1
DEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORYDEMAND THEORY
DR. MOHAMMAD ABDUL MUKHYI, SE.,MM
Tabel Utillitas Total dan Utilitas MarginalTabel Utillitas Total dan Utilitas Marginal
Harga baju per helai
(Rp)
Jumlah baju yang
dikonsumsi
Uang yang dikeluarkan
(Rp)
Total Utility (TU)
Marginal Utility (MU)
25.000 1 25.000 50.000 50.000
25.000 2 50.000 125.000 75.000
25.000 3 75.000 185.000 60.000
25.000 4 100.000 225.000 40.000
25.000 5 125.000 250.000 25.000
25.000 6 150.000 250.000 0
25.000 7 175.000 225.000 -25.000
25.000 8 200.000 100.000 -125.000
2
Px = harga barang X
X = nama barang
U = utilitas
U(x) = Px.X
U(x) – Px.X = Dx → permintaan barang X
TU = 17X + 20Y – 2X2 - Y2
Jika diketahui:
uang yang ada Rp. 22.000
harga barang X (Px) = Rp. 3000
harga barang Y (Py) = Rp. 4000
Ditanya:
1. Berapa barang X dan Y yang dikonsumsi
2. Berapa besarnya nilai kepuasan total, barang X
dan barang Y
3
KESEIMBANGAN KONSUMENKESEIMBANGAN KONSUMEN
Y
0 X
E
IC2
IC1
IC3
BL2 BL1
Y1
X1
Maksimisasi Kepuasan
Fungsi utiliti : U = BP = 3200
Fungsi anggaran Y = 2P + 1B
4
1. Bila yang menjadi kendala adalah anggaran dan utility
adalah tujuannya, maka syarat optimum adalah
2Py
B Y 2Py.Y B Py.Y Py.Y By
2Px
BX 2Px.X B Px.X Px.X Bx
:maka YPy, XPx karena
y x
0
0
..(),(
=→=⇔+=
=→=⇔+=
=
=→=⇔=→=
→=→=−=∂
∂
→=→=−=∂
∂
−+−=
XPxYPyPy
Px
MUy
MUx
Py
MUy
Px
MUx
Py
MUy
Py
XPyX
Y
U
Px
MUx
Px
YPxY
X
U
BYPyXPxYXU
X
X
λλ
λλ
λλ
λ
OPTIMUM SYARAT
2. Bila yang menjadi kendala adalah utility dan anggaran adalah tujuannya, maka syarat optimum adalah
2/11-2/11-
2/12/1
2
2
2
1
)Py(Px.U.Py )Px(Py.U.Px B
Py
PxUPy
Px
PyUPxB
Py
PxPy
Px
PyPx B
disediakan harus yangAnggaran
.0.
....
...
+=
+
=→+=
=⇔=
=→=→=→=−=∂
∂
+=→+=
=→=→=→+=
−
−
UU
UPy
PxY
UPx
Py
UY
UPx
PyXU
Px
PyX
X
UPyPxUXPyPx
X
B
UXPyXPxBX
UPyXPxB
Y
UXatau
X
UYYXUYPyXPxB
5
DEMAND FOR A COMMODITYDEMAND 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%
6
P
0 Q1
P P
Q2 Qx0 0
2 2 2
1 1 1
3 2 52 1 3
d1 d2 d3
Individual 1 Individual 2 Pasar
Permintaan Kentang di IndonesiaPermintaan Kentang di Indonesia
Permintaan kentang untuk periode 1980-2008:QdQdQdQdSSSS = 7.609 = 7.609 = 7.609 = 7.609 –––– 1.606P1.606P1.606P1.606PSSSS + 59N + 947I + 479P+ 59N + 947I + 479P+ 59N + 947I + 479P+ 59N + 947I + 479PWWWW + 271+ 271+ 271+ 271tttt....QdS = quantitas kentang yang dijual per tahun per
1.000 Kg.PS = harga kentang per kgN = 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 = 1Bagaimana bentuk fungsi permintaan kentang?
7
Elastisitas Harga PermintaanElastisitas Harga Permintaan
Elastisitas Titik :
Elastisitas Busur :
Q
P x
P
Q
P/P
Q/Qd
hargaperubahan %
diminta yangjumlah perubahan %d
p
p
∂
∂=
∂
∂=
=
E
E
2/)QQ(
2/)PP( x
P
Q d
Q/n
P/n x
P
Q d
21
21p
p
+
+
∂
∂=
Σ
Σ
∂
∂=
E
atau
E
Elastisitas KumulatifElastisitas Kumulatif ::
Q
P x
P
Q d
Q/n
P/n x
P/N
Q/N d
p
p
Σ
Σ
∂Σ
∂Σ=
Σ
Σ
∂Σ
∂Σ=
E
atau
E
Elastisitas Silang :
Qx
Py x
Py
Qx
Py/Py)(
Qx/Qx)(c
Y barang hargaperubahan %
diminta yang X barangjumlah perubahan %c
xy
xy
∂
∂=
∂
∂=
=
E
atau
E
8
Elastisitas Pendapatan :
Qd
Y x
Y
Qd
Qd
Y x
Y
Qdy
pendapatanperubahan %
diminta yang barangperubahan % y
Σ
Σ
∂
∂=
∂
∂=
=
E
atau
E
Elastisitas Harga, Total Revenue, Marginal Revenue :
TR = P . Q
MR = ∆TR / ∆Q
+=
pE
1 1P MR
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
9
0
100
200
300
400
500
600
700
800
900
1000
0 200 400 600 800
output
TR ($)
TR
output
0
100
200
300
400500
600
700
800
900
1000
0 200 400 600 800
TR
($)
D
MR = 6 – Q/50
TR = 6Q – Q2/100
Q = 600 – 100P
22
114
2
114 =
−=
−+=MR
Qx = 1,5 – 3,0Px + 0,8I + 2,0Py – 0,6Ps + 1,2A
Qx = penjualan kopi merek XPx = harga kopi merek XI = pendapatan disposibel per kapita per tahunPy = harga kopi pesaingPs = harga gula per kiloA = 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
10
6,02
12,1E
15,02
50,06,0E
8,12
8,12E
12
2,50,8 E
32
23E
A
XS
XY
I
P
=
=
−=
−=
=
=
=
=
−=
−=
Tingkat Elastisitas :
SupplySupply
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, ….)
11
Hypothetical Industry
Supply Curve for New
Domestic Automobiles
Hypothetical Industry Supply Curves
for New Domestic Automobiles at
Interest Rates of 6%, 8%, and 10%
13
Comparative Statics of Changing Supply
Comparative Statics of Changing Demand
and Changing Supply Conditions
14
Demand and
Supply Curves
ObjectivesObjectives
• 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
15
Approaches to Demand EstimationApproaches 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
16
(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 = α + β X1t + γ X2t + ut
Multiplicative Yt = α X1tβ X2t
γ et
ln Yt = ln α + β ln X1t + γ 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
17
Transit ExampleTransit Example
Y P T I H
YEAR Riders Price Pop. Income Parking Rate
1966 1200 15 1800 2900 50
1967 1190 15 1790 3100 50
1968 1195 15 1780 3200 60
1969 1110 25 1778 3250 60
1970 1105 25 1750 3275 60
1971 1115 25 1740 3290 70
1972 1130 25 1725 4100 75
1973 1095 30 1725 4300 75
1974 1090 30 1720 4400 75
1975 1087 30 1705 4600 80
1976 1080 30 1710 4815 80
1977 1020 40 1700 5285 80
1978 1010 40 1695 5665 85
Y P T I H
YEAR Riders Price Pop. Income Parking Rate
1979 1010 40 1695 5800 100
1980 1005 40 1690 5900 105
1981 995 40 1630 5915 105
1982 930 75 1640 6325 105
1983 915 75 1635 6500 110
1984 920 75 1630 6612 125
1985 940 75 1620 6883 130
1986 950 75 1615 7005 150
1987 910 100 1605 7234 155
1988 930 100 1590 7500 165
1989 933 100 1595 7600 175
1990 940 100 1590 7800 175
1991 948 100 1600 8000 190
1992 955 100 1610 8100 200
20
Linear Transit DemandDependent Variable: RIDERS
Method: Least Squares
Date: 03/31/02 Time: 18:22
Sample: 1966 1992
Included observations: 27
Variable Coefficient Std. Error t-Statistic Prob.
C 85.43924 492.8046 0.173373 0.8639
PRICE -1.617484 0.495976 -3.26122 0.0036
POPULATION 0.643769 0.262358 2.453782 0.0225
INCOME -0.047475 0.012311 -3.85616 0.0009
PARKING 1.943791 0.349156 5.567113 0
R-squared 0.960015 Mean dependent var1026.222
Adjusted R-squared 0.952745 S.D. dependent var 94.25756
S.E. of regression 20.48984 Akaike info criterion 9.043312
Sum squared resid 9236.342 Schwarz criterion 9.283282
Log likelihood -117.0847 F-statistic 132.0525
Durbin-Watson stat 1.384853 Prob(F-statistic) 0
Riders = 85.4 – 1.62 price …
Pr Elas = -1.62(100/955) in 1992
Multiplicative Transit DemandDependent Variable: LRIDERS
Method: Least Squares
Date: 03/31/02 Time: 18:26
Sample: 1966 1992
Included observations: 27
Variable Coefficient Std. Error t-Statistic Prob.
C 3.24892 3.26874 0.993937 0.3311
LPRICE -0.13716 0.021873 -6.27052 0
LPOPULATION 0.613645 0.409148 1.49981 0.1479
LINCOME -0.13077 0.039913 -3.27646 0.0034
LPARKING 0.166443 0.032361 5.143338 0
R-squared 0.973859 Mean dependent var6.929651
Adjusted R-squared 0.969107 S.D. dependent var 0.09061
S.E. of regression 0.015926 Akaike info criterion -5.27614
Sum squared resid 0.00558 Schwarz criterion -5.03617
Log likelihood 76.22788 F-statistic 204.9006
Durbin-Watson stat 0.93017 Prob(F-statistic) 0
Ln Riders = exp(3.25)P-.14 …
21
MTB > Regress 'Y' 4 'P' 'T' 'I' 'H';
SUBC> Constant; SUBC> Residuals 'RESI1';
SUBC> DW.
The regression equation is Y = 85 - 1.62 P + 0.644
T - 0.0475 I + 1.94 H
Predictor Coef Stdev t-ratio p
Constant 85.4 492.8 0.17 0.864
P -1.6175 0.4960 -3.26 0.004
T 0.6438 0.2624 2.45 0.023
I -0.04747 0.01231 -3.86 0.001
H 1.9438 0.3492 5.57 0.000
s = 20.49 R-sq = 96.0% R-sq(adj) = 95.3%
Analysis of Variance
SOURCE DF SS MS F p
Regression 4 221760 55440 132.05 0.000
Error 22 9236 420
Total 26 230997
Durbin-Watson statistic = 1.38
22
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
23
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, Τ, N)
(px=price of good x, Y=income, ps=price of substitute,
pc=price of complement, Τ=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?
24
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
25
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
26
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
27
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
28
Think of a demand function of general form:
Qi = α + β1Y - β2 pi + β3ps - β4pc + β5Z + ε
whereQi = 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 α and βi ?
α and βi 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
29
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 = α + βX + ε
where
Y = dependent variable
X = independent variable
α = intercept
β = 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:
XY βα +=ˆ
30
Observed Combinations of Output and Labor inputObserved Combinations of Output and Labor input
Skatter Plot
0
100
200
300
400
500
600
0 100 200 300 400 500 600 700 800
L
Q
Q
YY −ˆ
Regression with Excel
SUMMARY OUTPUT
Regression Statistics
Multiple R 0,959701
R Square 0,921026
Adjusted R Square0,917265
Standard Error47,64577
Observations 23
ANOVA
df SS MS F Significance F
Regression 1 555973,1 555973,1 244,9092 4,74E-13
Residual 21 47672,52 2270,12
Total 22 603645,7
CoefficientsStandard Errort 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
Evaluate statistical significance of regression coefficients using t-test and statistical significance of R2 using F-test
31
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
σ
µ−=
XZ
Z For the normal distribution:
p
t-test: test of statistical significance of each estimated
regression coefficient
• βi = estimated coefficient
• H0: βi = 0
• 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
iSE
t i
β
β=
32
Sum of Squares
Sum of Squares cont’d
TSS = Σ(Yi - Y)2
(total variability of the dependent variable about its mean Y)
RSS = Σ(Ŷi - Y)2
(variability in Y explained by the sample regression)
ESS = Σ(Yi - Ŷi)2
(variability in Yi unexplained by the dependent variable x)
This regression line gives the minimum ESS among all possible straight lines.
33
The Coefficient of Determination
• Coefficient of determination R2 measures how well the line fits the scatter plot (Goodness of Fit)
�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”
TSS
ESS1
TSS
RSSR
2 −−−−========
F-test
• The null hyphotesis in the F-test is
H0: β1= 0, β2= 0, β3= 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 F-distribution vary a lot depending on the degrees of freedom (# of variables vs. # of observations)
– Look at p-value (”significance F”)
34
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?
35
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
36
Coefficients
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)
37
Identification Problem
• Can arise when all effects on Y are not accounted for by
the predictors
Q
P
Q
P S
D3
D2
D1
Can demand be upward sloping?!
OR…?
D?!
Multicollinearity
• A significant problem in multiple
regression which occurs when there is a
very high correlation between some of
the predictor variables.
38
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.
39
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 X2 X3
Y 1.00 -.45 .81 .86
X1 -.45 1.00 -.82 -.59
X2 .81 -.82 1.00 .91
X3 .86 -.59 .91 1.00
Correlation Matrix
Autocorrelation
• Correlation between consecutive observations
• Usually encountered with time series data
– E.g. seasonal variation in demand
� Creates a problem with t-tests: insignificant variables may appear significant
time
D
40
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:
ttt yy ˆ−=ε
∑
∑
=
=
−−
=n
t
t
n
t
tt
d
1
2
2
2
1)(
ε
εε
The Interpretation of d:
The Durbin-Watson value d will always be
0 ≤ d ≤ 4
40 2
No correlation
Strong negative correlation
Strong positive correlation
41
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 α and β coefficients
3. Check the “goodness” of the model (R2, global F-test, individual t-test for each β 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!
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