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Unformatted text preview: mp;&'&),5<#829= !"# &-.')3',:):,''%'7)#.2),6') 6+7-=+.,#&)-.,'78'%,):6-/,:)-. 5/),6')%7-8')+/)9)/#&&:;),6')<123',) &-.')3',:)/&#,,'7 #.2),6') 6+7-=+.,#&)-.,'78'%,):6-/,: +1, + ,-' -.( ,-( '* '( + # '* # ! ! 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 in. 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 x intercept is smaller but the vertical intercept has not changed. Moreover, the slope Py has become steeper P (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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