OUTRIGHT FORWARDS
MINI CASE
suppose that U.S. company is expecting to receive 10 million CHF in 3 months and to
pay 1 million EUR in 1 week
the company is willing to hedge these future payments and to lower CHF and EUR
currency exposure
in your opinion th

of y1 (MPPxy1) and the marginal product of x in the
production Maximization in a Two-Output Setting 261 of
y2 will be zero. As MPPxy1 and MPPxy2 approach zero,
1/MPPxy1 and 1/MPPxy2 become very large, and
approach infinity. If MPPxy1 and MPPxy2 were exact

Taylor p. 42). Now consider the factor beam for the
homothetic production function representing the
expansion path, or least cost combination of inputs. The
production surface arising above the expansion path
represents the production function for the use

lots of chemicals and other inputs; a small farmer uses
small amounts of fertilizer, chemicals, and other inputs.
This correlation leads to multicollinearity problems
which, if severe enough, make it impossible to estimate
the production elasticities for

(Moreover, if a single farmer were to acquire all the
world's farmland, the purely competitive assumptions
would no longer hold!) Every farmer faces capital
constraints limiting the ability to borrow money for the
purchase of more inputs. Perhaps the fact

that 16.78 R = p1y1 + p2y2 The Lagrangean is 16.79 L
= g(y1, y2) + R(R ! p1y1 ! p2y2) The corresponding first
order conditions are 16.80 g1 ! Rp1 = 0 16.81 g2 ! Rp2
= 0 16.82 R ! p1y1 ! p2y2 = 0 By rearranging and
dividing equation 16.80 by equation 16.81

determined by the model and the value of the objective
function when the solution was found. Shadow prices or
imputed values for an additional unit of each input are
found in Table 22.5. Table 22.4 Linear Programming
Enterprise
Solution )
Corn 50 acres Wh

could afford to pay for an additional unit of an input.
These shadow prices are the same as Lagrangean
multipliers in that they give the increase in the objective
function (in this case, returns over variable costs) of an
additional unit of the input. Thi

demand analysis for agricultural problems at varying
levels of aggregation. The duality principles can be
illustrated using simple multiplicative functions of the
Cobb-Douglas type. However, the specific focus in this
chapter is on the development of empi

the assumed constant parameters of the production
function. If prices for inputs are available and constant,
all of the information needed to obtain the
corresponding dual cost function can be obtained from
the production function. The coefficients or par

space. If R1 + R2 > 1, Isoproduct contours representing
constant incremental increases in input bundle (x) use
will be positioned closer and closer together. If R1 + R2 =
1 Isoproduct contours will be equally spaced. If R1 + R2 <
1, isoproduct contours al

specific applications of a mathematical theorem known
as the envelope theorem. The proofs of the envelope
theorem, Shephard's lemma, and Hotelling's lemma are
adapted from those found in Beattie and Taylor (Chapter
6). More detailed and rigorous proofs ca

such as equation 15.1 could provide valuable information
about elasticities of substitution faced by farmers when
attempting to choose among possible products. The
could be used as a guide in making agricultural policy.
With knowledge of product space ela

Lagrange's method would not find a solution in stage III
where the Lagrangean multiplier is negative. The partial
derivative g11 can be interpreted as the slope of the
marginal cost function for y1. The derivative g22 has the
same interpretation for y2. M

that the function coefficient for the underlying
production function is strictly less than 1. The profit
function representing the least cost method of
generating a specific amount of profit, and corresponding
to the dual cost function can be written as 2

coefficient that appears at the intersection of the pivotal
row and the pivotal column, 2 in this case. This results in
a table with a new row x2 labeled nx2 346 Agricultural
Production Economics 22.14
Column )
Row y1 y2 s1 s2 RHS x1 2 1 1 0 12 nx2 1/2 =

convenience. For example, the Cobb-Douglas, CES and
Translog production functions discussed in this
publication all generate isoquant maps consistent with
these assumptions, under the usual parameter
restrictions, while the Transcendental does not. Consid

farmer has 100 acres of land. Steers, sows, and layers are
kept in confinement, so incremental units will not require
any more land. The farm has a wheat allotment limiting
wheat acreage to no more than 12 acres. Only 50 of the
100 available acres are sui

maximization problem or a corresponding minimization
problem subject to appropriate constraints. The primal
problem may be either a maximization or a minimization
problem. If the primal is a maximization problem, the
corresponding dual will be a minimizat

that would be required such that the output of both y1
and y2 is at its maximum. The farm manager has
available any amount of the input bundle x, and, at least
for the moment, the cost of the input bundle is of no
consequence. One way is to look at the fi

terms under the constant input price assumption is
24.3 vx = vf!1 (y) where v = the price of the input x. Not
all functions can be inverted. In general, a production
function can be inverted to generate the corresponding
dual cost function only if the ori

) If all
numbers appearing in the columns representing outputs
are 0 or negative, the optimal solution has been found. In
this example, the value at the intersection of the y1
column and the new objective row is positive, indicating
that production of y1

each output. The product price elasticity of demand by
the farmer for the input bundle x in the production of y1
is 1.5 and in the production of y2 is 2. These are obtained
from the formula !1/(1 ! ep). Each of these elasticities can
be interpreted as the

the specific output level y as defined by the expansion
path conditions. 372 Agricultural Production Economics
Equation 24.13 represents the total cost function that is
dual to the production function defined along the
expansion path factor beam. Any poin

y2 to be produced. The manager is then assumed to have
the right amount of x needed to globally Maximization in
a Two-Output Setting 271 maximize profits in the
production of both y1 and y2. The same level is needed
irrespective of whether the problem is

primal or dual is solved. 22.9 An Application The use of
linear programming in agricultural economics is
illustrated with a simple problem. The problem is
purposely kept small in order to shorten the explanation.
The problem illustrates how linear program

which is at least as large as xO in every input, then xO can
also produce y. One implication of this assumption is that
isoquant maps consisting of concentric rings are ruled
out, and that positive slopes on isoquants are not
allowed. (2) Marginal rates o

of tangency between the isocost line and the isoquant.
Maximization in a Two-Output Setting 269 The point of
tangency between the isorevenue line and the product
transformation function does not look the same as the
point of tangency between the isocost l

price of the product and solving the resultant equation
for y. Average cost associated with the least cost factor
beam is 24.15 AC* = C*/y = y[1/($1+$2)!1]Z. Since Z is
positive, average cost decreases when the partial
production elasticities sum to a num

Summary of chapter 8
Short run
It is a planning period over which the managers of a firm must consider one
or more of their factors of production as fixed in quantity.
A fixed factor of production = when the quantity of a factor of production
cannot be ch

Summary of chapter 7
Utility= it is satisfaction which is providing us from buying some goods or services
Total utility
If we could measure utility, total utility would be the number of units of utility that a
consumer gains from consuming something durin

Summary of chapter 9
Perfect competition is a model of the market based on the assumption that a large
number of firms produce identical goods consumed by a large number of buyers. There are
no brand preferences or consumer loyalties.
Price takers are ind

CP: 1,2,7
NP: 1,5
1. Which of the following would be considered long-run choices? Which are short run
choices?
1. A dentist hires a new part-time dental hygienist. Short run
2. The local oil refinery plans a complete restructuring of its production proces

Summary of chapter 5
Price elasticity of demand= percentage change in quantity demanded of particular goods
divided by percentage change in the prices.
We are counting it to get know, how the higher price will affect the demand.
Elasticity= how sensitive