one equation is redundant, and mechanically, the choice
of the equation to be omitted is arbitrary, but the
empirical results may not be invariant with respect to the
choice of the omitted equation unless an iterative
estimation procedure is used (cf. Hum

Resource Economics 13(1984) pp. 238-244. Humphrey,
D.B, and B. Wolkowitz. "Substituting Intermediates for
Capital and Labor with Alternative Functional Form: An
Aggregate Study. Applied Economics 8 (1976) pp. 59-68.
Koizumi, T. "A further Note on the Defi

nMF/Myj = 0 for all j = 1, ., m. The optimal yj is yj *.
Contemporary Production Theory: The Factor Side 377
First order conditions on the factor side require that
24.44 ML/Mxi = vi ! nMF/Mxi = 0 for all i = 1, ., n. The
optimal xi is xi *. Now differenti

Henderson and Quandt in factor space include only
values of D that lie between !1 and +4. In product space,
the values of n that lie between !1 and !4 generate
product transformation functions with an increasing rate
of product transformation, since equat

the m output case, the Allen like elasticity of substitution
(or transformation) (Aik p ) in product space between
input xi and xj evaluated at a constant input price wj is
defined as: 25.35 Aik p = (1/Rk)(Eij p ) where Eij p =
dlogyi /dlogpk, the cross-p

is greater than two, specific assumptions for the
calculation need to be made with regard to prices and
quantities of inputs other than i and j. Moreover, a
number of alternative definitions for the elasticity of
substitution are possible. The one-input,

Agricultural economists are usually interested in
disaggregating input categories into more than two
inputs. Thus the CES never was extensively used in
agricultural economics research. A more flexible
functional form was clearly needed for agricultural
ec

product space cannot generate product trans-formation
functions consistent with neoclassical theory and the
usual constrained optimization revenue maximization
conditions. 402 Agricultural Production Economics 25.4
CES-Like Functions in Product Space The

Studies 35:2(1968) pp. 225-236. Revankar, N. "A Class of
Variable Elasticity of Substitution Production Functions."
Econometrica 39:1. (1971) pp. 61-72. Sato, K. "A Two
Level CES Production Function." Review of Economic
Studies 34-2:98 (1967). pp. 201-218

Shadow Elasticity of Substitution estimate obtained from
this model, that is perhaps the closest to the Hicks'
definition, is not quite the long run measure envisioned
by McFadden. Inputs in the x vector other than i and j are
treated as variable in the s

elasticity of product supply. In factor space, the Allen
elasticity of substitution is proportional to the cross price
input demand elasticity evaluated at constant output.
Normally, as the price of the jth input increases, more of
the ith input, and less

for the existence of a corresponding dual cost function
are not necessarily more plausible in an applied setting
than other isoquant maps, but rather are a matter of
mathematical convenience. For example, the CobbDouglas, CES and Translog production funct

theorists is free disposal. Assuming positive factor prices,
no economic conditions could cause the firm to apply
units of a variable input beyond the point where output
is maximum. Beattie and Taylor (p. 91) indicate negative
factor prices could exist, f

hypothesis that the elasticity of substitution between
labor and capital is 1 may be tolerable in a 1928 study
dealing with a production process representing the
output of a society and utilizing capital and labor as
inputs. As will be empirically shown,

[email protected] Fax: (+39) 06 57053360 Web
site: http:/www.fao.org/catalog/inter-e.htm Photos on
front cover and page 3: All photos are from the FAO
Mediabase. THE STATE OF FOOD AND AGRICULTURE
FOOD AND AGRICULTURE ORGANIZATION OF THE
UNITED NA

increases the elasticity of substitution between input
pairs is desirable in that the producer is given additional
flexibility in dealing with changes in the relative prices of
the inputs that might occur due to shocks within the
factor markets. For examp

function (without linear homogeneity imposed ) is
24.84 y = A[$1x1 !D + $2x2 !D ] !1/D Suppose that the
marginal rate of substitution from some unknown
production function is given by 24.85 MRSx1x2 = $x1+D
where $ = a constant x = x2/x1 Taking logs 24.86

labour markets function better, vii providing laboursaving technologies and public goods and services, would
enable women to contribute more effectively to, and
benefit more fully from, the economic opportunities
offered by agricultural growth. There exis

56 Key messages 58 6. Closing the gender gap for
development 61 Part II World food and agriculture in
review 63 Trends in undernourishment 65 Food
production, consumption and trade during the crises 68
Recent trends in agricultural prices: a higher price

Machinery 0.0 1.540 2.808 (0.355) (0.199) Fertilizer 0.0 !
0.109 (.030) Energy
0.0 ) a
Standard errors in parentheses Contemporary Production
Theory: The Factor Side 395 24.17 Concluding Comments
Contemporary production theory focuses on the duality
that

Revenue and Profit Functions" in in M. Fuss and D.
McFadden eds. Production Economics: A Dual Approach
to Theory and Application, Vol 1. Amsterdam, North
Holland (1978). Mundlak, Yair. "Elasticities of Substitution
and the Theory of Derived Demand." Revie

a single input (or input vector x = cfw_x1,.,xn) for y in the
factor space model. The standard presentation of the
neoclassical theory of the firm usually specifies isoquants
in factor space with a diminishing (or possibly constant)
marginal rates of subs

appropriate so long as certain assumptions with regard to
the parameters are met. Indirect cost functions should be
homogeneous of degree one in all factor prices. A
doubling of all factor prices should exactly double cost.
Only relative prices enter the

pure number that indicates the extent to which one input
substitutes for another and hence indicates the shape of
an isoquant according to the "usual" definition
(Henderson and Quandt). The elasticity of substitution
can be represented by the ratio of two

P1 to point P2 (Figure 24.2). As one moves along an
isoquant from point P1 to point P2, two things happen.
First, the ratio of the inputs (x2/x1) changes. Second, the
slope of the isoquant as measured by MRSx1x2 at point
P2 is different from that at point

close linkage to the Cobb-Douglas. It is linear in the
parameters, which makes parameter estimation simple. It
is normally monotonically increasing with respect to the
use of each input under the usual parameter
assumptions. However, results depend upon t

transformation between output pairs are non-decreasing.
These assumptions are analogous 400 Agricultural
Production Economics in product space to the free
disposal and non increasing marginal rate of substitution
assumptions (McFadden, pp. 8-9) in factor

Allen, R.G.D. Mathematical Analysis for Economists New
York: Macmillan Co.(1938). Aoun, Abdessalem. "An
Econometric Analysis of Factor Substitution in U.S.
Agriculture 1950-1980." Unpublished PhD Dissertation.
Univ. of Ky. Dept. of Agr. Economics, 1983. A

represent the production process. Consider, for example
a CD type specification with no imposition of a particular
sum on $1 + $2. 24.78 y = A x1 $1 x2 $2 The marginal
rate of substitution of x1 for x2 is given by 24.79
MRSx1x2 = ($1/$2)(x2/x1) = MRSx1x2

energy and machinery over the three periods for which
the estimates are based. Other changes over the three
decades, although perhaps not quite as profound, are
also of interest. For example, the elasticity of substitution
between labor and energy is clea