Transcript DEMAND THEORY - Gunadarma University

DEMAND THEORY
DR. MOHAMMAD ABDUL MUKHYI, SE.,MM
DEMAND FOR A COMMODITY
Permintaan adalah sejumlah barang yang
diminta oleh konsumen pada
tingkat harga tertentu.
Teori Permintaan adalah menghubungkan
antara tingkat harga dengan tingkat
kuantitas barang yang diminta pada
periode waktu tertentu.
Fungsi Permintaan: QdX = ƒ(Px, Py, Pz, I, T,
Tech, ….)
Hypothetical Industry Demand Curves
for New Domestic Automobiles at
Interest Rates of 6%, 8%, and 10%
P
P
P
2
2
2
1
1
1
d1
0
2 3
Individual 1
d2
Q1
0
1
2
Individual 2
Q2 0
d3
3
5
Pasar
Qx
Permintaan Kentang di Indonesia
Permintaan kentang untuk periode 1980-2008:
QdS = 7.609 – 1.606PS + 59N + 947I + 479PW + 271t.
QdS = quantitas kentang yang dijual per tahun per
1.000 Kg.
PS
= harga kentang per kg
N
= rata-rata bergeral jumlah penduduk per 1 milyar.
I
= pendapatan disposibel per kapita penduduk.
PW
= harga ubi per kg yang diterima petani.
T
= trend waktu (t = 1 untuk tahun 1980 dan t = 2
untuk tahun 2008).
N = 150,73 I = 1,76 PW = 2,94 dan t = 1
Bagaimana bentuk fungsi permintaan kentang?
Elastisitas Harga Permintaan
Elastisitas Titik :
% perubahan jumlah yangdiminta
% perubahanharga
Q/Q Q P
Ed p 

x
P/P P Q
Ed p 
Elastisitas Busur :
Q P /n
Ed p 
x
P Q/n
atau
Ed p 
Q
(P1  P2 ) / 2
x
P (Q1  Q 2 ) / 2
Elastisitas Kumulatif :
Ed p 
 Q/N  P /n
x
 P /N  Q/n
atau
Ed p 
 Q  P
x
 P  Q
Elastisitas Silang :
% perubahan jumlah barang X yangdiminta
Ec xy 
% perubahanharga barang Y
atau
(Qx/Qx) Qx Py
Ec xy 

x
(Py/Py) Py Qx
Elastisitas Pendapatan :
Ey 
% perubahanbarang yangdimint a
% perubahanpendapat an
atau
Ey 
Qd
Y
Qd
Y
x

x
Y
Qd
Y
Qd
Elastisitas Harga, Total Revenue, Marginal Revenue :
TR = P . Q
MR = ΔTR / ΔQ


1

MR  P1 


E
p


Q = 600 – 100P
Diminta :
a. Buat fungsi pendapatan.
b. Hitung nilai pendapatan marginal.
c. Bila P = 4 dan EP = -2 hitung MR
Jawab:
a. Q = 600 – 100P  P = 6 – Q/100
b. TR = P.Q  TR = (6 – Q/100).Q = 6Q –
Q2/100
MR = 6 – Q/50
MR optimal = 0
0 = 6 – Q/50  Q = 300
TR ($)
1000
900
800
700
600
500
400
300
200
100
0
TR = 6Q – Q2/100
TR
TR ($)
0
200
1000
900
800
700
600
500
400
300
200
100
0
400
600
800
output
Q = 600 – 100P
D
0
200
output
400
600
MR = 6 – Q/50
800
1   1

MR  41 
  41    2
 2  2
Qx = 1,5 – 3,0Px + 0,8I + 2,0Py – 0,6Ps + 1,2A
Qx
Px
I
Py
Ps
A
=
=
=
=
=
=
penjualan kopi merek X
harga kopi merek X
pendapatan disposibel per kapita per tahun
harga kopi pesaing
harga gula per kilo
pengeluaran iklan untuk kopi merek X
Jika Px = 2; I = 2,5; Py = 1,8, Ps = 0.50 dan A = 1 berapa
Q?
Qx = 1,5 – 3,0(2) + 0,8(2,5) + 2,0(1,8) – 0,6(0,50) + 1,2(1) = 2
Tingkat Elastisitas :
2
E P  3   3
2
 2,5 
E I  0,8
 1
 2 
E XY
E XS
 1,8 
 2
  1,8
 2 
 0,50 
 0,6
  0,15
 2 
1
E A  1,2   0,6
2
Supply
Penawaran adalah sejumlah barang yang
ditawarkan oleh produsen ke konsumen
pada tingkat harga tertentu.
Teori Penawaran adalah menghubungkan
antara tingkat harga dengan tingkat
kuantitas barang yang ditawarkan pada
periode waktu tertentu.
Fungsi Penawaran: QdX = ƒ(Px, Py, Pz, I, T,
Tech, ….)
Hypothetical Industry
Supply Curve for New
Domestic Automobiles
Hypothetical Industry Supply Curves
for New Domestic Automobiles at
Interest Rates of 6%, 8%, and 10%
Surplus, Shortage, and Market Equilibrium
Comparative Statics of Changing Demand
Comparative Statics of Changing Supply
Comparative Statics of Changing Demand
and Changing Supply Conditions
Demand and
Supply Curves
Objectives
• Understand how regression analysis
and other techniques are used to
estimate demand relationships
• Interpret the results of regression
models
– economic interpretation
– statistical interpretation and tests
• Describe special econometric problems
of demand estimation
Approaches to Demand Estimation
• 1. Surveys, simulated markets, clinics
Stated Preference
Revealed Preference
• 2. Direct Market Experimentation
• 3. Regression Analysis
A. Difficulties with Direct Market Experiments
(1) expensive and risky
(2) never a completely controlled experiment
(3) infeasible to try a large number of variations
(4) brief duration of experiment
(1) Specify variables: Quantity Demanded, Advertising,
Income, Price, Other prices, Quality, Previous
period demand, ...
(2) Obtain data: Cross sectional v. Time series
(3) Specify functional form of equation
Linear Yt = a + b X1t + g X2t + ut
Multiplicative Yt = a X1tb X2tg et
ln Yt = ln a  b ln X1t + g ln X2t + ut
(4) Estimate parameters
(5) Interpret results: economic and statistical
Violating the assumptions of regression including
(1) Multicollinearity- highly correlated independent
variables
(2) Heteroscedasticity- errors do not have the same
variance
(3) Serial correlation- error in period t is correlated with
error in period t + k
(4) Identification problems - data from interaction of
supply and demand do not trace out demand
relationship
Transit Example
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
YEAR
19661200
19671190
19681195
19691110
19701105
19711115
19721130
19731095
19741090
19751087
19761080
19771020
19781010
Y
Riders
15
15
15
25
25
25
25
30
30
30
30
40
40
P
Price
1800
1790
1780
1778
1750
1740
1725
1725
1720
1705
1710
1700
1695
T
Pop.
2900
3100
3200
3250
3275
3290
4100
4300
4400
4600
4815
5285
5665
I
H
Income Parking Rate
50
50
60
60
60
70
75
75
75
80
80
80
85
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
YEAR
19791010
19801005
1981995
1982930
1983915
1984920
1985940
1986950
1987910
1988930
1989933
1990940
1991948
1992955
Y
Riders
40
40
40
75
75
75
75
75
100
100
100
100
100
100
P
Price
1695
1690
1630
1640
1635
1630
1620
1615
1605
1590
1595
1590
1600
1610
T
Pop.
5800
5900
5915
6325
6500
6612
6883
7005
7234
7500
7600
7800
8000
8100
I
H
Income Parking Rate
100
105
105
105
110
125
130
150
155
165
175
175
190
200
Linear Transit Demand
Dependent Variable: RIDERS
Method: Least Squares
Date: 03/31/02 Time: 18:22
Sample: 1966 1992
Included observations: 27
Variable
Riders = 85.4 – 1.62 price …
Pr Elas = -1.62(100/955) in 1992
Coefficient Std. Error t-Statistic Prob.
C
PRICE
POPULATION
INCOME
PARKING
85.43924
-1.617484
0.643769
-0.047475
1.943791
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.960015
0.952745
20.48984
9236.342
-117.0847
1.384853
492.8046 0.173373
0.495976 -3.26122
0.262358 2.453782
0.012311 -3.85616
0.349156 5.567113
0.8639
0.0036
0.0225
0.0009
0
Mean dependent var 1026.222
S.D. dependent var 94.25756
Akaike info criterion 9.043312
Schwarz criterion 9.283282
F-statistic
132.0525
Prob(F-statistic)
0
Multiplicative Transit Demand
Dependent Variable: LRIDERS
Method: Least Squares
Date: 03/31/02 Time: 18:26
Sample: 1966 1992
Included observations: 27
Variable
Ln Riders = exp(3.25)P-.14 …
Coefficient Std. Error t-Statistic Prob.
C
LPRICE
LPOPULATION
LINCOME
LPARKING
3.24892
-0.13716
0.613645
-0.13077
0.166443
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.973859
0.969107
0.015926
0.00558
76.22788
0.93017
3.26874 0.993937
0.021873 -6.27052
0.409148 1.49981
0.039913 -3.27646
0.032361 5.143338
0.3311
0
0.1479
0.0034
0
Mean dependent var 6.929651
S.D. dependent var 0.09061
Akaike info criterion -5.27614
Schwarz criterion
-5.03617
F-statistic
204.9006
Prob(F-statistic)
0
Ch 3: DEMAND ESTIMATION
In planning and in making policy
decisions, managers must have some
idea about the characteristics of the
demand for their product(s) in order to
attain the objectives of the firm or
even to enable the firm to survive.
Demand information about customer sensitivity to
 modifications in price
 advertising
 packaging
 product innovations
 economic conditions etc.
are needed for product-development strategy
• For competitive strategy details about customer
reactions to changes in competitor prices and the
quality of competing products play a significant role
What Do Customers Want?
• How would you try to find out
customer behavior?
• How can actual demand curves be
estimated?
From Theory to Practice
D: Qx = f(px, Y, ps, pc, , N)
(px=price of good x, Y=income, ps=price of substitute,
pc=price of complement, =preferences, N=number
of consumers)
• What is the true quantitative relationship between
demand and the factors that affect it?
• How can demand functions be estimated?
• How can managers interpret and use these
estimations?
Most common methods used are:
a) consumer interviews or surveys
 to estimate the demand for new products
 to test customers reactions to changes in the
price or advertising
 to test commitment for established products
b) market studies and experiments
 to test new or improved products in controlled
settings
c) regression analysis
 uses historical data to estimate demand functions
Consumer Interviews (Surveys)
• Ask potential buyers how much of the
commodity they would buy at different
prices (or with alternative values for the
non-price determinants of demand)
face to face approach
telephone interviews
Consumer Interviews cont’d
• Problems:
– Selection of a representative sample
• what is a good sample?
– Response bias
• how truthful can they be?
– Inability or unwillingness of the
respondent to answer accurately
Market Studies and Experiments
• More expensive and difficult technique
for estimating demand and demand
elasticity is the controlled market study
or experiment
– Displaying the products in several different
stores, generally in areas with different
characteristics, over a period of time
• for instance, changing the price, holding
everything else constant
Market Studies and Experiments cont’d
• Experiments in laboratory or field
– a compromise between market studies and
surveys
– volunteers are paid to stimulate buying
conditions
Market Studies and Experiments cont’d
• Problems in conducting market studies and
experiments:
a) expensive
b) availability of subjects
c) do subjects relate to the problem, do they
take them seriously?
BUT: today information on market behavior also
collected by membership and award cards
Regression Analysis and Demand Estimation
• A frequently used statistical technique in demand
estimation
• Estimates the quantitative relationship between the
dependent variable and independent variable(s)
 quantity demanded being the dependent variable
 if only one independent variable (predictor) used:
simple regression
 if several independent variables used: multiple
regression
A Linear Regression Model
• In practice the dependence of one
variable on another might take any
number of forms, but an assumption of
linear dependency will often provide an
adequate approximation to the true
relationship
Think of a demand function of general form:
Qi = a + b1Y - b2 pi + b3ps - b4pc + b5Z + ε
where
Qi = quantity demanded of good i
Y = income
pi = price of good i
ps = price of substitute(s)
pc = price of complement(s)
Z = other relevant determinant(s) of demand
ε = error term
Values of a and bi ?
a and bi have to be estimated from historical data
• Data used in regression analysis
 cross-sectional data provide information on
variables for a given period of time
 time series data give information about variables
over a number of periods of time
• New technologies are currently dramatically changing
the possibilities of data collection
Simple Linear Regression Model
In the simplest case, the dependent variable Y is
assumed to have the following relationship with the
independent variable X:
Y = a + bX + ε
where
Y = dependent variable
X = independent variable
a = intercept
b = slope
ε = random factor
Estimating the Regression Equation
• Finding a line that “best fits” the data
– The line that best fits a collection of X,Y data
points, is the line minimizing the sum of the
squared distances from the points to the line as
measured in the vertical direction
– This line is known as a regression line, and the
equation is called a regression equation
Estimated Regression Line:
Yˆ  a  bX
Observed Combinations of Output and Labor
input
Skatter Plot
600
Q
500
Q
400
Yˆ  Y
300
200
100
0
0
100
200
300
400
L
500
600
700
800
Regression with Excel
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,959701
R Square 0,921026
Adjusted R Square
0,917265
Standard Error
47,64577
Observations
23
Evaluate statistical
significance of
regression
coefficients using
t-test and
statistical
significance of R2
using F-test
ANOVA
df
Regression
Residual
Total
SS
MS
F
Significance F
1 555973,1 555973,1 244,9092 4,74E-13
21 47672,52 2270,12
22 603645,7
Coefficients Standard Error
t Stat
P-value Lower 95% Upper 95%Lower 95,0%
Upper 95,0%
Intercept
-75,6948 31,64911 -2,39169 0,026208 -141,513 -9,87686 -141,513 -9,87686
X Variable 11,377832 0,088043 15,64957 4,74E-13 1,194737 1,560927 1,194737 1,560927
Statistical analysis is testing hypotheses
• Statistics is based on testing hypotheses
• ”null” hypothesis = ”no effect”
• Assume a distribution for the data, calculate
the test statistic, and check the probability of
getting a larger test statistic value
For the normal distribution:
Z
Z
p
X 

t-test: test of statistical significance of each estimated
regression coefficient
• bi = estimated coefficient
• H0: bi = 0
t
bi
SE bi
• SEβ: standard error of the estimated coefficient
• Rule of 2: if absolute value of t is greater than 2,
estimated coefficient is significant at the 5% level (=
p-value < 0.05)
• If coefficient passes t-test, the variable has an impact
on demand
Sum of Squares
Sum of Squares cont’d
TSS = (Yi - Y)2
(total variability of the dependent variable about its
mean Y)
RSS = (Ŷi - Y)2
(variability in Y explained by the sample regression)
ESS = (Yi - Ŷi)2
(variability in Yi unexplained by the dependent
variable x)
This regression line gives the minimum ESS among
all possible straight lines.
The Coefficient of Determination
• Coefficient of determination R2 measures how well
the line fits the scatter plot (Goodness of Fit)
RSS
ESS
R 
 1
TSS
TSS
2
 R2 is always between 0 and 1
 If it’s near 1 it means that the regression line is a
good fit to the data
 Another interpretation: the percentage of variance
”accounted for”
F-test
• The null hyphotesis in the F-test is
H0: b1= 0, b2= 0, b3= 0, …
• F-test tells you whether the model as a whole explains
variation in the dependent variable
• No rule of thumb, because the values of the Fdistribution vary a lot depending on the degrees of
freedom (# of variables vs. # of observations)
– Look at p-value (”significance F”)
Special Cases:
• Proxy variables
– to present some other “real” variable, such as taste
or preference, which is difficult to measure
• Dummy variables (X1= 0; X2= 1)
– for qualitative variable, such as gender or location
• Linear vs. non-linear relationship
– quadratic terms or logarithms can be used
Y = a + bX1 + cX12
QD=aIb  logQD= loga + blogI
Example: Specifying the Regression Equation for Pizza Demand
We want to estimate the demand for pizza
among college students in USA
What variables would most likely affect
their demand for pizza?
What kind of data to collect?
Data: Suppose we have obtained cross-sectional data on randomly selected
30 college campuses (through a survey)
The following information is available:
 average number of slices consumed per month by
students
 average price of a slice of pizza sold around the
campus
 price of its complementary product (soft drink)
 tuition fee (as proxy for income)
 location of the campus (dummy variable is
included to find out whether the demand for pizza
is affected by the number of available substitutes);
1 urban, 0 for non-urban area
Linear additive regression line:
Y = a + b1pp + b2 ps + b3T + b4L
where
Y = quantity of pizza demanded
a = the intercept
Pp = price of pizza
Ps = price of soft drink
T = tuition fee
L = location
bi = coefficients of the X variables measuring the impact
of the variables on the demandfor pizza
Estimating and Interpreting the Regression
Coefficients
Y = 26.27- 0.088pp - 0.076ps + 0.138T- 0.544 L
(0.018) (0.018)* (0.020)* (0.087) (0.884)
R2 = 0.717
adjusted R2 = 0.67
F = 15.8
Numbers in parentheses are standard errors of
coefficients.
*significant at the 0.01 level
Problems in the Use of Regression Analysis:
• identification problem
• multicollinearity
(correlation of coefficients)
• autocorrelation
(Durbin-Watson test)
• normality assumption fails
(outside the scope of this course)
Identification Problem
• Can arise when all effects on Y are not accounted for by
the predictors
P
D?!
P
S
D2
D3
D1
Q
Can demand be
upward sloping?!
Q
OR…?
Multicollinearity
• A significant problem in multiple
regression which occurs when there is a
very high correlation between some of
the predictor variables.
Resulting problem:
Regression coefficients may be very misleading or
meaningless because…
– their values are sensitive to small changes in the
data or to adding additional observations
– they may even be opposite in sign from what
”makes sense”
– their t-value (and the standard error) may change
a lot depending upon which other predictors are in
the model
Multicollinearity cont’d
Solution:
Don’t use two predictors which are very highly
correlated (however, x and x2 are O.K.)
Not a major problem if we are only trying to fit the data
and make predictions and we are not interested in
interpreting the numerical values of the individual
regression coefficients.
Multicollinearity cont’d
• One way to detect the presence of multicollinearity is to
examine the correlation matrix of the predictor
variables. If a pair of these have a high correlation they
both should not be in the regression equation – delete
one.
Y
X1
Y
1.00
-.45
X1
-.45
1.00
X2
.81
-.82
X3
.86
-.59
X2
X3
.81
.86
-.82
-.59
1.00
.91
.91
1.00
Correlation
Matrix
Autocorrelation
• Correlation between consecutive observations
• Usually encountered with time series data
– E.g. seasonal variation in demand
D
 Creates a
problem with ttests:
insignificant
variables may
appear significant
time
A test for Autocorrelated Errors:
DURBIN-WATSON TEST
• A statistical test for the presence of autocorrelation
• Fit the time series with a regression model and then
determine the residuals:
n
 t  yt  yˆ t
d
2
(



)
 t t 1
t 2
n

t 1
2
t
The Interpretation of d:
The Durbin-Watson value d will always be
0d4
Strong
positive
correlation
0
No
correlation
2
Strong
negative
correlation
4
Multiple Regression Procedure
1. Determine the appropriate predictors and the form of
the regression model
– Linear relationship
– No multicollinearity
– Variables ”make sense”
2. Estimate the unknown a and b coefficients
3. Check the “goodness” of the model (R2, global F-test,
individual t-test for each b coefficient)
4. Use the fitted model for predictions (and determine
their accuracy)
Additional Comments:
• OCCAM’S RAZOR. We want a model that does a
good job of fitting the data using a minimum number
of predictors. A high R2 is not the only goal; variables
used should be ”meaningful”
• Don’t use more predictors in a regression model than
5% to 10% of n
• Correlation is not causality!
FORECASTING
• Expert opinion –based methods
– Delphi method
• Data-based methods
– Time series analysis
• History can predict the future?
– Regression analysis
• Forecast the values of the Xi’s to get Y
• Assumes the relationship between Xi’s and Y
does not change