The Theory of Water and Utility Pricing - Global Drinking Water Management and Conservation - page 81

We can rewrite ( 5.20 )as

Þ ¼ ð 1 þ kÞ x i dp i
dx i

k ð p i MC i

or

ð p i MC i Þ

¼ ð 1 þ kÞ
k

1
E I

ð 5 : 21 Þ

p i

Since

x i
p i :

dp i
dx i

E i ¼

“ ”

over marginal costs should be propor-
tionate to the inverse of the elasticity; the more inelastic the demand, the higher the
markup.
While some considered Ramsey pricing to have been a path-breaking contri-
bution to economics, its principles were largely forgotten even though it was
rediscovered and expanded upon by Pigou, Boiteux, and Samuelson. Its history was
explored in an article by Baumol and Bradford ( 1970 ), and the principle has since
been widely recognized and accepted by economists and practitioners. For example,
in 1983 the US Interstate Commerce Commission adopted Ramsey pricing as the
underlying principle it would follow in the regulation of railroad rates. The
American Water Works Association (AWWA) also seems to favor Ramsey Pricing,
although they do not call it that (Overcast 2012 ).

Equation ( 5.21 ) says that the markup

To quote Baumol and Bradford ( 1970 ):
Ramsey prices are an outstanding example of the use of pure economic theory to derive an
operational solution to a difficult set of practical problems. It may also be as definitive as
any second-best theorem (Baumol and Bradford 1970 , p. 88).

Pareto optimality requires that the prices be those which elicit such a set of
outputs and purchase quantities that it is impossible to increase the welfare of any
one individual without harming anyone else. The de

nitive character of Ramsey
pricing is surprising in the light of the conclusions suggested by much of the
“ literature, that where additional constraints are superimposed on the

usual requirements of optimality, one can expect no simple and straightforward
results to emerge (Lipsey and Lancaster 1956 ). The Lipsey-Lancaster result is
important; it states, roughly, that when there are many factors that make the economy
depart from optimality,

second-best ”

“ “fixing” ” any one will not get the economy “ closer ” to the

social optimum. Thus “ piecemeal ” optimization cannot bring welfare to being

“ closer first-best optimum which is the competitive general equilibrium.

The question of what is

” to the

and how and whether it can be approached in
a piecemeal manner to arrive at a second-best optimum has been to a large measure

“ rst-best ”