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,-( '* '( + # '* # ! ! Figure 2: An increase in I shifts the budget line out. Figure 3: An increase in PX rotates the budget line in. Figure 2: (Left) An increase in I shifts the budget line out. (Right) An increase in Px rotates the budget line
price of good X reduces the consumer’s purchasing power.
Of course, a decrease of I shifts the budget line in. What does a change in I mean for
As an exercise, try drawing the original graph (with PX = 1, PY = 2 and I = 10) and
the consumer’s budget constraint? As you can see in the ﬁgure, an increase in I results in
the new graph of the budget line that results when PY increases from 2 to 3. What happens
a larger set of bundles of goods to choose from (and vice versa for a decrease in I ). In that
to the consumer’s purchasing power in this case?
case, we say that the consumer’s purchasing power has increased. 1.2 2 How does a change in price a↵ect the budget line Optimal Choice
2 A consumer’s optimal choice is the bundle of goods that is a↵ordable (i.e. within her budget
Let’s start with a change in PX . Recall the formula for the budget line
constraint) and gives her the highest possible utility. This choice problem can be represented
by a constrained optimization problem (remember from chapter 1?). For example, if the How does a change in a price affect the budget line? Let’s consider the effect of a change in Px using
the budget line formula Px x + Py y = I . If we increase Px while holding Py and I constant, the horizontal
intercept is smaller but the vertical intercept has not changed. Moreover, the slope Py has become steeper
(more negative). Thus, the graph of the budget line rotates in along the horizontal axis holding ﬁxed the
vertical intercept. This is illustrated in the right panel of Figure 2 using our example when Px increases
from 1 to 2. Notice that the budget constraint of the consumer is smaller when Px is larger. An increase in
the price of good x reduces the consumer’s purchasing power. 3 Optimal Choice A consumer’s optimal choice (optimal consumption bundle) is the bundle of goods that is most preferable
within her budget constraint. If the consumer preferences are represented by a utility function, the optimal
choice can be found as the solution to the following constrained optimization problem:
maximize U ( x, y)
x ,y 0 subject to (5) Px x + Py y I . Here,
• the objective function is the utility function U ( x, y);
• the endogenous variables are the amount of the goods purchases x and y;
• the exogenous variables are 1. the prices of the goods Px and Py 1
2. the consumer’s income I • the constraints of the problem are given by
1. the budget constraint;and Y x0+ willysometimes I constraints will alwaysconsumer would usually c...
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This document was uploaded on 09/21/2013.
- Summer '13