Name : Jakai Walker
Date : June 28th, 2016
Module One Project Option 1
Instructions
Part 1: How's the weather?
Investigate the weather forecast in your city.
Record the high and low temperatures that are forecast for the next 7 days in the
table below. In

and other agricultural inputs. Some even argued that
rising fuel prices would eventually lead back to a labororiented agriculture more broadly consistent with
agriculture in the nineteenth century, but the mix of
inputs used in agriculture changed very li

variable. In the long run, the marginal product of the
bundle of inputs that comprise the resources or factors of
production for the society should be proportionate to the
change in the size of the bundle, or the amount of
resources available to the socie

corresponding to: a. The inflection point. b. Maximum
MPP. c. Maximum APP. d. Maximum TPP. 3. If the
production function is a polynomial consistent with the
neoclassical three stage production function (see
Problem 5, Chapter 2), show that the level of x

functions. Table 9.1 Relationships between the Function
Coefficient, the Dual Cost Elasticity, and Returns to
Scale )
Degree of Function Cost Homogeneity Coefficient
Elasticity Input Returns to n E R Prices
Scale ) 0.0
0.0 Infinite Constant ? 0.1 0.1 10.0

pseudo scale lines exist and converge at some finite level
of input use along the expansion path. The convergence
of the pseudo scale lines represents the global point of
profit maximization. If the function coefficient is equal to
1, the pseudo scale lin

output (y). Along an isoquant, a diminishing marginal rate
of substitution is usually a result of the law of diminishing
returns that applies to the underlying production
functions for each input. Consider a production function
12.1 y = ax1 + bx2 The marg

v2) Similarly, for input x1, 10.31 x1 = C/($2v1$1 !1 + v1)
Inputs x1 and x2 are now defined totally in terms of cost
C, the input prices (v1 and v2) and the parameters of the
production function. Inserting equations 10.30 and
10.31 into the original produ

Agricultural economists in developing countries need to
be vitally concerned with respect to the elasticities of
substitution for the major agricultural commodities being
produced. For example, the extent to which labor is free
to move out of agriculture

of production for input x1 is 11.22 ,1 = "1 + (1x1 +
(3x2x1 Along the ridge line for x1, the production
elasticity for x1 is zero. This implies that 11.23 "1 + (1x1
+ (3x2x1 = 0 or 11.24 x1(1 + (3x2) = !"1 11.25 x1
= !"1/(1 + (3x2) The amount of x1 requir

and x2 contained in the input bundle. For example, if
each unit of the bundle consists of 2 units of x1 and 1
unit of x2, then w1 is 2, and w2 is 1. The cost of 1 unit of
the input bundle is 9.19 v1w1 + v2w2 = V The inverse
production function is 9.20 X =

transformation of labor and capital into output. Rather, it
was chosen because it retained the two key economic
assumptions of the day (diminishing returns to each
input and constant returns to scale) and because its
parameters were easy to obtain from ac

appearance, this is a production function of the Cobb
Douglas type. Suppose that the price of both x1 and x2 is
$1 per unit. The Lagrangean would be 10.43 L = x1x2 +
8(C ! 1x1 ! 1x2) With the corresponding first order
conditions 10.44 ML/Mx1 = x2 ! 18 = 0

and all incremental units of output cost more that they
generated in additional revenue. The total loss is (p ! V)y,
where y is the number of units of output produced. Only
if p were equal to V would the manager be indifferent to
producing or shutting dow

function y = Ax1 "x2 $ For each case, does there exist the
following? a. A global point of output maximization. b. A
global point of profit maximization (assume constant
input and output prices). c. A series of points of
constrained output maximization. 1

available, all of the information needed to obtain the
corresponding dual cost function can be obtained from
the production function. The coefficients or parameters
of a Cobb Douglas type of production function uniquely
define a corresponding dual cost fu

general functional forms that would encompass a
number of explicit specifications as special cases. In the
1960s and 1970s, the direction of research both in
general and in agricultural economics increasingly turned
to the problem of determining the exten

of a bundle of x1 and x2 is declining. 180 Agricultural
Production Economics Diagrams E and F illustrate a Cobb
Douglas type of production function in which the
individual elasticities of production for each input are less
than 1 but the elasticities of p

12.16 MRSx1x2 = bx or 12.17 x = (1/b)MRSx1x2
Therefore 12.18 dx/dMRSx1x2 (the change in the input
ratio with respect to a change in the marginal rate of
substitution) = 1/b 12.19 (MRSx1x2)/(x2/x1) = bx/x
Hence, the elasticity of substitution for a Cobb!Do

positioned closer to the axis of the input with the larger
elasticity of production. To reemphasize, the general
shape of the isoquants for a Cobb Douglas type of
function are not conditional on the values of the
individual production elasticities. As lon

will depict stage II everywhere. If the function coefficient
is less than 1, there will normally be a point of global
profit maximization at a finite level of input use. Pseudo
scale lines exist and will intersect on the expansion path
at this finite leve

gasoline. The elasticity of substitution between the
capital embodied in a new automobile and gasoline was
clearly positive. The elasticity of substitution between
input pairs may differ significantly among various farm
enterprises. There still appear to

production sum to a number other than 1, or in a case
where there are more than two inputs or factors of
production. 10.4 Some Characteristics of the Cobb
Douglas Type of Function The Cobb Douglas type of
function is homogeneous of degree E$i . The return

exact center of the rings occurs at x1 = !"1/(1, x2 = !"2/(2.
The first-order conditions for profit maximization can be
derived by setting the marginal rate of substitution equal
to the negative ratio of the input prices (!v1/v2). The
resultant equation d

versus farm labor. Farmers often complain about the
prices for tractors and other farm machinery, but changes
in the mix of inputs toward tractors and farm machinery
would not have taken had it not been economic. Farmers
look for the point of least-cost-c

substitution came into being. Actually, several formulas
were developed. For example, Heady proposed that the
elasticity of substitution (esh) should be equal to the
percentage change in the use of x2 divided by the
percentage change in the use of x1 12.2

zero. Since illustrations of the neoclassical production
function show a declining elasticity of production as the
use of the input increases, the transcendental production
functions of greatest interest are those in which ( is
negative. Halter et al. wor

and h are constants and j is nonzero, the function is a
general two input transcendental, without any particular
restriction of the form of j. If j = (1x1 + (2x2, the function
is the standard transcendental. The Cobb Douglas
function with Other Agricultur

11.1 y = A (1 ! R1 x1 )(1 ! R2 x2 ) where A, R1 and R2 are
parameters to be estimated. The parameters R1 and R2
would normally be expected to fall between zero and 1.
The sum of R1 + R2 would normally be less than or equal
to 1. An example of the Spillman

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example, adding the term 'without recourse' to a negotiable instrument signifies that the endorser shall
not be liable if the instrument is dishonored. *"W