What's the relationship between the Average Physical Product Curve and the Marginal Physical Product Curve? Why does the Marginal Physical Product curve slope downwards so soon?

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Both the average physical product (APP) curve and the marginal physical product (MPP) curve are ultimately based on the total product curve.  All three curves are shown in the graphs below.

The total product curve (left graph) measures the output of production (vertical axis) as measured against the amount of a particular input of production (horizontal axis).  An input of production can be a raw material, machinery, labor, or capital.  The peak of the curve (labelled point A on the graph) represents the maximum production output based on the variable input.  Additional input results in diminishing returns, or a drop in the output despite increasing input.

The APP curve measures the specific amount of output obtained from each additional unit of input.  Mathematically, it is obtained by drawing a straight line from the origin (where the two axes intersect at point (0,0)) to each point on the total product curve and plotting the slope of each line.  Since the slopes of these lines do not change radically, the APP is actually a rather flat looking curve. 

The MPP curve is the measure of the change in output per unit of input.  Mathematically, it is obtained by plotting the derivative of each point on the total product curve (slope of the tangent line to the curve at each point).  This is why the MPP hits the horizontal axis at the peak of the total production curve (because the tangent line at the peak has a slope of 0).

So the relationship between the two is that the MPP measures the rate of change of output while the APP measures the actual output levels.  So the MPP acts as a driver for the APP since the rate of change will directly affect the average output.  This is why the MPP curve drops off so much more quickly than the APP.  In order for the average output to drop, the rate of (negative) change in the output must change even more so to have that effect.

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