Unformatted text preview: Total physical product (TPP) is the same as total product (TP) and the output level (y).
The vertical axis of a production function can be labeled as TPP, y or output, or have all
of these names. Marginal product (MP) is the incremental change in output associated with a one unit
change in the use of the input that is allowed to vary. Marginal product is sometimes also
called marginal physical product (MPP), since product is measured in physical quantities
(bushels, pounds) rather than in value (dollar) units. The change in output (TPP or y) is abbreviated ATPP or Ay. The greek letter delta (A) can
be read as the word "change". The change in input is abbreviated by Ax. Marginal physical product is Ay/Ax or as ATPPZAx. Using calculus, at a point these terms become
dTPP or dy for the change in TPP at a point and dy/dx for MPP Constant marginal product (MPP, that is Ay/Ax or dy/dx at a single point) occurs when
the production function increases at a constant rate. For the production function y = 2x,
marginal product of each incremental unit of x is constant at 2 units. That is, Ay/Ax = 2.
A production function y = bx also has a constant marginal product of b, where b is dy/dx
and b can be any positive number. Increasing marginal product (MPP) occurs when the production function increases at an
increasing rate. Each incremental unit of x produces more and more additional output,
and there is increasing marginal returns to the variable input. MPP increases as
incremental units of input (x) are added. Decreasing, or diminishing marginal product (MPP) occurs when the production function
increases at a decreasing rate. Each additional unit of x produces less and less additional
y. As the use of x increases, MPP decreases. A neoclassical production function has a
region of increasing marginal product near the origin where the x and y axes intersect.
The inﬂection point separates the region of increasing marginal product from the region
of diminishing marginal product. With additional units of input (x), the function (TPP)
reaches a maximum. At maximum TPP, MPP is zero. Beyond the maximum, total
product (TPP) begins to decline. MPP is negative at input levels beyond the input level
producing the maximum TPP level. The law of diminishing returns states that as units of a variable input are added to other,
ﬁxed inputs, eventually a point is reached where each additional unit of input produces
less and less additional output. This law should be named the law of diminishing
marginal returns since it refers to what happens to marginal, not total product. The law of diminishing returns begins at input level corresponding with the inﬂection
point, and holds for all input levels beyond. If the law of diminishing returns is to hold,
MPP must be decreasing, but MPP may be positive or negative. The inﬂection point also
corresponds with the input level that produces the maximum MPP. Average Physical Product (AP or APP) is the ratio of output to the (variable) input level. APP can be written as the ratio output/input, y/x, or TPP/x. APP is thus obtained by
simply dividing the output by the input. 5 ...
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- Spring '10