In production analysis, ________ of an input is defined as the change in output per unit of change in that input, when all other inputs are held constant.

Introduction / Context:
Understanding how output responds to changes in inputs is central to the theory of production in microeconomics. Economists use several related concepts: total product, marginal product and average product. This question focuses on identifying which of these terms is defined specifically as the change in output due to a one unit change in a particular input, holding all other inputs constant.

Given Data / Assumptions:

• We are examining the effect of changing one input while other inputs remain fixed.
• The quantity of output changes when the quantity of the chosen input changes.
• The definition involves change in output per unit change in the input.
• Options include marginal product, production function, total product and average product.

Concept / Approach:
Marginal product of an input is defined as the additional output produced when one more unit of that input is employed, keeping other inputs unchanged. In simple notation, marginal product (MP) equals change in total product divided by change in the quantity of the input. Total product is the total output produced by a given quantity of the input; average product is total product divided by the quantity of the input. The production function describes the overall relationship between inputs and output, not just the incremental effect of one input.

Step-by-Step Solution:
Step 1: Focus on the phrase “change in output per unit of change in the input”. Step 2: Recall that marginal product is defined as MP = change in total product / change in input quantity. Step 3: Distinguish marginal product from total product (which is total output) and average product (output per unit of input, TP divided by quantity). Step 4: Recognise that the description exactly matches the definition of marginal product. Step 5: Select “Marginal product” as the correct answer.

Verification / Alternative check:
Generate a small numerical example. Suppose total output is 100 units when 5 units of labour are used and 120 units when 6 units of labour are used, holding other inputs fixed. The change in output is 20 units and the change in labour is 1 unit; so marginal product of labour is 20 units. This calculation uses the change in output divided by change in input, which is precisely the definition given in the question, confirming that it refers to marginal product.

Why Other Options Are Wrong:
Production function: This describes the overall relationship between inputs and output, often written as Q = f(L, K, etc.), but it does not itself represent the incremental change per unit of input.
Total product: This is the total quantity of output produced by a given amount of the input, not the change in output when the input changes by one unit.
Average product: This is defined as total product divided by the quantity of the input, representing output per unit of input, not the change in output due to a marginal change in input.

Common Pitfalls:
Students sometimes confuse average product with marginal product because both involve “per unit” language. The key distinction is that average product uses total output divided by total input, whereas marginal product uses the change in output divided by the change in input. Remembering that marginal refers to change or increment helps correctly identify marginal product when you see a definition involving change in output per unit change in input.

Final Answer:
The quantity defined as change in output per unit change in an input, with other inputs constant, is the marginal product of that input.