Wilson
Hedonic Prices
pχ, = py 2 (∂f√⅜yX⅜y∕∂χ,y) (з)
i=l
where θqjy∕∂xiy is the marginal yield of
characteristic j in the production of y from
input i, and Py ∂fy∕∂qjy is the value of the
marginal product of characteristic j used
in the production of y. This can be inter-
preted as the marginal implicit price of
the characteristic, or the imputed price of
the j,h characteristic in the production of
y, and is also frequently referred to as the
“hedonic price.”2
Equation (3) states Ladd’s hypothesis
that the observed price for each input is
equal to the summation of the values of
the marginal yield of the characteristic of
the input in the production of the output.
In other words, the purchase price of an
input equals the sum of the marginal im-
plicit prices of the characteristics pos-
sessed by the input, multiplied by the
marginal yield of those characteristics.
Equation (3) is sometimes called the he-
donic price function and is simply a re-
statement of the first order condition. It
indicates that the market price for inputs
depends on the characteristics which they
possess.
tained in each unit of x∣y. It follows that the pro-
duction function can be restated as:
qy = Gy(xly, x2y, . . . , xny, xjly, xj2y, . . ., xπmy).
Using the function of a function rule for differen-
tiating (2), setting the results equal to zero, and
solving for Pxi yields Equation (3).
2 The theoretical model developed here is strictly de-
mand oriented. In particular, Equation (3) is a mod-
el of the demand for input characteristics in pro-
duction, and does not consider the supply of the
input characteristics (Ladd and Martin, p. 30). The
implicit assumption is that the supply of an input
characteristic is perfectly inelastic with respect to
its marginal implicit price in any given time period.
Only recently has the goods characteristics litera-
ture discussed market equilibrium properties (Ro-
sen and Edmunds).
Empirical Model
The hedonic price function in (3) is
simplified by setting Py(∂fy∕∂qjy) = Bj. The
ɪɪl
right hand side of (3) becomes ɪ βι⅜y∕
i-ɪ
θxiy which is the value of the marginal
yield of characteristic j from the ith input.
It is simplified further by assuming that
Bj is constant and that θqjy∕<9xiy = xjiy where
Xjiy is the quantity of characteristic j con-
tained in each unit of xiy which is assumed
constant. With these assumptions, the he-
donic price function can be written as
P. = Σ Bi(xjiy) (4)
where Bj is the marginal implicit price for
characteristic j.3 This equation provides the
empirical hypothesis that for each input
purchased, prices can be expressed as the
sum of the products of the marginal yield
of the characteristic and the marginal im-
plicit price of the characteristic. Standard
regression analysis is one method to test
hypotheses about the behavior of the pa-
rameters and to estimate values of the
characteristics of the inputs.4
Prices of malting barley vary across
shipments in response to protein levels and
kernel plumpness and with respect to
grades and varieties. Protein and plump-
ness are not in the grade standards but are
the most important identifiable character-
istics of barley for malting. A minimum
level of protein is important because it acts
as a source of nitrogen for yeast metabo-
lism and growth during fermentation and
3 The economic implications of these assumptions are
that yields of the characteristics are constant, and
that Pxi is linearly related to Xjiy (i.e., the marginal
implicit prices are constant).
4 An alternative methodology would be to develop a
linear programming model of a process, and the
shadow prices would represent the marginal im-
plicit prices (Ladd).
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