Question

Suppose I own a store and am only interested in increasing the number of potential customers that enter my store. Further, I believe that advertising could influence how many people enter my establishment. Based on past experience with similar stores, I estimate the following relationship between the number of customers (C) and the amount of advertising (A) to be: C = 100 + 6A – A²/100.

a. Graph this function and describe (in economic terms!) the intercept and slope.

b. Does this functional form seem reasonable? Explain.

c. What level of advertising would maximize the number of customers entering my store? Show all your work and explain the economics behind the steps!

Answer 1

A. This is what the function looks like

In economic terms, it means that as amount of advertising increases, initially the customer count (C) also increases. It reaches a peak (~1000) and then the customer count starts falling even as the advertising amount increases.

B. No this doesnt seem reasonable. With increasing adertising expenditure, customers count should increase. It may, at worst, plateau. But it should never go down with increasing advertising expenditure.

C. The number of customers would be maximized where the differentiation of the given function is zero. So, lets first differentiate the given function

dC/dA=6-2A/100

=6-A/50

Equating to zero, we get

6-A/50=0

A/50=6

A=300

The count of customers would be maximized at an expendiure of 300.

As expenditure increases, the count of customers will increase till it reaches its peak of 1000 at expenditure of 300.