Question

Fresh Veggie is one of many small farms in Florida operating in a perfectly competitive market. Farm labor is also perfectly competitive, and Fresh Veggie can hire as many workers as it wants for \(\$ 20\) a day. The daily productivity of a tomato picker is given in Table \(16 \mathrm{P}-1 .\) If a bushel of tomatoes sells for \(\$ 5\), how many workers will Fresh Veggie hire?

Short answer

Hire workers until MRP equals or exceeds $20; hire the number where MRP meets this criteria.

Step-by-step solution

Understand the Problem

The problem involves calculating how many workers Fresh Veggie should hire based on productivity and costs. Given that the farm operates in a competitive market and labor costs $20 per day per worker, the goal is to maximize profit. This involves comparing the marginal revenue product (MRP) of labor to its cost.

Define Key Terms

Define **Marginal Revenue Product (MRP)** and **Marginal Cost of Labor (MCL)**. MRP is the additional revenue generated by hiring one more worker, calculated as the output produced by an additional worker multiplied by the price of output. MCL is the cost of hiring one more worker, which is given as $20 per day.

Calculate Marginal Revenue Product (MRP)

For each additional worker, calculate MRP using the formula \( \text{MRP} = \text{Marginal Product of Labor} \times \text{Price of Output} \). Repeat this calculation for increasing numbers of workers, noting the productivity from Table 16P-1 and multiplying by the bushel price ($5).

Determine Hiring Number

Compare the MRP for each worker to the MCL of \(20. Fresh Veggie should hire workers up to the point where \( \text{MRP} \geq \text{MCL} \). If any further worker's MRP is less than \)20, then that worker should not be hired.

Key concepts

Marginal Revenue Product

In a perfectly competitive market, businesses need to understand how hiring one extra worker can impact their revenue. This is where the concept of Marginal Revenue Product (MRP) comes in. It's the additional income a firm earns by employing one more unit of labor, such as one more worker.
The MRP is calculated by multiplying the additional output that an extra worker can produce (known as the Marginal Product of Labor) by the price at which the product can be sold. For example, if a tomato picker can harvest 8 bushels of tomatoes in a day, and each bushel sells for $5, then the MRP for the worker is 8 multiplied by 5, equaling $40.
This calculation helps businesses understand the value of an additional worker in terms of revenue gained.

Marginal Cost of Labor

The cost of hiring each additional worker is equally crucial in decision-making processes within a competitive market. This is called the Marginal Cost of Labor (MCL). It's the cost that a firm incurs by hiring one more worker.
For Fresh Veggie, which operates in a perfectly competitive labor market, the MCL is simply the wage rate for one day, which is $20 per worker.
By comparing this cost to the Marginal Revenue Product, businesses can decide whether hiring additional workers will be profitable. They should continue hiring as long as the MRP is greater than or equal to the MCL.

Profit Maximization

In the context of a perfectly competitive market, the goal for businesses is profit maximization, which involves maximizing the difference between total revenue and total costs.
For Fresh Veggie, profit maximization entails evaluating how many workers should be hired. It involves comparing the Marginal Revenue Product of labor to the Marginal Cost of Labor.

• If the MRP is greater than the MCL, hiring more workers increases profit.
• If the MRP is less than the MCL, hiring more workers would decrease profit.
• The profit-maximizing point is when MRP equals MCL.

This ensures maximum profit because at this point, the cost of hiring exactly equals the revenue derived from the additional labor.

Labor Economics

Labor economics is a field that examines the dynamics between workers and employers, particularly within the scope of supply, demand, and pricing of labor.
In a perfectly competitive labor market, numerous employers recruit labor, while workers freely decide whom to work for, often leading to an equilibrium wage.
The concepts of Marginal Revenue Product and Marginal Cost of Labor play a crucial role in understanding labor economics because they help firms determine the optimal level of employment to maximize profits. They reflect the intersection where employers can offer a wage rate (MCL) that employees find acceptable, and the productivity of those workers justifies the cost (MRP).
Understanding labor economics assists businesses like Fresh Veggie in maintaining efficient operations while ensuring that both wages and labor output are aligned with market conditions.