Economic growth and economic development 570

Introduction to Modern Economic Growth
meaning that the greater is the number of differentiated varieties that the individual
consumes, the higher is his utility. More specifically, consider the case in which
c1 = ... = cN =

EC
,
N

so that the individual spends a fixed amount of expenditure EC distributed equally
across all N varieties. Substituting this into (12.6), we obtain
ả
à
1
EC
EC
, ...,
, y = N 1 EC + v (y) ,
U
N
N
which is strictly increasing in N (since ε > 1) and implies that for a fixed total
expenditure EC , the larger is the number of varieties over which this expenditure
can be distributed, the higher is the utility of the individual. This is the essence of
the love-for-variety utility function. What makes this utility function convenient is
not only this feature, but also the fact that individual demands take a very simple
iso-elastic form. To derive the demand for individual varieties, let us normalize the
price of the y good to 1 and denote the price of variety i by pi and the total money
income of the individual by m. Then the budget constraint of the individual takes
the form
N

X

(12.7)

i=1

pi ci + y ≤ m.

The maximization of (12.6) subject to (12.7) implies the following first-order condition between varieties:

à

ci
ci0

ả 1

=

pi
for any i,i0 .
pi0

To write this first-order condition in a more convenient form, let us define
ÃN
! ε
X ε−1 ε−1
C≡
ci ε
i=1

as the index of consumption of the N varieties. Moreover, let P denote the price
index corresponding to the consumption index C. Then this first-order condition
for i0 = j and i 6= j imply:
(12.8)

³ c ´− 1ε
j

C

=

pj
for j = 1, ..., N.
P
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