of MCL can significantly affect a firm's hiring strategy and its bottom line.

Marginal Revenue Product (MRP)

The Marginal Revenue Product (MRP) is a critical concept for firms, especially in monopsonistic markets. It represents the additional revenue a firm generates by employing one more worker. For a business, knowing the MRP is essential to ensure that the cost of hiring an extra employee does not exceed their contribution to the company's revenue.

The MRP is calculated by taking the extra output produced by the additional worker and multiplying it by the market price of that output. This figure helps the firm decide how many workers to employ. If the MRP is greater than or equal to the MCL, it makes economic sense for the company to hire more workers; if it's lower, hiring additional workers would not be cost-effective.

In our exercise, the MRP is constant at $13 for each unit of labor. This simplifies the analysis as it allows for direct comparison with MCL to find the optimal employment level. Typically, however, MRP would decrease as more workers are hired due to the Law of Diminishing Returns, which states that adding more of one factor of production, while holding others constant, will at some point yield lower per-unit returns.

Profit Maximizing Employment

Profit maximizing employment is a fundamental goal for businesses looking to optimize their workforce based on economic principles. To achieve this, firms must consider the balance between the MCL and MRP for each additional worker. The employment level is profit-maximizing when MRP equals MCL. At this point, the cost of hiring an additional worker is exactly covered by the revenue they generate, and hiring any more workers would start to decrease profits.

Through careful analysis of the costs and benefits associated with hiring each additional worker, a monopsonist can determine the optimal number of workers to hire in order to maximize profits. In the textbook exercise, the firm finds that employing five workers is the most profitable; the MCL for the sixth worker exceeds the constant MRP, which would reduce the firm's profit.

It's essential for students to recognize this equilibrium point, as going beyond would mean incurring more cost than revenue, leading to lower profits. The exercise brings to light the finesse required in workforce planning and the significance of understanding labor-related economic concepts to make informed business decisions that align with profit-maximization objectives.