What's the relationship between the Average Physical Product Curve and the Marginal Physical Product Curve? Why does the Marginal Physical Product...

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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