# Lecture 1: Eco200

We lied! ﻿$CS_{0=\alpha =\ 32}$﻿

﻿$CS_{1}=abc=\ 50$﻿

The lie: Better off by ﻿$\ 18$﻿

Only true if IIG (Income Independent Good)

Like dental care. Something you need regardless of income.

• Not many things are IIG. For normal goods, you over-estimate and for inferior goods underestimate.
• We need to look only at the substitution effect, not the income effect.
• We use the Hicksian demand curve ﻿$\left ( H_{x}\right )$﻿ to measure actual change.

### Given:

﻿$u=xy$﻿ ﻿$w=24$﻿ ﻿$P_{y}=2$﻿ ﻿$Px^{2}=4$﻿ ﻿$Px^{2}=1$﻿

What is the max WTP (willing to pay)?

H.A.I.C= highest, affordable, indifference curve.

﻿$MRs=\frac{MUx}{MUy}=$﻿ ﻿$\frac{2U}{3x}$﻿ ﻿$\frac{2U}{2x}=y$﻿ ﻿$\frac{2U}{2y}=x$﻿ ﻿$\therefore = \frac{y}{x}$﻿

﻿$\frac{2U}{3x}$﻿

﻿$O-cost_{x}:$﻿ ﻿$\frac{Px}{Py}=\frac{4}{2}$﻿ or ﻿$\frac{1}{2}$﻿ with club

﻿$TAN:MRS=O-cost$﻿ ﻿$\frac{y}{x}=\frac{4}{2}\rightarrow y=2x$﻿

﻿$B-line:$﻿ ﻿$4x=2y=24$﻿

﻿$Sub$﻿ ﻿$TAN$﻿ ﻿$into$﻿ ﻿$B-line: 4y\times4x=24$﻿ ﻿$x=3,$﻿ ﻿$y=6,$﻿ ﻿$U=18$﻿

1.) ﻿$A\left ( 3,6 \right )$﻿ ﻿$Ux+2y=24$﻿

2.) ﻿$C\left (12 ,6 \right )$﻿ ﻿$x+2y=24$﻿ ﻿$TAN= \frac{y}{x}=\frac{1}{2}$﻿ ﻿$2y=x$﻿

﻿$Sub:$﻿ ﻿$2y+2y=2y$﻿ ﻿$y=6,$﻿ ﻿$x=12,$﻿ ﻿$U=72$﻿

3.) ﻿$C\left (6 ,3\right )$﻿ utility as bundle ﻿$A$﻿ ﻿$xy=18$﻿

﻿$TAN$﻿ as bundle ﻿$C$﻿ ﻿$2y=x$﻿

﻿$Sub:$﻿ ﻿$2y^{2}=18$﻿ ﻿$y=3,$﻿ ﻿$x=6$﻿

﻿$Cost=$﻿ ﻿$6+2\left ( 3 \right )=\ 12$﻿

﻿$CBL=$﻿ ﻿$x+2y=12$﻿

﻿$\therefore$﻿ Max willing to pay is ﻿$24-12=\ 12$﻿

Compensating variation is CV is max willing to pay .

How much do we need to vary your income to compensate the price change? Ordinary D curve: ﻿$D_{x}=\frac{w}{^{2Px}}=\frac{12}{Px}$﻿ ﻿$CS\int_{1}^{4}\frac{12}{Px} 2Px=12 In Px\int_{1}^{4}$﻿

﻿$= 16.335$﻿ less than 18

The consumers are better of by ﻿$\ 16.335$﻿ CU is ﻿$\ 12$﻿ . Why would you only pay ﻿$\ 12$﻿ to get ﻿$\ 13$﻿?

Because this is wrong! Ordinary D overstates benefit of normal goods.

﻿$H_{x}$﻿ utility ﻿$xy=18$﻿ ﻿$Sub:$﻿ ﻿$\frac{1}{2}Px$﻿ ﻿$V^{2}=18$﻿

﻿$TAN$﻿ ﻿$\frac{y}{x}=\frac{Px}{2\left ( Py \right )}$﻿ ﻿$y=\frac{1}{2}Px$﻿ ﻿$x^{2}=\frac{36}{Px}$﻿ ﻿$y=\frac{36}{\sqrt{Px}}$﻿

﻿$H_{x}$﻿ ﻿$6Px-^{\frac{1}{2}}$﻿

Real ﻿$CS:$﻿ ﻿$\int_{1}^{4} 6Px-^{\frac{1}{2}}OPx=1L Px^{\frac{1}{2}}\int_{1}^{4}$﻿ ﻿$=12=CV$﻿

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