Question

Estimating Demand for Super Detergents:

Here is the story: Branded Products, LLC., based in Sharjah, UAE, is a leading producer and marketer of household laundry detergent and bleach products. About a year ago, Branded Products rolled out its new Super Detergent in 15 regional markets following its success in test markets. Branded Products, LLC. hired a marketing consulting firm to perform a test marketing of product called Super Detergent. The marketing consultants collected data on average household income (M), the population of the marketing area (N), and the price of a rival brand of Detergents (PR). At the end of the month, total demand of Super Detergent (Q) were tabulated to provide the following data from which the consultants estimated an empirical demand function for the product.

Table 1

Regional Markets	P	M	PR	N	Q
1	3.00	45,586	2.75	274,000	7,952
2	3.00	37,521	3.50	13,450	8,222
3	3.00	41,333	2.64	54,150	7,166
4	3.25	47,352	2.35	6,800	6,686
5	3.25	51,450	2.75	11,245	7,715
6	3.25	27,655	3.15	54,500	6,643
7	3.50	30,265	2.55	26,600	5,155
8	3.50	39,542	3.00	158,000	7,127
9	3.50	41,596	2.75	22,500	5,834
10	3.75	42,657	2.45	46,150	5,093
11	3.75	36,421	2.89	8,200	5,828
12	3.75	47,624	2.49	38,500	6,590
13	4.00	50,110	3.15	105,000	6,228
14	4.00	57,421	2.80	92,000	7,218
15	4.00	38,450	2.90	38,720	5,846

Using the marketing data from the 15 test markets shown above, estimate the parameters of the linear empirical demand function:

Q=a+bP+cM+dPR+eN

If any of the parameter estimates are not significant at the 5% level of significance, drop the associated explanatory variable from the model and estimate the demand function again.

1. Using the data in Table 1, specify a linear functional form for the demand for super detergent, and run a regression to estimate the demand for super detergent.

2. Using Excel Data Analysis, estimate the parameters of the empirical demand function specified in part a. Write your estimated demand equation.  

If price of the super detergent is AED3.50 per liter, average household income is AED 45, 000, the price of rival brand detergents is AED 3.00 per liter and the population (N) is 75, 000.

3. Calculate the estimated elasticity of Demand for super detergent. Is demand elastic or inelastic? Explain.

4. What is the estimated income elasticity of demand for super detergent? Is Super Detergent a normal or inferior good? Explain.

5. By using the appropriate tests, evaluate the significance of the regression as a whole and the significance of the individual parameters at 5 percent level of significance.

6. Interpret the R² value.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.931858
R Square	0.868358
Adjusted R Square	0.815702
Standard Error	412.6313
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	4	11231314	2807829	16.49097	0.000211
Residual	10	1702646	170264.6
Total	14	12933960
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	5386.978	1644.323	3.276106	0.008344	1723.197	9050.758	1723.197	9050.758
P	-1853.35	318.7362	-5.81468	0.00017	-2563.54	-1143.16	-2563.54	-1143.16
M	0.07665	0.015486	4.949606	0.000579	0.042145	0.111156	0.042145	0.111156
PR	1562.048	378.2161	4.130042	0.002044	719.3304	2404.766	719.3304	2404.766
N	0.001404	0.00162	0.867225	0.406147	-0.0022	0.005013	-0.0022	0.005013

price elasticity of demand is inelastic as 1% rise in price of super detergent reduces quantity demanded of super detergent by 0.9083%, which is less than 1%.

super detergent is a normal good as 1% rise in average hosuehold income increases the demand for super detergent by 0.483%

As per the summary output of the regression, p-value for price of super detergent (P), average household income (M) and price of rival brand of detergent (PR) is 0.05. Therefore, above 3 variables are statistically significant at 5% level of significance

Since the p-value for population in the marketing area is more than 0.05, population variable is not statisically significant

p-value for F-test statistic is 0.000211 is less than 0.05, therefore above regression is statistically signficant and we reject the null nypothesis that slope coefficients are 0

R-square for the regression is 0.8683

This means 86.83% of variation in demand of super detergent is explained by variables including price of super detergent, price of rival brand of detergent, average household income and population in marketing area