The table and questions involve calculating Marginal Product (MP) and Average Product (AP), as well as analyzing labor productivity. I will break down the calculations and solutions step by step.

Step 1: Definitions

1. Marginal Product (MP): The additional output produced when one more unit of labor is added. $MP = \text{Change in Total Product (TP)} / \text{Change in Workers (Labor)}.$
2. Average Product (AP): The total output per worker. $AP = \text{Total Product (TP)} / \text{Number of Workers}.$

Step 2: Complete the Table

Let’s calculate MP and AP for the provided data:

Step 3: Addressing Questions

Question 5:

Using the data:

• Marginal Product (MP) decreases after the third worker.
• Average Product (AP) peaks between 3 and 4 workers, then declines.

Question 6:

When labor increases:

• Marginal Product of Labor starts to decrease after the third worker due to diminishing returns.
• Correct answer: $\text{b) decrease}$.

Question 7a:

The production function for footballs is $y(x) = 7\sqrt{x}$. The marginal product of labor (MP) is the derivative of $y(x)$: $MP = \frac{dy}{dx} = \frac{7}{2\sqrt{x}}.$

Question 7b:

The average product of labor (AP) is: $AP = \frac{y(x)}{x} = \frac{7\sqrt{x}}{x} = \frac{7}{\sqrt{x}}.$

Would you like a detailed explanation of any step or further clarification? Let me know!

Here are 5 related questions to extend your understanding:

1. What are the economic implications of diminishing marginal returns in production?
2. How is the relationship between MP and AP reflected in this table?
3. What happens to total product when MP becomes negative?
4. How can firms use MP and AP to decide on the optimal number of workers?
5. How does the square root production function compare to linear functions in terms of MP?

Tip: Always analyze both MP and AP trends together to understand labor productivity and diminishing returns!