Lecture 1: Eco200

We lied!

CS0=α=$32CS_{0=\alpha =\$ 32}

CS1=abc=$50CS_{1}=abc=\$ 50

The lie: Better off by $18\$ 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 (Hx)\left ( H_{x}\right ) to measure actual change.


Given:

u=xyu=xy w=24w=24 Py=2P_{y}=2  Px2=4Px^{2}=4  Px2=1Px^{2}=1

What is the max WTP (willing to pay)?

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


MRs=MUxMUy=MRs=\frac{MUx}{MUy}= 2U3x\frac{2U}{3x} 2U2x=y\frac{2U}{2x}=y 2U2y=x\frac{2U}{2y}=x =yx\therefore = \frac{y}{x}

2U3x\frac{2U}{3x}

Ocostx:O-cost_{x}: PxPy=42\frac{Px}{Py}=\frac{4}{2}  or 12\frac{1}{2} with club

TAN:MRS=OcostTAN:MRS=O-cost yx=42y=2x\frac{y}{x}=\frac{4}{2}\rightarrow y=2x

Bline:B-line: 4x=2y=244x=2y=24

SubSub TANTAN  intointo  Bline:4y×4x=24B-line: 4y\times4x=24 x=3,x=3,  y=6,y=6, U=18U=18

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

2.) C(12,6)C\left (12 ,6 \right ) x+2y=24x+2y=24 TAN=yx=12TAN= \frac{y}{x}=\frac{1}{2} 2y=x2y=x

Sub:Sub:  2y+2y=2y2y+2y=2y y=6, y=6, x=12,x=12, U=72U=72

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

TANTAN as bundle CC 2y=x2y=x

Sub:Sub:  2y2=182y^{2}=18  y=3,y=3, x=6x=6

Cost=Cost=  6+2(3)=$126+2\left ( 3 \right )=\$ 12

CBL=CBL= x+2y=12x+2y=12

\therefore Max willing to pay is 2412=$1224-12=\$ 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: Dx=w2Px=12PxD_{x}=\frac{w}{^{2Px}}=\frac{12}{Px}

CS1412Px2Px=12InPx14CS\int_{1}^{4}\frac{12}{Px} 2Px=12 In Px\int_{1}^{4}

=16.335= 16.335 less than 18

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

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

HxH_{x} utility xy=18xy=18 Sub:Sub: 12Px\frac{1}{2}Px V2=18V^{2}=18

TANTAN  yx=Px2(Py)\frac{y}{x}=\frac{Px}{2\left ( Py \right )} y=12Pxy=\frac{1}{2}Px x2=36Pxx^{2}=\frac{36}{Px} y=36Pxy=\frac{36}{\sqrt{Px}}

HxH_{x} 6Px126Px-^{\frac{1}{2}}

Real CS:CS: 146Px12OPx=1LPx1214 \int_{1}^{4} 6Px-^{\frac{1}{2}}OPx=1L Px^{\frac{1}{2}}\int_{1}^{4} =12=CV=12=CV





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