Question

Recently, some college alumni started a moving service for students living on campus. They have three employees and are debating hiring a fourth. The hourly wage for an employee is \(\$ 18\) per hour. An average moving job takes three hours. The company currently does three moving jobs per week, but with one more employee, the company could manage five jobs per week. The company charges \(\$ 80\) for a moving job. [LO 16.1, 16.2] a. What would be the new employee's marginal product of labor? b. What is the value of that marginal product? c. Should the moving service hire a fourth worker?

Short answer

The new employee's marginal product is 2 jobs/week, its value is \$160, and yes, the service should hire a fourth worker.

Step-by-step solution

Calculate Marginal Product of Labor

The marginal product of labor (MPL) is the additional output (in this case, moving jobs) attributed to the new employee. Currently, the company does 3 jobs per week with 3 employees. With a fourth employee, they can do 5 jobs per week. Thus, the MPL is the difference in the number of jobs:\[ \text{MPL} = 5 \, \text{jobs} - 3 \, \text{jobs} = 2 \, \text{jobs} \]

Calculate the Value of Marginal Product

The value of the marginal product of labor (VMPL) is calculated by multiplying the MPL by the price received per unit of output (here, the charge for a moving job):\[ \text{VMPL} = \text{MPL} \times \text{Price per job} = 2 \, \text{jobs} \times \\(80 = \\)160 \]

Consider the Cost of Hiring

The cost of hiring the new employee is their wage per hour times the number of hours per week they will be working. It takes 3 hours per job, and the new employee will help complete 2 additional jobs per week:\[ \text{Weekly Hours} = 2 \, \text{jobs/week} \times 3 \, \text{hours/job} = 6 \, \text{hours/week} \]\[ \text{Cost} = 6 \, \text{hours} \times \\(18 = \\)108 \]

Decision on Hiring

Comparing the value of the marginal product to the cost of hiring, we see that the value (\\(160) is greater than the cost (\\)108). Therefore, hiring the new employee is beneficial for the company.

Key concepts

Understanding Value of Marginal Product

The value of the marginal product (VMPL) is a crucial concept in economics that evaluates the benefit of hiring an additional employee. It tells us how much revenue a business can earn by hiring one more worker. To find the VMPL, we multiply the **marginal product of labor** (the extra work or output thanks to a new worker) by the price of that output.

In our scenario, the new worker's marginal product is making two extra moving jobs each week. Since the company charges $80 per job, we calculate the VMPL as follows:

• Marginal Product of Labor (MPL): 2 jobs
• Price per job: $80
• VMPL = MPL × Price per Job = 2 × $80 = $160

Thus, the additional employee could potentially generate $160 more in revenue each week.

The Role of Cost-Benefit Analysis

A cost-benefit analysis helps businesses make good decisions by comparing the expected benefits of an action to its costs. This is important for understanding whether hiring another worker will actually bring in more money than it costs.

In the moving company example, the benefit is the value brought by the new employee, which is $160. The cost involves the wages paid to that employee, calculated as:

• Hours needed: 2 jobs × 3 hours/job = 6 hours
• Wage per hour: $18
• Total cost = 6 hours × $18 = $108

As outlined, the benefit ($160) exceeds the cost ($108), indicating a positive outcome. This positive margin shows it's advantageous for the company to make the hire.

Making a Smart Hiring Decision

A hiring decision isn't just about numbers; it's about ensuring the business grows efficiently. Here, we should consider if hiring another worker will result in extra revenue higher than the additional costs, like wages.

For our moving company:

• The cost of hiring the additional worker is $108 per week.
• The benefit, captured by the value of the marginal product, is $160 per week.

Since $160 is greater than $108, hiring the fourth worker is a smart financial move.

Beyond just the numbers, consider factors like worker reliability and workload management to ensure long-term success and sustainability.

Fundamentals of Labor Economics

Labor economics studies how labor resources are allocated, looking at both employees and employers' perspectives. It shows how wages are determined by supply, demand, and productivity.

In this context, labor supply is the number of people available to work, while labor demand is the need businesses have for workers to produce goods or services.

Applied to our example, the supply side is the group of workers available at $18 per hour. The demand side is represented by the moving company's need to complete more jobs. When analyzing labor economics, it's evident that:

• Firms will hire more workers as long as the Marginal Benefit (VMPL) surpasses the marginal cost (wages).
• Understanding how productivity affects wages and hiring decisions helps firms operate efficiently.

Summarizing, clear insights into how labor economics operates can aid businesses in making educated hiring strategies.