Question

Wanda's is a fish store that hires students to pack the fish. Students can pack the following amounts of fish: $$\begin{array}{cc} \begin{array}{c} \text { Number of } \\ \text { students } \end{array} & \begin{array}{c} \text { Quantity of fish packed } \\ \text { (pounds) } \end{array} \\ \hline 1 & 20 \\ 2 & 50 \\ 3 & 90 \\ 4 & 120 \\ 5 & 145 \\ 6 & 165 \\ 7 & 180 \\ 8 & 190 \end{array}$$ The fish market is competitive and the price of fish is \(50 \mathrm{c}\) a pound. The market for packers is competitive and their market wage rate is \(\$ 7.50\) an hour. Calculate the value of marginal product of labor and draw the value of marginal product curve.

Short answer

VMP values: [10, 15, 20, 15, 12.5, 10, 7.5, 5]. Plot these to form the VMP curve.

Step-by-step solution

Understand the Problem

The task is to calculate the value of the marginal product (VMP) of labor and then draw the VMP curve. Marginal product (MP) is the additional output generated by employing one more worker. VMP is calculated by multiplying the MP by the price of the output (fish).

Calculate Marginal Product (MP)

Calculate the additional pounds of fish packed by each additional student.For example:- MP of 1st student = 20 (since it's the first student)- MP of 2nd student = 50 - 20 = 30- MP of 3rd student = 90 - 50 = 40Continue this for each student.

Calculate Value of Marginal Product (VMP)

Use the price of fish (50 cents or $0.50) to calculate VMP. VMP = MP × Price of fish.For example:- VMP of 1st student = 20 × 0.50 = 10- VMP of 2nd student = 30 × 0.50 = 15- VMP of 3rd student = 40 × 0.50 = 20Continue this for each student.

Detailed VMP Calculations

Perform the detailed calculations for each student:- MP of 4th student = 120 - 90 = 30, VMP = 30 × 0.50 = 15- MP of 5th student = 145 - 120 = 25, VMP = 25 × 0.50 = 12.5- MP of 6th student = 165 - 145 = 20, VMP = 20 × 0.50 = 10- MP of 7th student = 180 - 165 = 15, VMP = 15 × 0.50 = 7.5- MP of 8th student = 190 - 180 = 10, VMP = 10 × 0.50 = 5

Plot the VMP Curve

Plot a graph with the number of students on the x-axis and the Value of Marginal Product (VMP) on the y-axis. Plot the points and connect them to visualize the downward sloping VMP curve.

Key concepts

Marginal Product of Labor

To understand how to calculate the Value of Marginal Product (VMP), it's crucial to first grasp the concept of the Marginal Product of Labor (MP). The MP measures the extra output a business gains from employing one additional worker. Imagine your classroom getting another student; how much more work can get done? That's fundamentally what MP measures. In Wanda's fish store example:

• The MP of the 1st student is simply the amount of fish packed by that student, which is 20 pounds.
• For the 2nd student, the MP is the additional amount of fish packed compared to what one student can pack: 50 pounds - 20 pounds = 30 pounds.
• This process continues for each subsequent student.

Knowing the MP helps businesses decide how many workers to hire to maximize production without wasting resources.

Competitive Market

A competitive market is where numerous buyers and sellers interact, and nobody can control the price. Everyone in the market, including fish sellers and packers at Wanda's, are generally price takers. They accept the market price as given. In this scenario, the price for fish is fixed at 50 cents per pound. Hence, determining how many workers to employ depends on how much additional fish a student can pack and the revenue generated from selling that fish. In competitive markets, wages (how much workers are paid) are also determined by market forces. Employers, like Wanda, will continue to hire students as long as the VMP (value those workers bring in) is greater than or equal to their wage.

Wage Rate

The wage rate is what workers earn per hour of work. In competitive labor markets, the wage rate is set by supply and demand. For Wanda's fish store, the wage rate is $7.50 an hour. This wage rate becomes a critical part of hiring decisions. Employers will hire workers until the point where the VMP equals the wage rate. If the VMP is higher than the wage rate, it's profitable to hire more workers. Conversely, if the VMP is lower, it's not beneficial. For example, if the VMP of the 5th student is 12.5 dollars, and the wage rate is 7.50 dollars, Wanda should hire the 5th student because the VMP exceeds the wage rate.

VMP Curve

The VMP curve visually represents the relationship between the number of workers and their contribution to total revenue. It shows how the VMP changes as more workers are hired. Typically, the curve is downward sloping, indicating diminishing returns—meaning each additional worker adds less to the total output than the previous one. To plot the VMP curve for Wanda's fish store:

• Place the number of students on the x-axis.
• Value of Marginal Product on the y-axis.
• Plot each calculated VMP, for instance, 0 students = 0, 1 student = 10 dollars, 2 students = 15 dollars, etc.

Connect these points to visualize how VMP decreases with each additional student. This curve helps the store decide the optimal number of workers to employ.