In production theory, the short run relationship between a variable input and the resulting level of output, while all other inputs are held constant, is referred to as what?

Introduction / Context:
Production theory in microeconomics studies how inputs are transformed into outputs. In the short run, some inputs are fixed while others are variable. The relationship between a single variable input, such as labour, and the level of output, when other inputs are held fixed, is important for understanding concepts like total product, marginal product and average product. This question asks you to identify which term describes this basic relationship between the variable input and output.

Given Data / Assumptions:

• We are in the short run, where at least one input is variable and others are fixed.
• The relationship is between the quantity of the variable input and total output.
• All other inputs are held constant.
• Options include total product, average product, isoquant and the long run.

Concept / Approach:
Total product (also called total physical product) of a variable input is the total quantity of output produced by the firm for different levels of that input, given that all other inputs are fixed. It is a function that shows how output changes as the variable input changes. Average product is the output per unit of variable input and is derived by dividing total product by the quantity of the input. Marginal product, although not listed here, is the change in total product resulting from a one unit change in the variable input. An isoquant shows combinations of two inputs that produce the same level of output and is not just a simple relationship between one variable input and output.

Step-by-Step Solution:
Step 1: Identify that the question describes output as a function of a single variable input, with other inputs fixed. Step 2: Recall that total product measures the total amount of output produced as the variable input changes. Step 3: Distinguish total product from average product, which is total product divided by input units, and from isoquants, which involve two inputs. Step 4: Conclude that the relationship described is best named total product.

Verification / Alternative check:
Visualising the typical total product curve can help. As more units of the variable input are employed, total product initially increases at an increasing rate, then at a diminishing rate, and may eventually decline. This curve directly represents how output depends on the variable input, with other inputs fixed. The question wording about the relationship between variable input and output matches this concept exactly, confirming total product as the correct term.

Why Other Options Are Wrong:
Average product: This is defined as total product divided by the quantity of the variable input and represents output per unit, not the full relationship between input and total output.
Isoquant: An isoquant shows combinations of two inputs that yield the same output level, and is used in long run multi input analysis, not simply the one variable input short run relationship described in the question.
The long run: The long run is a time period concept in which all inputs are variable, not a specific function linking one variable input to output.

Common Pitfalls:
Students sometimes confuse the definitions of total, average and marginal product because they are closely related. A useful approach is to remember that total product is the basic function of output versus input, average product divides total output by input units, and marginal product focuses on the change in output. Recognising this hierarchy helps avoid mistakes and makes it easier to match definitions to the correct term in exam questions.

Final Answer:
The relationship between a variable input and output, with other inputs held constant, is called total product of that input.