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

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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...
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