Question

Carl the clothier owns a large garment factory on an isolated island. Carl's factory is the only source of employment for most of the islanders, and thus Carl acts as a monopsonist. The supply curve for garment workers is given by \\[ L=80 w \\] where \(L\) is the number of workers hired and \(w\) is their hourly wage. Assume also that Carl's labor demand (marginal revenue product) curve is given by \\[ L=400-40 M R P_{L} \\] a. How many workers will Carl hire to maximize his profits and what wage will he pay? b. Assume now that the government implements a minimum wage law covering all garment workers. How many workers will Carl now hire and how much unemployment will there be if the minimum wage is set at \(\$ 4\) per hour? c. Graph your results. d. How does a minimum wage imposed under monopsony differ in results as compared with a minimum wage imposed under perfect competition (assuming the minimum wage is above the market-determined wage)?

Short answer

Answer: In a monopsony labor market, imposing a moderate minimum wage may lead to an increase in employment, as the monopsonist employer has pricing power and is not paying the competitive wage. In contrast, in a perfectly competitive labor market, a minimum wage set above the market-determined wage usually results in a decrease in employment due to increased labor costs for employers.

Step-by-step solution

1. Understanding labor supply and labor demand equations

The given labor supply curve is \(L = 80w\), and the labor demand curve is \(L = 400 - 40MRP_L\).

2. Equating labor supply and labor demand equations

In order to find the equilibrium point between the labor supply and labor demand, we need to set them equal to each other: \(80w = 400 - 40 MRP_L\).

3. Solve for MRP_L

The next step is to solve the above equation for \(MRP_L\): \(40 MRP_L = 400 - 80w\) \(MRP_L=10-2w\).

4. Monopsony condition

Under a monopsonist labor market setting, the marginal cost of labor (\(MC_L\)) is always greater than the wage rate \((w)\), so we have: \(MC_L>w\).

5. Calculate MC_L

The marginal cost of labor can be calculated as the derivative of the total cost of labor (\(TCL\)): \(TCL = wL = w(80w)\) \(MC_L = \frac{d(TCL)}{dL} = 80 + 160w\).

6. Equate MRP_L and MC_L and solve for w

To find the equilibrium wage, set \(MRP_L\) equal to \(MC_L\) and solve for \(w\): \(10 - 2w = 80 + 160w\) \(170w = 70\) \(w = \frac{70}{170} \approx \$0.412\) per hour.

7. Determine the number of workers hired

After obtaining the wage rate, plug it back into the labor supply equation, and we'll get the number of workers hired: \(L = 80w = 80(0.412) \approx 33\) workers. So, Carl will hire 33 workers and pay an hourly wage of about \(\$0.412\) per hour to maximize his profits.

8. Imposing a minimum wage

With the minimum wage imposed at \(\$4\) per hour, calculate the number of workers Carl will hire: \(L = 80w = 80(4) = 320\) workers.

9. Calculate the unemployment rate

To find the unemployment rate, compare the number of workers Carl would have hired without the minimum wage to the number he is hiring now: \(Unemployment = 320 - 33 = 287\) workers. So, there will be 287 unemployed workers after the implementation of the \$4 per hour minimum wage.

10. Comparing minimum wage imposition under monopsony vs perfect competition

A key difference between minimum wage imposition under monopsony and perfect competition is the employment impact. Under monopsony, a moderate minimum wage increase may lead to an increase in employment since the employer has pricing power and is not paying the competitive wage. In contrast, under perfect competition, a minimum wage set above the market-determined wage typically leads to a decrease in employment due to employers facing increased labor costs.

Key concepts

Labor Supply

Labor supply refers to the total number of workers willing to work at different wage levels. In the exercise, the labor supply curve is depicted as \( L = 80w \), where \( L \) represents the number of workers and \( w \) represents the wage rate. This linear equation suggests a direct relationship between the wage rate and the number of workers. As wages increase, more workers are willing to enter the labor market, thus increasing the labor supply.

Imagine if wages were higher, say from part-time work becoming more appealing. More workers would be keen to join even at different hours. This part of economics aligns with real-world behavior where better pay motivates more workers to accept jobs or shift from other sectors.

Labor Demand

Labor demand is the need for workers by employers based on the productivity and cost of labor. Our exercise uses the equation \( L = 400 - 40 MRP_L \) to represent this, where \( MRP_L \) is the Marginal Revenue Product of Labor. In simple terms, it indicates how many workers a business wants to hire depending on the productivity (or worth) of added workers.

The labor demand curve typically slopes downward, meaning as wages (cost per worker) increase, businesses will hire fewer workers unless their productivity also rises. Companies need to balance costs with output value, ensuring they get the maximum benefit from each worker. This helps explain why during economic slowdowns, job offers might decrease as firms focus on maximizing output with existing staff rather than incurring additional labor costs.

Minimum Wage

A minimum wage is the lowest amount an employer can legally pay their workers. In the exercise, a minimum wage of $4 is introduced, impacting how many workers Carl hires. It is a tool governments use to ensure workers receive fair pay that meets living standards.

Implementing a minimum wage can have varying effects based on market conditions. In monopsony settings, it might increase employment because employers have more control over wages. In a competitive market, however, it might reduce jobs as firms would rather operate with fewer workers than pay higher wages.

For Carl's factory, setting a minimum wage forces an increase in hiring up to 320 workers compared to the 33 without it. Yet, this also creates unemployment where the available jobs (320) don't meet the increased labor supply (possibly all islanders willing to work).

Marginal Revenue Product

The Marginal Revenue Product (MRP) of Labor is the additional revenue a firm earns from hiring an extra worker. In our exercise, it is part of the labor demand equation \( L = 400 - 40 MRP_L \). This concept helps employers decide the optimal number of workers needed by aligning labor cost with output revenue.

For Carl, understanding MRP is crucial as it shows the value each worker brings to his garment production. In monopsony, the aim is to employ until the extra cost of hiring one more worker equals the extra revenue generated.

By determining that \( MRP_L = 10 - 2w \), Carl can calculate precisely how much a worker contributes alongside their cost to produce profit while ensuring efficiency. The MRP thus acts as a benchmark for sound hiring decisions, helping maintain business profitability even with wage regulation like minimum wages.