Question

Fluidyne Corporation manufactures and sells water filters. The economic forecasting unit of the company has supplied the following demand equation

QB=    2000 -     5PB +   2.5PC   +   0.82Y   + 0.6AB

          (1200)       (1.5)       (1.2)            (0.5)      (0.2)

Where,

QB=quantity sold

PB=price per unit

PC=average unit price of competitor’s product

Y=income per household

AB=advertising expenditure

           

            R2= 0.86

S.E.E=5

Standard error of coefficients in parentheses (1200) (1.5) (1.2,) (0.5) , ( 0.2)

Given, PB=$50,    PC=$45,      AB=$12,500      Y=$2,000

1. Does each independent variable have a significant effect on the sales of Fluidyne water filters?
2. Interpret the coefficient of variables that are significant?
3. Interpret the coefficient of determination(R²)
4. Determine the monthly quantity demanded sold (QB) for water filter?
5. Is the quantity demanded for water filter (QB) sensitive to its own price?
6. Is water filter a luxury or necessity?

Answer 1

(a) Given the coefficients and standard errors, the t-statistics can be calculated as the ratio of coefficients to their respective standard errors, under the individual null hypothesis that the coefficients are different from zero. In terms of significance, the coefficients of own price, competitor price and advertising expenditure are significant at 5% level of significance as their absolute t-statistics are greater than 1.96, which is the critical value at 5% level of significance. On the otherhand, income per household is not significant at 5% level.

(b) Interpretation of the significant coefficients:

If the price of water filter increases by one unit, the sales decreases by 5 units and vice versa. On the other hand, if the price of competitor product increases by one unit, its sales of water purifier increases by 2.5 units and vice versa. Similarly, if the advertising expenditure increases by ine unit, sales increases by 0.6 unit.

(c) The value of coefficient of determination is 0.86. It means that the independent variables considered in the regression explain 86% of variation collectively in the sales of water purifier.

(d) Given the values Pb = $50, Pc = $45, Y = 12500, AB = 2000 and the regression coefficients, the monthly quantity demanded can be estimated as:

2000 - 5(50) + 2.5(45) + 0.82 (12500) + 0.6(2000) = 13312.5

(e) The own price elasticity of demand shows the sensitivity of demand to its price, which can be calculated as d(Qb)/d(Pb) * (Pb/Qb), where d(Qb)/d(Pb) = - 5 from the regression results, Pb = $50 and Qb = 13312.5. Hence, own price elasticity of demand = -5(50)/13312.5 = - 0.019. Since |elasticity| = |- 0.019| = 0.019 < 1, the demand is inelastic in nature. Hence, the sales of water purifier is not sensitive to its price.

(f) In terms of luxury/necessity, we need to look at the income elasticity of demand, which can be calculated as follows. Income elasticity of demand = d(Qb)/d(Y) * (Y/Qb), where d(Qb)/d(Y) = 0.82 from the regression results, Y = 12500 and Qb = 13312.5. Hence, income elasticity of demand = 0.82(12500)/13312.5 =  0.770. Since income elasticity < 1, it is a necessity. For lucury, it should be > 1.