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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
MGMT 7730 - © 2011 Houman Younessi
50
Bread
Potatoes6
40
30
20
10
1 2 3 4 5
B
A
Indifference Curves must not intersect
A’
Lecture 3
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
50
Bread
Potatoes6
40
30
20
10
1 2 3 4 5
I2I1
H
K
Effect of Price Change
Lecture 3
MGMT 7730 - © 2011 Houman Younessi
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
$2.00
5 10 15 20 25 30 35
4.2064.0
4.25.1225
6.18.0
QP
QP
Lecture 3
MGMT 7730 - © 2011 Houman Younessi
Deriving Market Demand Curve
Market demand curve is the horizontal sum of all the individual demand curves.
In other words, to find the total quantity demanded, we add up all the individual quantities demanded by each and every consumer in the
market at that price.
Price
Quantity1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Lecture 3
MGMT 7730 - © 2011 Houman Younessi
Deriving Market Demand CurveAn Empirical Approach
Based on directly obtaining demand information through consumer interviews and market experiments
Let us start with a simplified case of only one factor influencing the quantity demanded in the market. Let us say Price.
Through various means we obtain the following data regarding demand at various prices
Price ($)
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
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
MGMT 7730 - © 2011 Houman Younessi
Trend AnalysisCorrecting for Seasonal and Cyclical Variation
Lecture 3
MGMT 7730 - © 2011 Houman Younessi
Trend AnalysisCorrecting for Irregularity