Question

You are interested in estimating the effect of advertising expenditures on sales of a particular item. You propose that the relationship between sales (measured by monthly sales revenue in a given city in 1000s of GBP), price (in GBP), and advertising expenditures advert (measured by monthly expenditures, also in 1000s of GBP) can be expressed by the following model:

sales = β0 + β1price + β2advert + β3advert2 + u
Based on a sample of 75 observations, you estimate this model by OLS. The equation below gives the estimated

coefficients and standard errors in parentheses:

sales = 110 − 7.64 price + 12.2 advert − 2.77 advert . (6.8) (1.05) (3.56) (.941)\

4. (e) How would you express the estimated effect of an increase in advertising expenditure if the current expenditure is already £2,000p.m.? Interpret this estimated effect.

5. (f) What level of advertising expenditure does this model suggest is optimal? (I.e. when does £1 advertising lead to £1 in sales at the margin?, assuming all other costs are sunk)

2

Answer 1

e. d(sales)/d(advert) = 12.2 - 2.77(2advert) (I think it should be advert² in the estimated eqation wirh beta₃)

= 12.2 - 2.77(2)(2) (when advert is 2000 and note that advert is measured in = 1.12 ,000)

This implies that when advertisement expenditure increases by 1 GBP sales increases on average by 1.12 GBP when existing advertisement expenditure is 2000 GBP

f. Optimal advertisement expenditure is given by the condition d(sales)/d(advert) = 1 i.e.

12.2 - 2.77(2advert) = 1

advert = 12.2/5.54 = 2.20 or 2200 GBP