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Pindyck/Rubinfeld, Microeconomics, Eighth Edition Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall.
where a, b, and c are positive. Is this total cost function consistent with the presence of economies or diseconomies of scale With economies or diseconomies of scope If each product were produced by itself there would be neither economies nor diseconomies of scale. To see this, define
the total cost of producing H alone (
TCH) to be the total cost when
S 0. Thus
TCH
aH.
Similarly,
TCS
bS. In both cases, doubling the number of units produced
doubles the total cost, so there are no economies or diseconomies of scale. Economies of scope exist if
SC > 0, where, from equation (7.7)
in the text 1 2
1 2
1 2
( )
( )
( , )
( , )
C qC qC q qSCC q q
In our case,
C(
q1
)
is
TCH,
C(
q2
)
is
TCS,
and
C(
q1
,
q2
) is
TC. Therefore,
(
)
aH bSaH bS cHScHSSCaH bS cHSaH bS cHS
Because
cHS (the numerator) and
TC (the denominator)
are both positive, it follows that
SC > 0, and hence there are economies of scope.