revenues accruing to the farm firm. Moreover, the
equations representing the first order conditions can be
divided by each other: Maximization in the Two-Input
Case 115 6.67 pf1/pf2 = v1/v2. Note that
) From Table
2.1, 160 pounds of nitrogen per acre will result in a corn
yield or TPP of 123 bushels per acre. The concept of a
function has a good deal of impact on the basic
assumptions underlying th
problem for the mathematician. The saddle is level in the
middle, but it slopes upward at both ends and downward
at both sides. A saddle looks like neither a hill nor a
valley, but is a combination of
On the expansion path: VMPx1/v1 = VMPx2/v2 = 0 Global
output maximization VMPx1/v1 = VMPx2/v2 < 0 Stage III
for both inputs; the profit-maximizing farmer would not
operate here VMPx1/v1 = VMPx2/v2 = 0
< 0 6.86 pf11pf22 ! pf12pf21 > 0 6.87 p2 (f11f22 !
f12f21) > 0 Since p2 is positive, the required signs on the
second-order conditions are the same for both profit and
yield maximization. 6.8 Concludi
was the rapid growth in the use of the computer as a
device for estimating or measuring relationships within
an economy. Economists now routinely use techniques
for estimating models in which the comp
producers. Production of hogs and cattle in the United
States is often closer to a purely competitive environment
in which a large number of farm firms take prices
generated by overall supply and dema
at the top of the hill is zero in all directions. It is not
possible to distinguish the bottom of a valley from the
top of a hill simply by looking at the slope at that point,
because the slope for bo
bundle of the two inputs x1 and x2. Suppose that the
proportion of each input contained in the bundle is
defined by the expansion path. If the expansion path has
a constant slope, then as one moves up
remainder of the text. Rather, reliance will be placed on
the purely competitive model as the starting point for
much of our analysis, with modifications made as needed
to meet the particular features
the maximum output given the budgeted dollars C or
subject to the budget constraint. Another approach is to
think of the amount of output represented by a particular
isoquant as being fixed. Then the
rationale, it seems unlikely that 140 pounds of nitrogen
would produce a yield of 119 bushels, and a more likely
guess might be 120 or 121 bushels. These are only
guesses. In reality no information ab
regard to what to produce given available land, labor,
machinery, and equipment. The manager must not only
decide how much of each particular commodity to be
produced, but also how available resources
economy. Economists rely heavily on what is sometimes
called comparative statics. The economic relationships
are often represented by a graph: for example, a graph
showing a supply curve and a demand
variable, but nature presents other challenges. Cattle
develop diseases and die, and crops are affected by
insects and disease. Most farmers would scoff at
economic theory that assumes that a producti
for a maximum are 6.11 f1 = 10 ! 2x1 = 0 6.12 x1 = 5
6.13 f2 = 10 ! 2x2 = 0 6.14 x2 = 5 The critical values for
a function is a point where the slope of the function is
equal to zero. The critical val
indicated earlier, the data contained in Table 2.1 assume
that there is some residual nitrogen in the soil on which
the corn is grown. The nitrogen is in the soil because of
decaying organic material
competition, the consumer has complete knowledge with
respect to prices. Most importantly, with perfect
competition the producer is assumed to have complete
knowledge of the production process or func
Like the earlier saddle points, a minimum exists in one
direction and a maximum in another direction at a value
for x1 and x2 of 0.25, but the saddle no longer is parallel
to one of the axes, but rath
) Production
with One Variable Input 17 The corn yields (TPP)
generated by the production function in Table 2.2 are not
the same as those presented in Table 2.1. There is no
reason for both functions
conclusions is reassuring. The use of mathematics as a
tool for presenting production theory does not mean that
the marginal principles change. Rather, the mathematics
provides further insight as to w
of x produces more and more additional y. Hence the law
of diminishing returns does not hold here either. Notice
that as the use of input x is increased, x becomes more
productive, producing more and
nitrogen produces 123 bushels of corn, the yield at 140
pounds might be (115 + 123)/2 or 119 bushels per acre.
However, incremental increases in nitrogen application
do not provide equal incremental i
Production 14 Agricultural Production Economics 2.1
What Is a Production Function? A production function
describes the technical relationship that transforms
inputs (resources) into outputs (commoditi
Budget Constraints 121 7.3 ($100/$3.00)@($100/$5.00)
= ($100/$3.00)@($5.00/$100) = $5.00/$3.00 = 1.67 In
equation 7.3 , the budget constraint has a constant
slope of 5/3 or 1.67. Under the assumption
assuming that the second input is fixed. This is not the
global point of profit maximization, since only one input
is allowed to vary. For input x1, this is where pMPPx1/v1
= 1, assuming that x2 is fi
fixed or "sunk" once they have been applied. At the start
of harvest, the only variable input is the labor, fuel, and
repairs to run the harvesting equipment and to move the
grain to market. This view
what a negative quantity of an input might be. Functions
might be expressed in other ways. The following is an
example: If x = 10, then y = 25. If x = 20, then y = 50. If x =
30, then y = 60. If x = 4
greatest. There is no other point more profitable (Figure
7.4). The global point of profit maximization, where
profits are greatest when both inputs can be varied, is at
once a point on the expansion