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GSM5000 MANAGERIAL ECONOMICS

PBL 1: SOFT DRINK DEMAND ESTIMATIONLECTURER:DR. SAIFUZZAMAN BIN IBRAHIM (Putra Business School, 2013)

•You have been appointed as a member of a consultation team who is working on this very important assignment for a soft drink company. The main task is to evaluate factors affecting the soft drink consumption. Therefore, you should revise the knowledge of demand analysis and carry out an investigation on the possible determinants of the demand for the product. The consultant should also describe the methodology of a multiple linear regression and its purpose in estimating a demand function.

•The consultant should then run a multiple linear regression in linear and multiplicative forms based on the data provided by the company and report on the estimated result. They will have to evaluate the estimated demand equations both in linear and multiplicative forms, select the one, which can best describe the consumption. The consultant will also have to obtain the estimated values of the various demand elasticities from the estimated coefficients of the regression and explain the meaning of each elasticity. From the demand equation, the consultant should recommend how to improve the soft drink consumption.

CASE SYNOPSIS

a. Estimate the demand for soft drinks using a multiple linear regression in both linear and multiplicative forms.

b. Provide an economic interpretation for each of the estimated coefficients.

c. Calculate the price and income elasticity and interpret them.

d. Using economics and statistical criteria, determine the ‘best’ demand specification.

e. Based on your answer in part (d), estimate a new demand equation by omitting price from the regression equation. Observe the bias introduced into the parameter estimate for income.

f. Now omit both price and temperature from the regression equation. Should the marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighbourhood? Why or Why not?

REQUIREMENTS

a. Estimate the demand for soft drinks using a multiple linear regression in both linear and multiplicative forms.

b. Provide an economic interpretation for each of the estimated coefficients.

•Price per Six-Pack, P : For a unit increase in Price will result in 242.88unit decrease in annual cans per capita consumption.

•Income per Capita, Y : For a unit increase in Income, Y will result in 1.22unit increase in annual cans per capita.

•Mean Temperature, T : For a unit increase in Temperature, T will result in 2.92unit increase in annual cans per capita consumption.

c. Calculate the price and income elasticity and interpret them.

Linear Model

Q = 514.89 - 242.88P + 1.22Y + 2.92TPrice elasticity, Ep = δQ/δP x P/Q

= -242.88*(2.19/160.76) = -3.13

Multiplicative Model

LogQ = 1.06 - 3.19LogP + 0.22LogY + 1.11LogTPrice elasticity, Ep = -3.19

Interpretation on Price Elasticity: Based on the calculated price elasticity, the consumption on soft drink is price elastic in nature. This means that for a 1% increase in price will result in more than 1% decrease in quantity demanded for soft drinks.

Linear Model

Q = 514.89 - 242.88P + 1.22Y + 2.92TIncome elasticity, Ey = δQ/δY x Y/Q

= 1.22*(17.89/160.76) = 0.14

Multiplicative Model

LogQ = 1.06 - 3.19LogP + 0.22LogY + 1.11LogTIncome elasticity, Ey = 0.22

Interpretation on Income Elasticity: Based on the calculated income elasticity, a positive income elasticity indicates that soft drink is a normal goods.

d. Using economics and statistical criteria, determine the ‘best’ demand specification.

For Price, the R-squared is 0.5683 which is within the 0.4 to 0.6 range. Hence it has moderately strong correlation.

1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.70

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f(x) = − 311.846795546307 x + 845.671342479204R² = 0.568340813089516

PRICE

QLinear (Q)

For Income, the R-squared is 0.1094 which is within the range of 0 to 0.2. This indicates a very weak correlation.

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f(x) = − 5.2291364535267 x + 254.316941331575R² = 0.109384897902991

INCOME

QLinear (Q)

For Temperature, the R-squared is 0.4555 which is within the range of 0.4 to 0.6. Hence it has moderate strong correlation.

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f(x) = 4.90943341463823 x − 104.028354385162R² = 0.455489167363356

TEMPERATURE

QLinear (Q)

Conclusion: The best demand specification is to remove income per capita from the regression equation as the variable has a low correlation to the equation.

e. Based on your answer in part (d), estimate a new demand equation by omitting price from the regression equation. Observe the bias introduced into the parameter estimate for income.

When the independent variable of Price is removed from the equation, the R-Squared value drops from 0.66 to 0.47. Thus the strength of correlation falls under moderate range (0.4 to 0.6). The variables have a low association with the dependent variable as only 47% in quantity demanded are explained by the independent variables.

f. Now omit both price and temperature from the regression equation. Should the marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighbourhood? Why or Why not?

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f(x) = − 5.2291364535267 x + 254.316941331575R² = 0.109384897902991

INCOME

QLinear (Q)

•The graph above shows the weak relationship between Income and Quantity Demanded. Thus, the marketing plan should not be designed based on the income per capita factor as it does not strongly correlated with the demand of soft drink cans.

•Whether they market the product at low income groups or otherwise, it will not affect the quantity demanded that much. We strongly believe that the company should not design their marketing plan to relocate most canned drink machines into low-income neighbourhood.

•In addition, as some variables i.e. price and temperature were removed from the equation, it is unwise to rely solely on income factor to design on marketing plan as there exists a bias.

•Instead of wasting resources in trying to influence a variable that is weakly related to the dependant variable, the company should focus on other variables such as pricing as the critical component of their marketing plan. Since price is strongly related to Quantity Demanded, the company can stimulate the demand for their soft drink by giving discounts and "buy one, free one" (BOGO) promotions.

THE END

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