Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand...

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Demand

Transcript of Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand...

Page 1: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Demand

Page 2: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Consumer Demand

Consumer’s demand functions:

( )mppxx ,, 2111 =

( )mppxx ,, 2122 =

Page 3: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Changes in Income Given Prices

Page 4: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Normal Goods

Both goods 1 and 2 are normal

2x

1x

X

Y 0,, 211

>∂

mmppx

0,, 212

>∂

mmppx

Page 5: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

An Inferior Good

Good 1 is normal.Good 2 is inferior:

2x

1x

X Y0

,, 212<

∂∂

mmppx

Page 6: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Income Offer and Engel Curves

m

1x1x

2x Income Offer Curve Engel Curve

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Cobb-Douglas

Demand function for good 1:

Demand function for good 2:

2x

1x

*2x

*1x

11

pmcx =

( )2

2 1pmcx −=

Page 8: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Cobb Douglas

Income Offer Curve: Engel Curve:

2x

1x

m

1x

cp1

Page 9: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Perfect Substitutes

2x

1x

1−

2

1

pp−

*1x

Demand function for good 1:

if

if

if

21 pp <11 / pmx =

( )11 /,0 pmx =

01 =x 21 pp >

21 pp =

Page 10: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Perfect Substitutes (with )

2x

1x

m

1x

Income Offer Curve:

21 pp <

Engel Curve:

1p

Page 11: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Perfect Complements

Optimal choice:

Budget line:

Demand function for goods 1 and 2:

*1x

*2x

1x

2x12 xx =

12 xx =

mxpxp =+ 2211

2121

ppmxx+

==

Page 12: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Perfect Complements

Income Offer Curve: Engel Curve:2x

1x 1x

m

21 pp +

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Homothetic Preferences

Consumer’s preferences only depend on the ratio of the two goods:

If Then, for

Example: Cobb-Douglas, Perfect substitutes, Perfect Complements.Properties: straight income offer curve and Engel curve.

),(~),( 2121 yyxx

),(~),( 2121 tytyxtxt0>t

Page 14: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Luxury Good

m

1x

Page 15: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Necessary Good

m

1x

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Changes in Prices

Fix income and price of one good and change price of the other.

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Ordinary Goods

Price of good 1 decreases.Demand for good 1 increases.

2x

1x

YX

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Giffen Goods

Price of good 1 decreases.Demand for good 1 decreases.

2x

1x

X

Y

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Price Offer and Demand Curves

Price Offer Curve: Demand Curve:

2x

1x

1p

1x

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Perfect Complements

Price Offer Curve: Demand Curve:2x

1x

1p

1x

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Substitutes

Good 1 is a substitute for good 2 when:

( ) 0,,2

211 >∂

∂p

mppx

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Complements

Good 1 is a complement to good 2:

( ) 0,,2

211 <∂

∂p

mppx

Page 23: Demand - Carnegie Mellon University · Price Offer and Demand Curves Price Offer Curve: Demand Curve: x2 x1 p1 x1. Perfect Complements Price Offer Curve: Demand Curve: x2 x1 p1 x1.

Inverse Demand Function

Consider a demand function

The inverse demand function is

Cobb-Douglas example:

( )mppxx ,, 2111 =

( )111 xpp =

11

pmcx =

11

xmcp =

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Inverse Demand Curve

Inverse Demand Curve

1p

1x

Optimal choice:

Suppose:(composite good)Rearrange:

12 =p

MRSpp −=

2

1

MRSp −=1