A set dened as b px py i x y px x py y

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ned as B( Px , PY , I ) = {( x, y) : Px x + Py y I } (2) The budget line is the set of goods that exactly exhaust all of the consumer’s income: the set of basket ( x, y) such that Px x + Py y = I (3) 1 to rearrange the expression as: The budget line is the boundary of the budget constraint. For graphical purposes, it is useful to rearrange I PX Y= X Equation (3) as PY PY Px I y= (4) Notice that this has a slope of PX , a horizontalx + intercept of PIX and a vertical intercept of PY Py Py I PY . Px I For slope of 10. We graph and a vertical intercept Notice that this has a example, set PX = 1, PY = 2 and I = intercept Py the budget line and budget Py with a horizontal constraint in Figure 1.1 Figure 1 shows the budget line and the budget set when Px = 1, Py = 2, and I = 10: I Px . For example !"#$%&'( )*)+,-.'/)012' ! "#$!%&' !"#$%&'&()* +), '&(-+. +,-.'/)3'/ "#$( %&)* ( ! Figure 1: A budget line and set Figure 1: A Budget Line and Budget Set 2.1 1.1 change in change and price affect the budget How does a How does a incomein income aect the budget lineline? Recall the formula for the budget line Recall the formula for the budget line Px x + Py y = I . Now suppose we increase I and hold Px and Py constant. To maintain this equation, we have to increase either x or y or both: since the right hand side is PX X + PY Y = I. higher, we must make the left hand side higher. Thus, in the space of goods ( x, y) the graph of the budget x line must shift out. suppose we increase I and hold PX Py has not changed, the new budget line must be parallel Now Moreover since the slope and PY constant. To maintain this equation, we P to the old one. have to increase eitherseeor Y or both:notice that both the vertical we must make the intercepts of the Another way to X this is to since the right hand side is higher, and horizontal graph rise with left hand side higher.The left panel ofof goods (X, Y ) the graph of the budget line must budget line in our an increase in I . Thus, in the space Figure 2 illustrates what happens to the example when income increase fromthe= 10 to PI = 12. changed, the new budget line is parallel shift out; moreover, since I slope PX has not Y What does a change in income I mean for the consumer’s budget constraint? As you can see in the 1 All figures are courtesy of Irene Trela. to an one. Another way see this is in a that both the of bundles of figure,the old increase in Itoresults to noticelarger set vertical and horizontal goods to choose from (and vice versa for a intercepts decrease inofIthe In that case, we say thatFigure consumer’shappens to ). graph increase with an increase in I . the 2 illustrates what purchasing power has increased. 2 the budget line in our example when income increase from 10 to 12. !"#$%&'( )*+,#,-+.)+/)#)0123',)4-.' ! "# $%&' &( ! !"#$%&'())*+,-.)/-)#)0123'.)4,5' 5/),6')%7-8')+/)9)7-:':;),6')<123',) "# $%&' "! $%&( )$&'*%%%%%%&'( , + "! $%&( )%$%&'* 6-),57/$'),578'#9'9:).+');123'.)&,5') 9+,-.9)%#8#&&'&)/1.<#829= 6-),57/$')2'78'#9'9:).+');123'.)&,5' 9+,-.9)%#8#&a...
View Full Document

This document was uploaded on 09/21/2013.

Ask a homework question - tutors are online