The average product for X given Y = 2 units is shown in column 4 of Table 7.2 and in Figure 7.2(b).

For a continuous total product function, as illustrated in Figure 7.3(a), marginal product equals the slope of the total product curve, whereas average product equals the slope of a line drawn from the origin to a point on the total product curve. The average and marginal products for input X can be determined in this manner, and these points are plotted to form the average and marginal product curves shown in Figure 7.3(b).

Three points of interest, A, B, and C, can be identified on the total product curve in Figure 7.3(a). Each has a corresponding location on the average or marginal curves. Point A is the inflection point of the total product curve. The marginal product of X (the slope of the total product curve) increases until this point is reached, after which it begins to decrease. This can be seen in Figure 7.3(b) where MPX reaches its highest level at A'.

The second point on the total product curve, B, indicates the output at which the average product and marginal product are equal. The slope of a line from the origin to any point on the total product curve measures the average product of X at that point, whereas the slope of the total product curve equals the marginal product. At point B, where X2 units of input X are employed, a line from the origin is tangent to the total product curve, so MPX = APX. The slopes of successive lines drawn from the origin to the total product curve increase until point B, after which their slopes decline. The average product curve rises until it reaches B, then declines. This feature is also shown in Figure 7.3(b) as point B'. Here again, MPX = APX and APX is at a maximum.

The third point, C, indicates where the slope of the total product curve is zero and the curve is at a maximum. Beyond C the marginal product of X is negative, indicating that increased use of input X results in a reduction of total product. The corresponding point in Figure 7.3(b) is C', the point where the marginal product curve intersects the X-axis.

law of diminishing returns

As the quantity of a variable input increases, the resulting rate of output increase eventually diminishes

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