In production theory, which of the following is an alternative way of representing a production function, showing different input combinations that yield the same output?

Introduction / Context:
Production theory studies how firms transform inputs such as labour and capital into outputs using a production technology. A production function is one way to describe this relationship mathematically. Graphically, economists often use isoquants to depict the same information in a visual form. This question asks whether you recognise that isoquants are an alternative way to represent the production function, particularly when analysing choices between two variable inputs.

Given Data / Assumptions:
- We are dealing with a firm that uses multiple inputs to produce output.
- The production function summarises how different input quantities are transformed into output.
- The options mention the short run, the long run, isoquants, and average product.
- We assume a standard two input case, typically labour and capital.

Concept / Approach:
A production function expresses output as a function of inputs, for example Q = f(L, K), where L is labour and K is capital. For a given level of output, say Q0, there may be many combinations of labour and capital that produce this quantity. The set of all such combinations can be drawn in a two dimensional graph as a curve called an isoquant. Each isoquant corresponds to a specific level of output, similar to how indifference curves correspond to specific levels of utility in consumer theory. Therefore, isoquants are an alternative graphical representation of the underlying production function.

Step by Step Solution:
Step 1: Recall that a production function describes the maximum output obtainable from different combinations of inputs. Step 2: Recognise that an isoquant is a curve that connects all combinations of inputs that yield the same output level. Step 3: Since each isoquant corresponds to a particular output level of the production function, a family of isoquants graphically represents the production function. Step 4: Option C explicitly defines an isoquant as combinations of inputs that produce a given level of output, which is the correct alternative representation. Step 5: Options A and B refer to time periods of production analysis, not to graphical representations of the production function. Step 6: Option D refers to average product, which is a separate concept measuring output per unit of input, not an alternative way to represent the entire production function.

Verification / Alternative check:
Imagine a firm that can produce 100 units of output using different mixes of labour and capital. For example, it might use 10 units of labour and 5 units of capital, or 8 units of labour and 7 units of capital, and so on. Each of these combinations satisfies the same production function level Q = 100. Plotting these pairs of labour and capital on a graph and joining them gives an isoquant for Q = 100. Repeating this for Q = 120, Q = 140, and so on produces a set of isoquants, which visually depict the firm's production possibilities. This confirms that isoquants represent the production function in an alternative, graphical form.

Why Other Options Are Wrong:
Option A is wrong because the short run is a time period concept in which at least one input is fixed, but it is not a graphical representation of a production function.
Option B is wrong because the long run is another time period concept in which all inputs can vary; again, it is not an alternative way to represent the production function itself.
Option D is wrong because average product describes output per unit of a specific input and is usually plotted as a separate curve; it does not show combinations of inputs that yield the same output.

Common Pitfalls:
Students sometimes confuse isoquants with indifference curves because both are drawn in two dimensional diagrams and have similar shapes. The key difference is that isoquants relate to production, while indifference curves relate to consumer preferences. Another pitfall is to think that the terms short run and long run describe diagrams rather than analytical time frames. Remembering that isoquants map input combinations for fixed output levels will help you clearly identify option C as the correct answer.

Final Answer:
An isoquant curve showing combinations of inputs that produce a given level of output.