In production theory, which concept is defined as the output produced per unit of a variable input, such as output per worker?

Introduction / Context:
Within the framework of production theory, economists define several key measures that describe how output responds to changes in inputs. These include total product, marginal product and average product. Understanding the difference between these measures helps in analysing concepts like returns to a factor and productivity of labour or capital. This question asks specifically for the name of the measure that captures output per unit of a variable input, for example output per worker when labour is the variable factor.

Given Data / Assumptions:
• The focus is on a variable input, such as labour. • The concept is defined as output per unit of that variable input. • Four related terms are given as options: marginal product, production function, total product and average product. • We must recall which term matches the definition.

Concept / Approach:
Average product of an input is defined as total output divided by the quantity of that input. For labour, average product of labour equals total output divided by the number of workers, which is effectively output per worker. Marginal product of an input, by contrast, is the additional output produced when one extra unit of the input is employed, holding other inputs constant. Total product refers simply to the total quantity of output produced at a given combination of inputs. The production function is the overall relationship between inputs and output. Thus, the concept that directly matches output per unit of a variable input is average product.

Step-by-Step Solution:
Step 1: Recall the formula for average product of an input. It is total product divided by the number of units of that input. Step 2: Recognise that this formula expresses output per unit of the input, for example output per worker when labour is variable. Step 3: Compare this with marginal product, which measures only the extra output due to a small increase in the input. Step 4: Note that total product is a total level of output, not output per unit. Step 5: Remember that the production function is the relationship between all inputs and total output, not a per unit measure. Step 6: Conclude that average product is the correct term for output per unit of a variable input.

Verification / Alternative check:
Consider a numerical illustration. Suppose a firm employs 10 workers and produces 100 units of output. Total product is 100 units. Average product of labour equals 100 divided by 10, which is 10 units per worker. If an eleventh worker raises total output to 108 units, marginal product of the eleventh worker is 8 units, not 10. This example clearly shows that average product corresponds to output per worker, whereas marginal product corresponds to extra output from one more worker. This confirms that the name we seek is average product.

Why Other Options Are Wrong:
Marginal product measures incremental output from an additional unit of input, not the average output per unit of input.

Total product is the overall output level and does not convey any per unit information about the productivity of individual units of input.

The production function describes how output depends on various input quantities but is not itself a per unit measure like output per worker.

Common Pitfalls:
Many students initially confuse average product and marginal product because both involve changes in output and are often plotted on the same diagram. A helpful memory aid is to associate average with the usual idea of total put over number of units and to associate marginal with the idea of extra or additional. Another pitfall is to treat the term production function as a catch all answer whenever inputs and outputs are mentioned. Keeping these concepts clearly differentiated improves accuracy in exam questions and in understanding how firms measure and improve productivity.

Final Answer:
The concept defined as output produced per unit of a variable input is the Average product of that input.