Question

One of the leading television providers has estimated the following demand equation after analyzing 36 regional markets:

  Q =   + 25,000 – 45P + 20A + 25Pc - 30Ac + 110 I

   (12000) (20.2) (14)   (9)      (48)       (50)                     

          R^{2   =} 0.86           F = 28.52

          The variables and their assumed values are

          Q = Quantity

          P = Price of the basic Model = 1200 (dollars)

          A = Advertising Expenditures = 90 (thousand dollars)

Pc = Average price of the competitor’s product = 1400 (dollars)

Ac = competitor’s advertising expenditures = 80 (thousand dollars)

  I = per capita income = 60 (thousand dollars)

1. 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, pricing, and production policies?
2. What would be the effect of a 6 unit increase in the competitor’s advertising expenditures?
3. What would be the change in your advertising expenditures to offset your competitor’s strategy?
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 mentioned.
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 conducting an F-test.

Answer 1

Answer:-

Given That:-

One of the leading TV producers has estimated the following demand equation after analyzing 36 regional markets:

Q =   + 25,000 – 45P + 20A + 25 - 30+ 110 I

            (12000)  (20.2)  (14)    (9)      (48)       (50)

R2   = 0.86         F = 28.52

The variables and their assumed values are:

Q = Quantity

P = Price of the basic Model = 1200 (dollars)

A = Advertising Expenditures = 90 (thousand dollars)

= Average price of the competitor’s product = 1400 (dollars)

= competitor’s advertising expenditures = 80 (thousand dollars)

I = per capita income = 60 (thousand dollars)

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, pricing, and production policies?

Quantity is not clear from above. Assuming quantity is 12000 (In case the value is different, you can change it to the right value and use the same approach) as given below the estimating equation.

Price elasticity of quantity demanded =  

= -45 * (1200/12000)

= -4.5 (-45 is slope value for price)

Similarly, the advertising exp.of quantity demanded = 20*(20000/12000)= 33.33

the average price of the competitor’s product elasticity of quantity demanded = 25*(1400/12000) = 2.91

the competitor’s advertising expenditures elasticity of quantity demanded = -30*(80000/12000) = -200

the per capita income elasticity of quantity demanded = 110*(60000/12000) = 550

Per capita income has the highest positive impact on the demand for refrigerators and competitor’s advertising expenditures have the highest negative impact on the demand for refrigerators. Based on the results, any firm would most likely produce more in those markets where per capita income is higher and a firm has to make high expenditure on advertising in those markets where competition is very high.

b. What would be the effect of a 6 unit increase in the competitor’s advertising expenditures?

A 6 unit increase in competitor’s advertising expenditures would reduce the demand of refrigerators by -6*30=180 units.

c. What would be the change in your advertising expenditures to offset your competitor’s strategy?

Change in advertising expenditures to offset the competitor’s strategy would be to increase own adv. expenditure by 9 units (20*9 = 180 units)

d. Conduct a t-test for the statistical significance of each variable. Discuss the results of the t-tests in light of the policy implications mentioned.

the t-test = (coefficient value/std. error of the coefficient); assuming value in the parenthesis is standard error of variables -

For P, t-test value is = -45/20.2 = 2.22

For A, t-test value is = 20/4 = 5

For Pc, t-test value is = 25/9 = 2.77

For Ac, t-test value is = -30/48 = -0.625

For I, t-test value is = 110/50 = 2.2

Since the critical value of the t-test at a 5% level of significance is 1.96, all variables except Ac is significant. This result indicates that changes in P, A, PC and I would lead to significant changes in quantity demanded and hence producers should take into account these variables while taking production decisions.

e. What proportion of the variation in sales is explained by the independent variables in the equation? How confident are you about this answer?  Explain conducting an F-test.

86% variation is explained by the independent variables as given by the R-square value of the estimation. F test providies the joint significance of all independent variables. F-statistics suggest variables are jointly significant.

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