Lecture 3 MGMT 7730 - © 2011 Houman Younessi Rational Choice – Consumer behavior 50 Bread Potatoes 6 40 30 20 10 12345 I1 I2 A B Indifference Curves A’

Lecture 3

MGMT 7730 - © 2011 Houman Younessi

Rational Choice – Consumer behavior

50

Bread

Potatoes6

40

30

20

10

1 2 3 4 5

I1

I2

A

B

Indifference Curves

A’

Welcome to Carbland

Lecture 3


50

Bread

Potatoes6

40

30

20

10

1 2 3 4 5

B

A

Indifference Curves must not intersect

A’

Lecture 3


Style

MPG

H R SStyle

MPG

H R S

High marginal rate of substitution of MPG for style

Low marginal rate of substitution of MPG for style

Marginal Rate of Substitution

Lecture 3


Marginal Rate of Substitution

The marginal rate of substitution of good X for Y is defined as the number of units of good Y that must be given up if the consumer , after

receiving the extra unit of good X is to remain indifferent

The absolute value of the slope of the indifference curve is the marginal rate of substitution

Lecture 3


Utility

MPG

12

3

Style

Houman’s indifference curves

Which one provides the greatest utility?

Utility measures the level of satisfaction attached to a given market basket

Lecture 3


Budget Line

50

Bread

Potatoes6

40

30

20

10

1 2 3 4 5

$40 Budget lines

$20 Budget lines

XY

X

YY

XXYY

QP

P

P

BQ

or

BPQPQ

Slope of the budget line

Lecture 3


Equilibrium Market Basket

50

Bread

Potatoes6

40

30

20

10

1 2 3 4 5

I2I1

I3

H

H= Equilibrium market basket for $40 budget line and bread price $0.80 and potato price of $10

Lecture 3


50

Bread

Potatoes6

40

30

20

10

1 2 3 4 5

I2I1

H

K

Effect of Price Change

Lecture 3


Deriving an Individual’s Demand CurveWe said at the price of $0.80 for bread, demand was 25 loaves (equilibrium)

At $1.60 a loaf, demand was 12.5 loaves (again equilibrium)

We have two points on the demand line, so we can plot it!!

Price

Quantity demanded

Demand for bread

$0.40

$0.80

$1.20

$1.60

$2.00

5 10 15 20 25 30 35

4.2064.0

4.25.1225

6.18.0

QP

QP

Lecture 3


Deriving Market Demand Curve

Market demand curve is the horizontal sum of all the individual demand curves.

In other words, to find the total quantity demanded, we add up all the individual quantities demanded by each and every consumer in the

market at that price.

Price

Quantity1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Lecture 3


Deriving Market Demand CurveAn Empirical Approach

Based on directly obtaining demand information through consumer interviews and market experiments

Let us start with a simplified case of only one factor influencing the quantity demanded in the market. Let us say Price.

Through various means we obtain the following data regarding demand at various prices

Price ($)

Quantity (tons)

18 1.72

16 2.03

14 4.2

12 3.8

10 7

8 8.1

6 8.2

4 11

Lecture 3


Demand Data

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12

Quantity

Pri

ce

P=a+bQ

Lecture 3


Method of Least Square

Y1

Y’1

Y2

Y’2Y3

Y’3

Y4

Y’4

244

233

222

211 )()()()( YYYYYYYY

Must minimize:

In general we must minimize:

2

1

)( ii

n

i

YY

But: ii bXaY

Substituting, we get:2

1

)( i

n

ii bXaYM

Which we must minimize

We know that the expression above would be a minimum if: 0

b

M

a

M

Lecture 3


n

iiii

n

iii

n

iii

n

iii

bXaYXb

bXaY

b

M

bXaYa

bXaY

a

M

1

1

2

1

1

2

0)(2)(

0)(2)(

Therefore we have:

Solving simultaneously and letting X and Y be the mean values of all

X and Y respectively, we have:

XbYa

XX

YYXXb n

ii

n

iii

1

2

1

)(

)((

alternatively

n

ii

n

ii

n

i

n

i

n

iiiii

XXn

YXYXnb

1

2

1

2

1 1 1

)(

))((

Lecture 3


Using the data in the table below:

Price ($)=Y

Quantity (tons)= X X2 Y2 XY

18 1.72 2.9584 324 30.96

16 2.03 4.1209 256 32.48

14 4.2 17.64 196 58.8

12 3.8 14.44 144 45.6

10 7 49 100 70

8 8.1 65.61 64 64.8

6 8.2 67.24 36 49.2

4 11 121 16 44

Total 88 46.05 342.0093 1136 395.84

Mean X 11

Mean Y 5.75625

44.1)05.46)(342(8

)88)(05.46()84.395(82

b

596.21)11(44.1756.5 a

XY 44.1596.21 So:

Price ($) Y'

18 19.12088

16 18.67478

14 15.55209

12 16.1277

10 11.52282

8 9.93989

6 9.795988

4 5.766715

Lecture 3


X-Y Plot

0

2

4

6

8

10

12

0 2 4 6 8 10

X

Y

X-Y Plot

0

2

4

6

8

10

0 2 4 6 8 10

X

Y

X-Y Plot

0

2

4

6

8

10

0 2 4 6 8 10

X

Y

X-Y Plot

0

5

10

15

20

25

0 2 4 6 8 10

X

Y

r2=1.00 r2=0.30

r2=0.90r2=0.00

Coefficient of Determination

Lecture 3


Coefficient of DeterminationWithout proof:

n

i

n

iii

n

i

n

iii

n

i

n

i

n

iiiii

YYnXXn

YXYXn

r

1 1

22

1 1

22

2

1 1 12

)()(

))((

Note also that:

n

i

n

iii

n

i

n

iii

n

i

n

i

n

iiiii

YYnXXn

YXYXn

rr

1 1

22

1 1

22

2

1 1 12

)()(

))((

is known as the correlation coefficient and is an important statistical entity

Lecture 3


Multiple Regression

When the relationship is dependent on more than one independent variable, multiple regression is used. For example when we wish to estimate the parameters for:

Q= aP+bI+cS+dAwhere

P is the average price of laptops in 2007I is the per capita disposable income in 2007

S is the average price of typical software packages in 2007

A is the average expenditure on advertising in 2007

The approach and interpretation remains the same but the analysis and the formula is far more complex than to be presented here. Fortunately most statistical software packages handle multiple regression easily.

Lecture 3


Non-linear RegressionThe models whose parameters have been estimated so far, have all be linear. How would we estimate the parameters of a model that is not linear?

For example:

caXY

or

eYY aX

2

0

We do so by employing a mathematical “trick” called linearization.

Lecture 3


Linearization

This is best done by example:

0

0

0

0

0

0

lnln

lnln

)ln(

ln)ln(

YaXY

aXYY

aXY

Y

eY

Y

eY

Y

eYY

aX

aX

aX

XacY

aXcY

aXcY

caXY

2

2

2

Lecture 3


Trend AnalysisMore about the value of Y

How do we get “more” reliable values of Y?

By looking and analyzing the TRENDS that Y has followed in the past

A trend is a relatively smooth, long term movement of a variable

There are usually four components to a trend:

-Regular trend

-Seasonal variation

-Cyclical variation

-Irregularity

Lecture 3


Trend AnalysisCorrecting for Seasonal and Cyclical Variation

Lecture 3


Trend AnalysisCorrecting for Irregularity

Documents

Lecture 3 MGMT 7730 - © 2011 Houman Younessi Rational Choice – Consumer behavior 50 Bread Potatoes 6 40 30 20 10 12345 I1 I2 A B Indifference Curves A’