Which of the following statements best describes the relationship between marginal product and marginal cost in production?

• A. When the marginal product decreases, the marginal cost of production declines.
• B. Marginal product and marginal cost are always unrelated.
• C. When the marginal product increases, the marginal cost of production declines.
• D. When the marginal product increases, the marginal cost of production also increases.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the definitions of marginal product (MP) and marginal cost (MC). Marginal product is the additional output produced by using one more unit of an input, typically labor. Marginal cost is the additional cost incurred by producing one more unit of output.
2. Step 2: Recognize the inverse relationship between marginal product and marginal cost. When marginal product increases, each additional unit of input produces more output, so the cost of producing an extra unit of output decreases.
3. Step 3: Express this relationship mathematically. Marginal cost can be written as \(MC = \frac{\Delta TC}{\Delta Q}\), where \(\Delta TC\) is the change in total cost and \(\Delta Q\) is the change in quantity produced. Since \(\Delta Q\) depends on marginal product, a higher marginal product means a larger \(\Delta Q\) for the same input increase, lowering \(MC\).
4. Step 4: Conversely, when marginal product decreases, each additional input adds less output, so marginal cost increases because producing one more unit of output requires more input and thus more cost.
5. Step 5: Conclude that the correct statement is: 'When the marginal product increases, the marginal cost of production declines,' reflecting the inverse relationship between marginal product and marginal cost.