Unformatted text preview: APP reaches a maximum at an input level geater than the level of input use that
maximizes MPP. This point can be found by drawing a line out of the origin with a
constant slope that just touches (becomes tangent to) the production function. This point
of tangency illustrates the level of input use for which the ratio of y/x that represents
APP is greatest. The slope of this line is the maximum possible ratio of y to x. Before this
point, APP is increasing: After this point, APP is declining. Unlike MPP, APP never
becomes negative because the smallest output (y or TPP) can become is zero. Therefore
the ratio of y/x can become no smaller than zero, since x is nonnegative (no negative
pounds of fertilizer or bushels of com!). APP intersects MPP from above at the same input quantity that maximizes MPP. More
input (x) is required for maximum APP than for maximum MPP. When MPP is greater
than APP, APP is increasing. When APP is declining, MPP is also declining. When
MPP is negative, APP is still positive. The elasticity of production measures the responsiveness of the output to changes in the
level of the input use. The elasticity of production is the percentage change in output (y)
divided by the percentage change in input (x). Like other elasticities, the elasticity of
production is a pure number that has no units. For example, an elasticity of production of
0.5 indicates that a one percent increase in input use will be accompanied by onehalf of
one percent increase in output. Another way of deﬁning the elasticity of production is as the ratio of MPP/APP. If the
elasticity of production is greater then 1, a 1 percent increase in input use will result in
greater than a 1 percent increase in output. Hence, if the elasticity of production is
greater than one, MPP must be greater than APP. If the elasticity of production is less
than one, a 1 percent increase in input use will result in less than a 1 percent increase in
output. Hence, this is the region where MPP is less than APP. When MPP equals APP, a
1 percent increase in input results in exactly a 1 percent increase in output. When MPP is
zero, the elasticity of production is also zero. When MPP is negative, the elasticity of
production is also negative, indicating that additional input will cause output (y, TPP) to
decline. Finding the quantity of input required to maximize proﬁts requires a number of
assumptions. These assumptions are: 1. The producer can purchase as much or as little '
input as is needed at a constant price. (Two implications of this assumption are no
"quantity discounts," and the producer does not need to increase wages paid in order to
obtain more workers.) 2. The output price is constant and known with certainty. (The
price might be "locked in" using the futures market. The individual producers are not "big
enough" to individually affect the market price by individual output decisions.) 3. The
production ﬁinction is known with certainty. (Droughts and disease do not occur. The
farmer knows exactly how much corn will be produced from each incremental pound of
fertilizer. This assumption is not very realistic for agriculture.)Proﬁt (H) is total revenue
(TR) less total cost (TC). Total revenue may be obtained by multiplying the price of the
product (y) by the quantity produced. Output and input are linked through the production
function y = ﬁx). Total value of the product (TVP) is total physical product (TPP or y)
multiplied by the price of the product. Another way of writing total value of the product 6 ...
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 Spring '10
 DrCarlDillion

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