Environmental Engineering Reference
In-Depth Information
5.2 The Dupuit-Hotelling Theory of Marginal Cost Pricing
In economic theory, the standard approach to pricing in public utilities is that price
should equal marginal costs, as this approach maximizes consumer surplus. This
policy prescription follows the seminal contributions by Dupuit
( 1854 ) and
Hotelling ( 1938 ). To quote from Hotelling ( 1938 ):
The common assumption, so often accepted uncritically as a basis of arguments on
important public questions, that every tub must stand on its own bottom, and that
therefore the products of every industry must be sold at prices so high as to cover not only
marginal costs but also all the fixed costs, including interest on irrevocable and often
hypothetical investments [This is] inconsistent with the maximum of social ef ciency.
He applied this principle to
all bridges, roads, railroads, waterworks, electric
power plants, and like facilities
; in other words, facilities supplied by the public
sector, irrespective of the level of jurisdiction. Thus on social ef
ciency grounds,
Hotelling, following Dupuit ( 1854 ), argued that the capital costs must be met
through general state revenues such as income and inheritance taxes, and land taxes.
What follows is an exposition of the marginal cost pricing rule as given by
Hotelling ( 1938 ).
5.2.1 The Derivation of the Marginal Cost Pricing Rule
Let there be n commodities qi i and n prices pi. i . Then the demand functions are:
p i ¼ fi i q 1 ; q 2 ; ...; q n
ð
Þ;
ð
i ¼ 1 ; 2 ; ...; n
Þ
ð 5 : 1 Þ
Then the consumers
'
surplus is
Z
ð f 1 dq 1 þ f 2 dq 2 þþ f n dq n Þ
ð 5 : 2 Þ
taken from an arbitrary set of values of the q
t is obtained by
subtracting from ( 5.2 ) a similar line integral of the marginal cost functions:
'
s. The net bene
g i ð q 1 ;
q 2 ; ...;
q n Þ
Now let
h i ¼ fi i g i
Then the total net bene
t is:
Z h i dq i
w ¼
ð 5 : 3 Þ
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