1. MANAGERIAL ECONOMICS 12th EditionBy
Mark Hirschey

2. Demand Estimation
Chapter 5

3. Chapter 5 OVERVIEW Interview and Experimental Methods
Simple Demand Curve Estimation
Simple Market Demand Curve Estimation
Identification Problem
Regression Analysis
Measuring Regression Model Significance
Measures of Individual Variable Significance

4. Interview and Experimental Methods
Consumer Interviews
Interviews can solicit useful information when market data is scarce.
Consumer opinions can differ from behavior.
Market Experiments
Controlled experiments can generate useful insight.
Experiments can be expensive.

5. Simple Demand Curve Estimation
Simple Linear Demand Curves
The best estimation method balances marginal costs and marginal benefits.
Simple linear relations are often useful for demand estimation.
Using Simple Linear Demand Curves
Straight-line relations can give useful approximations.

6. Simple Demand Curve Estimation
𝑃=𝑎+𝑏𝑄
Consider the linear demand:
when P=$12, Q=3,200 and P=$10, Q=4,000
12 =𝑎+𝑏 3200
12 =𝑎+𝑏 3200
minus
10 =𝑎+𝑏 4000
12 =𝑎−
12 =𝑎−8
2 =−800𝑏
𝑎=20
b =−0.0025
𝑃=𝑎+𝑏𝑄 is
𝑃=20−0.0025𝑄

7. Demand Curve and TR Maximization
𝑇𝑅=𝑃∙𝑄
= $20−$0.0025𝑄 𝑄
=$20𝑄−$ 𝑄 2
𝑀𝑅= 𝜕𝑇𝑅 𝜕𝑄
=$20−$0.005𝑄
$20−$0.005𝑄=0
$0.005𝑄=$20
𝑄=4000
and
𝑃=20− =$10
max 𝑇𝑅 =𝑃∙𝑄=4000∙$10=$40,000

8. Market Demand Curve Estimation
Shows total quantity customers are willing to buy at various prices under current market conditions.
Graphing the Market Demand Curve
Market demand is the sum of individual demand quantities, Q1 + Q2 = Q1+2.
Add quantities, not prices!

9. Market Demand Curve Estimation
𝑃 𝐷 =$100−$0.001 𝑄 𝐷
Domestic Demand
𝑃 𝐹 =$80−$0.004 𝑄 𝐹
Foreign Demand
𝑇𝐶=$1,200,000+$24𝑄
Total Cost
𝑃 𝐷 =$100−$0.001 𝑄 𝐷
𝑃 𝐹 =$80−$0.004 𝑄 𝐹
0.001 𝑄 𝐷 =100− 𝑃 𝐷
0.004 𝑄 𝐹 =80− 𝑃 𝐹
𝑄 𝐷 =100,000− 1000𝑃 𝐷
𝑄 𝐹 =20,000− 250𝑃 𝐹

10. Market Demand Curve Estimation
𝑄= 𝑄 𝐷 + 𝑄 𝐹
𝑄=100,000− 1000𝑃 𝐷 +
20,000− 250𝑃 𝐹
𝑄=120,000−1,250𝑃
1,250𝑃=120,000−𝑄
𝑃=$96−$0.0008𝑄
Market Demand

11. Market Demand Curve Estimation
𝑇𝑅=𝑃∙𝑄
= $96−$0.0008𝑄 𝑄
=$96𝑄−$ 𝑄 2
𝑀𝑅= 𝜕𝑇𝑅 𝜕𝑄 =$96−$0.0016𝑄
𝑇𝐶=$1,200,000+$24𝑄
𝑀𝐶= 𝜕𝑇𝐶 𝜕𝑄 =$24

12. Market Demand Curve Estimation
𝑀𝑅=𝑀𝐶
at profit maximization
$96−$0.0016𝑄=$24
$0.0016𝑄=$72
𝑄=45,000
𝑃=$96−$ ,000 =$60
𝜋=𝑇𝑅−𝑇𝐶
𝜋=$96𝑄−$ 𝑄 2 −($1,200,000+$24𝑄)
𝜋=−$ 𝑄 2 +$72𝑄−$1,200,000
𝜋=−$ , $72 45,000 −$1,200,000
𝜋=$420,000

13. Market Demand Curve Estimation
Domestic Demand
Market Demand
Foreign Demand

14. Identification Problem
Changing Nature of Demand Relations
Demand relations are dynamic.
Interplay of Demand and Supply
Economic conditions affect demand and supply.
Shifts in Demand and Supply
Curve shifts can be estimated.
Simultaneous Relations
Quantity and price are jointly determined.

15. Identification Problem
The demand curve “D” does not exist the data are for three shifting demand curves
All else equal w.r.t. demand determinants S1 D1
The problem:
“D” has higher elasticity than “D1”. P S1 P Q D D S2 S2 D2 P1 Q1 P1 Q1 S3 D3 S3 P2 Q2 P2 Q2 P3 Q3 P3 Q3 Q

16. Regression Analysis What Is a Statistical Relation?
A statistical relation exists metrics are related
A deterministic relation is true by definition.
Specifying the Regression Model
Dependent variable Y is caused by X.
X variables are independently determined from Y.
Least Squares Method
Minimize sum of squared residuals.

17. Regression Analysis . . . Direct Relation Inverse Relation No Relation
Unit Sales X . X .
Unit Sales X .
Unit Sales
Advertising
Price
Orbit of Jupiter

18. Regression Analysis . . . . . . . . . . . . 𝑚𝑖𝑛 𝑌− 𝑌 2
𝑚𝑖𝑛 𝑌− 𝑌 2
Regression Analysis fits a “Sum of Least Squares” line to the data Y .
Estimate or 𝑌 .
𝑏= 𝑛 𝑋𝑌 − 𝑋 𝑌 𝑛 𝑋 2 − 𝑋 2 . . . . .
Error or 𝑌− 𝑌 . . . .
Observation or 𝑌
𝑎= 𝑌 −𝑏 𝑋 𝑛 .
𝑌 =𝑎+𝑏𝑋
𝑌 = 𝑋 X

19. Regression Analysis 𝑋 𝑌 24 78 43
100 86 34 82 36 38 84 22 75 23 80 30 83 33 91 𝑋𝑌
𝑋 2
1872
576
4300
1849
2064
2788
1156
3096
1296
3192
1444
1650
484
1840
529
2490
900
3003
1089 𝑌 𝑈
79.50
-1.50
93.67
6.33
6.50
86.96
-4.96
88.45
-2.45
89.94
-5.94
78.01
-3.01
78.76
1.24
83.98
-0.98
86.21
4.79
𝑏= 𝑛 𝑋𝑌 − 𝑋 𝑌 𝑛 𝑋 2 − 𝑋 2 = − − =
𝑎= 𝑌 −𝑏 𝑋 𝑛 = 856− ∙ =
𝑌 = 𝑋

20. Regression Analysis
Regression equations can take on any functional form
𝑄=𝑎+𝑏𝑃
𝑄=𝑎+ 𝑏 𝑃 𝑃+ 𝑏 𝐴 𝐴+ 𝑏 𝐼 𝐼
𝑄= 𝑏 0 𝑃 𝑏 𝑃 𝐴 𝑏 𝐴 𝐼 𝑏 𝐼
The above multiplicative form is popular among economist because the exponents “bP” is the constant elasticity of the variable.
𝑄=4 𝑃 −0.4 𝐴 0.2 𝐼 0.003
has the constant price elasticity of – 0.4

21. Measuring Regression Significance
Standard Error of the Estimate (SEE) reflects degree of scatter about the regression line. Y X
𝑌 =𝑎+𝑏𝑋
Upper 95% confidence bound:
standard error of the estimate
𝑏 = Slope of curve 𝑌 𝑋 𝑎
Lower 95% confidence bound:
standard error of the estimate

22. Goodness of Fit Correlation shows degree of concurrence.
r = 1 means perfect correlation.
r = 0 means no correlation.
Coefficient of determination, R2.
R2 = 100% means perfect fit.
R2 = 0% means no relation.
Corrected coefficient of determination
Adjusts R2 downward for small samples.

23. Regression Analysis 𝑅 2 = 𝑌 − 𝑌 2 𝑌− 𝑌 2
𝑅 2 = 𝑌 − 𝑌 𝑌− 𝑌 2
Regression Analysis fits a “Sum of Least Squares” line to the data Y X 𝑌 𝑌
Unexplained variation
𝑌− 𝑌
Total variation
𝑌− 𝑌
Explained variation
𝑌 − 𝑌 𝑌
𝑎𝑑𝑗− 𝑅 2 =1−(1− 𝑅 2 ) 𝑛−1 𝑛−𝑝−1

24. F statistic Tells if R2 is statistically significant
Goodness of Fit Test
Do not Reject H0
Reject H0 F
 = 0.05
F = 2.69
Critical Value
 = 0.1
F = 2.14

25. Judging Variable Significance
t statistics compare sample characteristics to the standard deviation of that characteristic.
t > implies a strong effect of X on Y (90% conf.).
t > 1.96 implies an even stronger effect of X on Y (95% conf.)
Two-tail t Tests
Tests of effect.
One-Tail t Tests
Tests of magnitude or direction.

26. Judging Variable Significance
t – statistic
H0: b=0
Ha: b≠0
Reject H0
Reject H0
Do not Reject H0
 / 2 = 0.025
 / 2 = 0.025 z
– 1.96
1.96
 / 2 = 0.025
Critical Value = ± 1.96
Confidence Level = 95%
 / 2 = 0.05
Critical Value = ± 1.645
Confidence Level = 90%

27. Multiple Regression Example
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations 15
ANOVA df SS MS F
Significance F
Regression 4
Residual 10
Total 14
Coefficients
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept P Ps Pc I
-1.3E-05 Q P Ps Pc I 20 2
1.5 3
38000 30
2.5
2.3
22000 10
1.7
3.2
40000 15
1.9
2.8
25000 12
1.4
3.5
28000 28
2.7
2.2
17000 17
2.4
1.8
3.1
35000 14
3.8
2.1
2.9
20000 22
34000 32 25
36000
1.6
2.6
30000