Question

The table below shows the quantity of workers and total output for a local pizza parlor. Answer the following questions based on the table. $$ \begin{array}{c|c} \hline \text { Quantity of Workers } & \text { Total Output } \\ \hline 0 & 0 \\ \hline 1 & 5 \\ \hline 2 & \- \\ \hline 3 & 19 \\ \hline 4 & 24 \\ \hline 5 & 28 \\ \hline 6 & 26 \\ \hline \end{array} $$ a. When the owner hires 4 workers, what is average product of labor? b. What is the marginal product of the fifth worker? c. If the marginal product of the second worker is 6 , what is the total number of pizzas produced when 2 workers are hired? d. Assuming that the marginal product of the second worker is \(6,\) with which worker hired does the law of diminishing returns set in?

Short answer

a. The Average Product of 4 workers is 6. \n b. The Marginal Product of the 5th worker is 4. \n c. The Total Output when 2 workers are hired is 11. \n d. We can't definitively identify the worker with which the law of diminishing returns sets in without more 'marginal product' information for the 3rd and 4th workers.

Step-by-step solution

Calculate the Average Product of 4 workers

To calculate the Average Product of 4 workers, we need to take the Total Output when there are 4 workers and divide it by the number of workers. So it will be \( \frac {Total Output_{4} }{4} = \frac {24}{4} = 6\)

Calculate the Marginal Product of the fifth worker

The Marginal Product is simply the increase in output resulting from hiring an additional worker. So it can be calculated as the difference in total output between having 5 workers and 4 workers. Therefore, \(MP_{5} = Total Output_{5} - Total Output_{4} = 28 - 24 = 4\)

Calculate Total Output for 2 workers

It is stated that the marginal product of the second worker is 6, which is the increase in total output from having 2 workers compared to 1. So we know the total output when 2 workers are hired is the output with one worker plus the increase: \(Total Output_{2} = Total Output_{1} + MP_{2} = 5 + 6 = 11\)

Identify when the law of diminishing returns sets in

The law of diminishing returns sets in when the marginal product of labor decreases. Here we know that the marginal product of the 2nd worker is 6 and of the 5th is 4. But without knowing the marginal products for the 3rd and 4th workers, we can't definitively state where the law of diminishing returns sets in. More information is needed to make this determination.

Key concepts

Average Product of Labor

The average product of labor is an essential concept in understanding efficiency and productivity within a company, specifically when it comes to its workforce. It is calculated by dividing the total output by the number of workers employed to achieve that output. For instance, in the context of a pizza parlor mentioned in our exercise, the average product of labor for four workers is obtained by dividing the total number of pizzas (the output) by four. Mathematically, it's calculated as \( \frac{Total Output_{4}}{4} = \frac{24}{4} = 6 \). This result tells us that, on average, each worker is responsible for making six pizzas. Knowing the average product of labor can help businesses assess the productivity of their employees and make informed decisions on hiring or resource allocation.

In our exercise improvement advice, we emphasized the importance of clear calculations and context. To ensure students fully understand, it's necessary to explain not just the 'how' but also the 'why' behind these calculations. Understanding the average product of labor gives insight into the efficiency of the workforce and helps in forecasting the implications of hiring additional workers or making other changes to production processes.

Law of Diminishing Returns

The law of diminishing returns is a fundamental principle in economics that describes a point at which the level of benefits gained is less than the amount of money or energy invested. In the scope of labor and production, it indicates that adding more workers will eventually lead to a smaller increase in output per worker if other factors are constant. This concept is reflected in our pizza parlor example when we see that the marginal product (the additional output produced by an additional worker) begins to decrease.

In our step-by-step solution, we look for indications of when hiring more workers leads to less additional pizzas being made per worker. Although we don't have all the data, the marginal product of the fifth worker being lower than that of the second worker suggests the beginnings of the law of diminishing returns. Students must be able to recognize the pattern that as more workers are hired, the incremental gain in output will decrease, signaling that it may not be beneficial to continue adding labor without making other adjustments, such as improving technology or increasing workspace.

Total Output

Total output refers to the total amount of goods or services produced by a firm. It's crucial for students to understand how total output is influenced by different factors, like the number of workers. In the textbook exercise, we calculate the total output at various levels of employment to see how production changes. For example, when calculating the total number of pizzas produced when two workers are hired, we add the marginal product of the second worker to the total output of the first worker, giving us \( Total Output_{2} = Total Output_{1} + MP_{2} = 5 + 6 = 11 \).

It's important for students to note the relationship between individual worker productivity (marginal product) and the overall production (total output) of the business. The exercise advised clear articulation of this calculation and the underlying logic, so students are not merely performing arithmetic but understanding the relationship between labor and production.

Economic Production

Economic production is the process of creating goods or services using various inputs like labor, capital, and technology. The process is measured in terms of output. Our exercise exemplifies a small-scale view of economic production within a pizza parlor, offering insights into how changes in the quantity of labor affect the production output. When assessing economic production, it's important to consider factors like efficiency, cost-effectiveness, and the capacity of resources being utilized.

Students need to understand that the ultimate goal of optimizing economic production is to maximize output while minimizing costs. This balance can be tricky as the law of diminishing returns can affect labor's contribution to production. It is also essential to focus on the conditions under which workers are most productive and what combination of inputs yields the best results for the economic production of the business.