RPT = !dy2/dy1 25.15 dy2/dy1 = !(81/82)(y2/y1) (1+n)
The product transformation functions generated from the
CES-like function in product space are downsloping so
long as 81 and 82 are positive, irrespective of the value of
the parameter n. Differentiatin
looking at various functional forms is in terms of Taylor's
series Contemporary Production Theory: The Factor Side
387 expansions. For example, the Cobb-Douglas type
production function could be written as a first order
Taylor's series expansion of lny in
variable input. The Cobb-Douglas production might be
thought of in this regard as contemporary, rather than
neoclassical, but this is also true for the CES and Translog
specifications developed much later. The duality concepts
are closely linked to the ma
Paula de la O Campos, Stefano Gerosa, Yasmeen Khwaja,
Faith Nilsson and Panagiotis Karfakis (ESA); Francesca
Dalla Valle, Soline de Villard, Caroline Dookie, John Curry,
Zoraida Garcia, Denis Herbel, Regina Laub, Maria Lee,
Yianna Lambrou, Marta Osorio, H
jth output Total cost is given as 24.36 C = Evi xi . The
output expansion path defines the revenue maximizing
combination of outputs for the firm, in much the same
manner as the expansion path defines the least cost
combination of inputs. The indirect rev
which the elasticity of substitution is near zero. A flexible
facility is represented by a product space elasticity of
substitution that is strongly negative. Note 1 There is
considerable disagreement in the literature with regard
to terminology relating
24.68 [d(x2/x1)/d(v1/(v2)]/(v1/v2)/(x2/x1)] or as
dln(x2/x1)/dln(v1/v2) = (dlnx2 - dlnx1)/(dlnv1 ! dlnv2).
Equation 24.68 is the definition attributed to Hicks (See
also Varian, pp. 44-45). Notice, however, that v1/v2 is
equal to the MRSx1x2 only in compe
importance for empirical research. If the firm is operating
according to the assumptions embodied in the expansion
path 378 Agricultural Production Economics conditions
on both the factor and product sides, then product
supply and factor demand equations
total expenditures on input xi according to the expansion
path conditions. Thus, the expression xi *vi /C* = >i = Si
where Si is the cost share associated with the ith input.
The series of cost share equations thus becomes
Contemporary Production Theory:
usually be negative, and the Allen-like elasticity of
substitution in product space (Fijp) for most commodities
is negative. 25.8 Empirical Applications Many possibilities
exist for empirical analysis linked to agriculture based on
the models developed in
Am Application to U.S agriculture 1947 to 1974." in
Modeling and Measuring Natural Resource Substitution.
eds. E.R. Berndt and B.C. Field. The MIT Press, Cambridge
Mass., 1981. Christensen, L.R., D.W. Jorgenson, and L. J.
Lau. "Conjugate Duality and the T
underperforming in many developing countries, and one
of the key reasons is that women do not have equal
access to the resources and opportunities they need to
be more productive. This report clearly confirms that the
Millennium Development Goals on gende
2010 72 23. Indices of per capita food consumption by
geographic region, 200010 72 24. Indices of food
production by economic group 73 25. Indices of food
production by region, 200010 74 26. Indices of food
export volumes by geographic region, 200010 75 2
not the outputs are produced only in fixed proportion
with each other. 2 The concept of an elasticity of
substitution in product space is one mechanism for
resolving the problems with the joint and multiple
product terminology. The output elasticity of su
are more than two inputs, some input pairs may be
complements with each other, thus leading to a potential
negative elasticity of substitution for some of the input
pairs. The definition of an elasticity of substitution in an n
factor case is further comp
case of product space, revenue is maximized for the fixed
input quantity x, is substituted for minimization of costs
at a fixed level of output y( p. 292) in factor space. The
elasticity of substitution in two product one input space
(Debertin) is defined
than their male counterparts. Yet women are as good at
farming as men. Solid empirical evidence shows that if
women farmers used the same level of resources as men
on the land they farm, they would achieve the same yield
levels. The yield gap between men
for still other elasticity of substitution concepts. For
example, the Morishima elasticity of substitution
(Koizumi) is an example of a TOES elasticity of
substitution and is defined in terms of the AES as 24.74
FM i j = Sj (FA ij ! FA jj) = Eij ! Ejj Thi
technology. In product space, the corresponding
assumption is that there is a constant increase in revenue
associated with an increase in the size of the input
bundle. This implies 25.50 dR*/dx = *x = 1 25.51 E*ix
= 0 for i = 1, ., n 25.52 *xx = 0 410 Agr
products is "nearly" supplemental to the other. As n6 !1,
the products become more nearly competitive
throughout the possible combinations, with the diagonal
product transformation functions when n = !1 the limiting
case. Regions of product complementarit
25.44 logR* = logD + *1logp1 + *2logp2 + *11 (log p1) 2
+ *22(logp22) 2 + *12logp1logp2 +n1xlogp1logx +
n2xlogp2logx +nxlogx + nxx(logx) 2 Contemporary
Production Theory: The Product Side 409 Every point on
the translog revenue function in product space i
process involving n inputs and a single output is: 25.1 y
= f(x1,.,xn) with an isoquant representing a fixed
constant output arising from possible combinations of
the xi : 25.2 y = f(x1,.,xn) In product space, the
analogous equation linking the production
gender gap in access to productive resources. Women
control less land than men and the land they control is
often of poorer quality and their tenure is insecure.
Women own fewer of the working animals needed in
farming. They also frequently do not control
unlike anything possible with the CES or Cobb-Douglas
specifications, which produce isoquants that are
everywhere downward sloping. As was indicated in
Chapter 11, the HCH transcendental is 24.94 The Allen
elasticity of substitution for the HCH transcende
= 0 Partially differentiating 24.108 with respect to the
ith input price, assuming that restrictions 24.109 24.112 hold 24.113 MlnC*/Mlnvi = "i + E $ij lnvj +
(yilny + Ntit i = 1, ., 5 Invoking Shephard's lemma
24.114 MlnC*/Mlnvi = MC*/Mvi vi /C* =(xi vi
estimates of the cost share equations, the corresponding
Allen Elasticities of Substitution between input pairs and
the related measures can be derived. Brown and
Christensen derive the constant output partial static
equilibrium cross price elasticity of
prepared in close collaboration with Agnes Quisumbing
and Ruth Meinzen-Dick of IFPRI and Cheryl Doss of Yale
University. Background papers, partially funded by ESW,
were prepared by Cheryl Doss; Julia Behrman, Andrew
Dillon, Ruth Vargas Hill, Ephraim Nkon
Assuming that n 2 is 25.25 ,sp = [dlogyk ! dlogyi ]/
[dlogpi ! dlogpk] Equation 25.25 is representative of a
two-output, two-price (or TOTP) elasticity of product
substitution analogous to the two input two price (TTES)
elasticity of substitution in facto
The product transformation functions needed for the
existence of a corresponding dual revenue function are
not necessarily more plausible in an economic setting
than other product transformation functions, but are
rather a mathematical convenience. A Cobb