Lecture 4: Slutsky SE

Slutsky SE

  • We take away enough MM to make AA just affordable.
  • Since P changed, we can get to a higher utility for BB .

ABA\rightarrow B is SESE , BCB\rightarrow C  is IEIE

  • Figure cost AA with the new BLBL conditions. Adjust MM to get comp BLBL . Than may utility for this BLBL .Net b-base year & + equal some other year. How did consumption change from year b to year a If we use price at time b, we get the Laspeyres index. If we use price at time, we get the Paasche index.

Paasche \rightarrow qq index \rightarrow Pq=Px+x++Py+y+Px+xb+Py+ybP_{q}=\frac{Px^{+}x^{+}+Py+y^{+}}{Px^{+}x^{b}+Py+y^{b}}

  • If its >1,>1, Consumer is better at time ++
  • If its <1,<1, Just means unaffordable

Laspeyres \rightarrow qq index \rightarrow Lq=Pxbx++Pyby+Pxbxb+PybybLq=\frac{Px^{b}x^{+}+Py^{b}y^{+}}{Px^{b}x^{b}+Py^{b}y^{b}}

  • If its <1,<1, the consumer is better off at time bb .
  • If we use qq of time ++ we get the Paasche PP index \rightarrow Pp=Px+x++Py+y+Pxbx++PybybPp=\frac{Px^{+}x^{+}+Py^{+}y^{+}}{Px^{b}x^{+}+Py^{b}y^{b}}
  • If we use qq of time b, we get the Laspeyres LL index \rightarrow Lp=Px+xb+PybybPxbx++PybybLp=\frac{Px^{+}x^{b}+Py^{b}y^{b}}{Px^{b}x^{+}+Py^{b}y^{b}}
  • To compare the change in welfare, we have to set an index of change in total expenditure.

M=Px+xb+PybybPxbx++PybybM=\frac{Px^{+}x^{b}+Py^{b}y^{b}}{Px^{b}x^{+}+Py^{b}y^{b}}

  • If Pp>MPp>M , consumer is better off at time bb . If Lp<MLp<M , the consumer is better off at time ++ .

Perfect Complements

  • Income Effect== Total Effect- ( Because you can't substitute σ=0\sigma=0 )

Perfect Substitutes

  • Substitution Effect== Total Effect- (Because you will always substitute σ=0\sigma=0

Quasi-Linear Preferences

  • Sub Effect== Total Effect- (Because good c(x)c(x) is income independent).







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