Question

One of the leading washer and dryer manufactures has estimated the following demand equation based on the data from its 47 branch offices and dealerships across the country:

Q = 12,000 - 20P + 120A + 15Pc - 100Ac + 80I - 20Pd

(64000 (9) (80) (7) (64) (52) (9)

R² = 0.72 F = 20.15

The variables and their assumed values are

Q= Quantity

P = Price of basic model = 500

A = Advertising expenditures = 50

Pc = Average price of the competitors product = 600

Ac = Competitor's advertising expenditures = 30

I = per capita income = 75

Pd = price of the dryer = 600

a. Compute the elasticities for each variable. On this basis, discuss the relative impact that each variable has on the demand. What implications do these results have for the firm’s marketing and pricing policies?

b.   How concerned the company should be about the impact of a recession on its

      sales? Explain.

3. Do you think the firm should cut its price to increase market share? Explain.
4. Conduct a t-test for the statistical significance of each variable. Discuss the results of the t-tests in light of the policy implications mentione
5. What proportion of the variation in sales is explained by the independent variables in the equation? How confident are you about this answer? Explain

Answer 1

A)Q = 12,000 - 20P + 120A + 15Pc - 100Ac + 80I - 20Pd

dQ/dP=-20

Price Elasticity=(dQ/dP)(P/Q)=-20*(500/Q)=-10000/Q

Price has a negative or inverse relationship with quantity. More is the price less is the quantity demanded.

Advertisement Elasticity=(dQ/dA)(A/Q)=120*(50/Q)=6000/Q

Advertisement has a positive effect on demand i.e. with more expenditure on advertisements, there is more quantity demanded.

Pc elesticity=(dQ/dPc)(Pc/Q)=15*(600/Q)=9000/Q

The relation between quantity and competitors price is positive

Ac elesticity=(dQ/dAc)(Ac/Q)=-100(30/Q)=-300/Q

More the competitor spends on advertising, lesser is the quantity demanded.

I elasticity=(dQ/dI)(I/Q)=80*(75/Q)=6000/Q

More the per capita income more is the quantity demanded.

Pd elasticity=(dQ/dPd)(Pd/Q)=-20(600/Q)=-12000/Q

Inverse relationship. More is the price lesser is the quantity demanded.

B) The impact of a recession will be shown in the coefficients of per capita income. We found from the elasticity that more the per capita income more is the quantity demanded. i.e with more money in their pockets consumers will be able to buy the dryer. A recession will hit the per capita income which will reflect in the model.

C)The firm should not cut its price to increase its market share.Spending more on advertising than competitors, the company will reach more number of consumers at the same price.

D) t stat=coefficients/SE

Q = 12,000 - 20P + 120A + 15Pc - 100Ac + 80I - 20Pd

(64000 (9) (80) (7) (64)   (52) (9)

t stat .01875 2.22 1.5 2.1 1.56 1.53 2.22