In the theory of production, the average product curve usually has which characteristic overall shape?

Introduction / Context:
Production theory in microeconomics studies how output responds to changes in inputs. The average product curve describes output per unit of a variable input, such as labour, while other inputs are held constant in the short run. Understanding the shape of this curve is important for analysing efficiency, marginal productivity and different stages of production.

Given Data / Assumptions:

• We focus on the short run, where at least one factor, usually capital, is fixed.
• One variable input, such as labour, is increased while others remain constant.
• Technology and management practices are assumed to be given.
• We consider typical real world production where diminishing returns eventually set in.

Concept / Approach:
Average product is defined as total product divided by the quantity of the variable input. Initially, when small amounts of the variable factor are applied to the fixed factor, better use of capacity and specialisation cause average product to rise. After a certain point, crowding and overuse of the fixed factor lead to diminishing marginal returns and eventually cause average product to decline. This pattern of first increasing and then decreasing average product gives the curve an inverse U shape, rising to a maximum and then falling.

Step-by-Step Solution:
1. At low levels of the variable input, average product rises because workers can specialise and use fixed capital more efficiently. 2. With continued additions of the variable input, total product continues to increase but at a slower rate. 3. When marginal product starts to fall below average product, it pulls the average down, making the average product curve turn downwards. 4. Graphically, average product plotted against units of the variable input rises, reaches a maximum, and then declines. 5. This rising then falling pattern corresponds to an inverse U shape.

Verification / Alternative check:
In any standard textbook diagram, the total product, marginal product and average product curves are shown together. The total product curve first increases at an increasing rate and then at a decreasing rate. Marginal product rises, reaches a peak, and then falls, eventually going to zero or negative. The average product curve lies below marginal product when it is falling and above it when it is rising, and overall it forms an inverted U shape. This confirms the theoretical explanation.

Why Other Options Are Wrong:
Option A and C: X and V shapes do not match the standard pattern of rising then falling productivity; they would imply abrupt changes or a constant downward trend, which is not typical.
Option B: W shape would require average product to rise, fall, rise again and fall again, which is not how the law of variable proportions is usually represented.
Option E: A horizontal line would mean average product is constant regardless of additional units of the variable input, which contradicts the observed behaviour in real production processes.

Common Pitfalls:
Students sometimes confuse marginal product and average product curves and assume they must have identical shapes. Another error is to forget the link between total product and these measures. Remember that average product is total product divided by the number of units of the variable factor, and its shape is derived from how total product changes. Knowing that marginal product intersects average product at its maximum helps you remember that the average product curve is inverse U shaped.

Final Answer:
U shape that is inverse, rising then falling