Skyline University ECO6002: Managerial Economics Case Study Analysis

This case study analyzes the demand for Ozarka bottled water, utilizing regression analysis to estimate a linear demand function based on data collected from test markets. The solution includes hypothesis testing to assess the significance of regression coefficients and the overall model, determining the impact of price, household income, price of a rival brand, and marketing area on sales. It calculates price, income, and cross-price elasticities of demand to understand how changes in these factors influence sales. The analysis further explores a log-linear demand model, comparing it with the linear model in terms of R-squared, F-ratios, and t-ratios to assess the appropriateness of each specification. The study concludes with a comparison of elasticities between the linear and log-linear models, providing a comprehensive evaluation of demand estimation and its implications for managerial decision-making. The solution includes all the formulas, procedures, and regression outputs as asked in the assignment brief.

Running head: MANAGERIAL ECONOMICS
Managerial Economics
Name of the Student
Name of the University
Course ID

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Table of Contents
Part A...............................................................................................................................................2
Question 1....................................................................................................................................2
Question 2....................................................................................................................................6
Part B...............................................................................................................................................8
Question 1....................................................................................................................................8
Question 2....................................................................................................................................9
Question 3..................................................................................................................................10
Question 4..................................................................................................................................10
References......................................................................................................................................12

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Part A
The linear demand function to be estimated for Ozark Water Bottle is given as
Q=a+bP+cM+ dPR+eN
Result of the regression for estimating the above linear demand function is
Table 1: Linear regression result
Question 1
Significance of regression as a whole
Hypothesis
Null Hypothesis (H0): All the regression coefficient is equal to Zero

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Alternative Hypothesis (H1): At least one of the coefficient is significantly different from zero
Test statistics
In order to test overall significance F test statistics is used. The computed value of F test
as obtained from the regression is
F=16.491
Decision
The critical F value at 5% level of significance and (4, 10) degrees of freedom is 3.4780.
The computed F value exceeds critical F meaning rejection of null hypothesis of no overall
significance of the model (Gunst, 2018). The overall model therefore is statistically significant at
5% significance level.
Significance of individual parameters
Hypothesis
Null Hypothesis (H0): The regression coefficient is zero.
Alternative Hypothesis (H1): The regression coefficient is significantly different from zero
Test statistics
‘t’ test statistics is used for testing significance of individual parameters. Computed‘t’
value for the respective coefficients are as follows
Price
tP = Coefficient
Standard error

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¿ −1853.3476
318.7362
¿−5.8147
Household income
tM = Coefficient
Standard error
¿ 0.0767
0.0155
¿ 4.9496
Price of rival brand
tPR = Coefficient
Standard error
¿ 1562.0484
378.2161
¿ 4.1300
Population tN = Coefficient
Standard error
¿ 0.0014
0.0016
¿ 0.8672

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Decision
The critical t value at 5% level of significance with 10 degrees of freedom is 2.2281. The
absolute value of computed ‘t’ for price, household income and price of rival brand exceeds the
critical t implying rejection of null hypothesis that the coefficient is statistically insignificant.
The computed t for marketing area is less than the critical t indicating that the coefficient is not
statistically significant.
The coefficient of marketing area is not statistically significant at 2% level. The variable
therefore has been dropped from the model. Regression result for the new model is
Table 2: Regression result with new specification
a)
The final linear demand function as estimated is
^Q=5357.0788−1906.8618 P+ 0.0803 M +1615.6538 PR

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b. The estimated demand function explains approximately 86 percent variation in sales of Liquid
Ozarka.
Question 2
Demand function of Liquid Ozaraka is
^Q=5357.0788−1906.8618 P+ 0.0803 M +1615.6538 PR
With given price of Liquid Ozarka, average household income and price of rival bottled water
estimated sales is
^Q=5357.0788−1906.8618 P+ 0.0803 M +1615.6538 PR
¿ 5357.0788− (1906.8618 × $ 3.50 ) + ( 0.0803 × $ 45000 ) + ( 1615.6538× $ 3 )
¿ 5357.0788−6674.0163+ 3613.5+4846.9614
¿ 7143.52 7144
a)
Price elasticity of demand= dQ
dP × P
Q
¿−1906.8618× 3.50
7144
¿−1906.8618× 0.00049
¿−0.93
Computed price elasticity of demand <1, meaning that demand is inelastic.

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The required percentage increase in price to boost sales by 10 percent is (10/0.93) = 10.75
percent.
b) Income elasticity of demand= dQ
dM × M
Q
¿ 0.0803 × 45000
7144
¿ 0.0803 ×6.2990
¿ 0.51
Income elasticity of demand is positive meaning Liquid Ozarka is a normal good
(Cowell, 2018). In average household income boosts by 6 percent, it would cause sales of Liquid
Ozarka to increase by (0.51*6) = 3.06 percent.
c)
Cross price elasticity of demand= dQ
dPR × PR
Q
¿ 1615.6538 × 3
7144
¿ 1615.6538 ×0.00042
¿ 0.68
The cross price elasticity of demand has a positive sign which is expected. In case of
substitute goods since increase in price of one good increases demand for the substitute good the
cross price elasticity of demand becomes positive. Therefore, since Liquid Ozarka and its rival
brand bottled water are substitute good the expected sign of cross price elasticity is positive

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which is as obtained above (Fine, 2016). If the price of rival brand’s water bottle rises by 8
percent, sales of Liquid Ozarka will be increased by (0.68*8) = 5.44 percent.
Part B
Q=a Pb M c PR
d Ne
¿ , logQ=loga+blogP +clogM + dlog PR +elogN
Question 1
Table 3: Result of log-linear regression
The p value of market area is 0.5737 which is larger than value at 2% significance level
implying that the variable is not statistically significant (Darlington & Hayes, 2016). The
variable therefore is dropped from the model. The new regression model is given as
Table 4: Result of log-linear regression without ‘Market area’

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^Q=4.1421−0.9763 logP+ 0.4835logM + 0.7020logPR
Question 2
Table 5: Comparison of R square and F ratios between linear and log-linear demand model
Model
R
square F ratios
Linear 0.86 22.23
Log-linear 0.83 17.59
Table 6: Comparison of t ratios between linear and log-linear demand model
t ratios
Variables Linear Log linear
Price -6.1678 -5.4103
Income 5.4547 4.8039
Price of rival brand 4.3796 3.9179

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The R square value of the linear model is larger than the log linear model indicating a
better explanatory power of the linear model. F ratio of the linear model is greater than the log
linear model implying a greater overall significance. ‘t’ ratios for the regression coefficient in the
linear model have larger value compared to that of the log linear model. All these indicate a
better specification in the linear model compared to that in the log linear specification.
Question 3
Price elasticity of demand=−0.98
Income elasticity of demand =0.48
Cross price elasticity of demand=0.70
Table 7: Comparison of elasticity of demand between linear and log-linear model
Price elasticity and cross price elasticity in log linear model is greater than that in linear
model. The value of income elasticity of demand in the linear model in contrast is greater than
that in log linear model.
Question 4
Estimated demand with linear specification
logQ=4.1421−0.9763logP +0.4835 logM +0.7020 logPR

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¿ 4.1421−0.9763 ×log ( 3.50 ) +0.4835 × log ( 45000 ) +0.7020 × log ( 3.50 )
¿ 4.1421−1.2231+ 5.1804+0.7712
¿ 8.8707
Q=7120