The principle of diminishing average product can be visually confirmed from the production function graph without requiring calculations. For instance, the ray from the origin to point A is steeper than the ray to point B, showing a higher average product at A. This observation is generalizable: as one moves along the production function curve by increasing the number of farmers, the rays from the origin to these points become progressively flatter. This visual flattening of the rays directly illustrates the continuous decline in the average product of labor.

Graphical Evidence of Diminishing Average Product: Flatter Rays Along the Production Function

The diminishing average product of labor is a direct graphical consequence of the production function's concave shape. As the number of farmers increases, the production function's curve continues to rise but becomes progressively flatter. Consequently, rays drawn from the origin to points further along the curve will have increasingly flatter slopes, which visually represents the decline in the average product per farmer.

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The average product of labor at any given point on a production function graph can be visually and mathematically determined by the slope of a ray drawn from the graph's origin to that specific point. This slope is calculated by dividing the total output (the vertical distance) by the total labor input (the horizontal distance). For example, within Angela's model, the average product at a specific point T is represented by the slope of the ray from the origin to T. This principle applies generally to production functions.

Average Product of Labor as the Slope of a Ray from the Origin

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/.

To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

CORE Econ - The Economy 2.0: Microeconomics

The conceptual distinction between marginal and average product is visualized on the production function graph through two different slope measures. The marginal product at a given point is represented by the slope of the tangent to the production function at that point, mathematically denoted by the first derivative, $f'(x)$. The average product of labor (APL) at that same point is represented by the slope of a ray drawn from the origin to the point on the function, calculated as $APL = f(x)/x$.

Graphical Comparison of Marginal and Average Product

A specific calculation on the production function graph from Figure E5.2a illustrates the concept of Average Product of Labor (APL). At point P, where the labor input is 5 hours and the corresponding output is 19.04 units, the APL is calculated by dividing the total output by the total input. This value, $19.04 / 5 = 3.8$, represents the slope of the ray drawn from the origin to point P.

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