Certainly! Here’s a **structured and clear answer** based on the image you provided, including a **final summary**. --- # Problem Statement You are given a table with the number of workers (L), total output, marginal product of labor (MP), and average product of labor (AP). You are asked: 1. To find the output of 4 workers, given the marginal product of the 4th worker is 36 units and the output of 3 workers is 90 units. 2. To explain the relationship between marginal product and average product. --- ## 1. Calculating Output of 4 Workers **Given Data:** - Output with 3 workers ($Q_3$): 90 units - Marginal product of 4th worker ($MP_4$): 36 units **Formula for Marginal Product:** \[ MP_n = Q_n - Q_{n-1} \] where: - $MP_4$ = Output with 4 workers - Output with 3 workers \[ MP_4 = Q_4 - Q_3 \] \[ 36 = Q_4 - 90 \] \[ Q_4 = 36 + 90 = 126 \text{ units} \] --- ## 2. Relationship Between Marginal Product and Average Product - **Marginal Product (MP):** The additional output produced by one more unit of labor. - **Average Product (AP):** The total output divided by the number of workers. **Relationship:** - When MP > AP, AP rises. - When MP < AP, AP falls. - When MP = AP, AP is at its maximum. This is similar to how a grade average works: If your next test score is higher than your average, your average increases; if it’s lower, your average decreases. --- # Final Summary - The output with 4 workers is **126 units**. - The marginal product of labor affects the average product: when the marginal product is above the average product, it pulls the average up; when it’s below, it pulls the average down. The average product reaches its maximum when the marginal product equals the average product.

# Problem Statement You are tasked with answering three questions based on the data provided regarding workers, total output, marginal product of labor (MP), and average product of labor (AP). ## Questions 1. Calculate the output of 4 workers, given the marginal product of the 4th worker is 36 units and the output of 3 workers is 90 units. 2. Explain the relationship between marginal product and average product. 3. Provide a final summary. --- ## 1. Calculating Output of 4 Workers **Given Data:** - Output with 3 workers ($Q_3$): 90 units - Marginal product of the 4th worker ($MP_4$): 36 units **Calculation:** Using the formula for marginal product: \[ MP_n = Q_n - Q_{n-1} \] For the 4th worker: \[ MP_4 = Q_4 - Q_3 \] Substituting the known values: \[ 36 = Q_4 - 90 \] Solving for $Q_4$: \[ Q_4 = 36 + 90 = 126 \text{ units} \] --- ## 2. Relationship Between Marginal Product and Average Product - **Marginal Product (MP):** Additional output from hiring one more worker. - **Average Product (AP):** Total output divided by the number of workers. ### Relationship Dynamics: - **If MP > AP:** Average product increases. - **If MP < AP:** Average product decreases. - **If MP = AP:** Average product is maximized. This relationship indicates that the marginal product influences the average product, similar to how individual test scores affect your overall average. --- ## 3. Final Summary - The output with 4 workers is **126 units**. - The relationship between marginal product and average product indicates that the average product is influenced by the marginal product's level relative to it. The average product is at its highest when the marginal product equals the average product.