Y
X
*
Y
*
6c: The consumer’s optimum
In this section, we will introduce the idea of consumer optimization. Every consumer has
utility. Because the utility measure the happiness of a person, every consumer will try to
maximize their happiness. However, each individual only has limited amount of
I
dollars
to allocate. Therefore, we need to formulate the budget constraint as the following with n
goods
with price
. The amount of money to buy a
good
with price
is
. Since the total amount of spending on goods must less than
or equal to income
I
, then the budget constraint is:
.
(6.c.1)
To simplify our analysis, we only consider with two variables now. Then (6.c.1) become
Fig 6.c.1: The Utility maximization by using graphical method
From figure 6.c.1, we can imagine the indifferent curve moving outward. Then the utility
increases by that process. As the indifferent curve moving outward, the total expenditure
also increases. This process continues until the total expenditure exactly equal to the total
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 Spring '07
 Cheng
 Economics, Optimization, Utility, u2

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