Question

You are asked to work on a “stop smoking” campaign in an attempt to reduce health insurance costs. The organization is willing to spend $100,000 on the campaign, divided between broadcast advertising (TV and radio) and newspaper advertising. They ask you to advise them on the optimal allocation of this money.

1. The first task is to find estimates of how many people stop smoking in response to various combinations of broadcast and newspaper advertising. What information will this data provide?
2. Next, you find out the per unit price of 2 types of advertising. Why?
3. Describe how you would use the information gathered in a and b to determine the optimal allocation of the $100,000.
4. Illustrate the optimal allocation on a graph.

Answer 1

a) This date will firstly tell us whether the different campaign methods affect smoker's quitting significantly or not. If it does then whether there is significant difference in smoker's quitting due to different campaigns. All these can be done by performing a regression and a 2 sample t test respectively.

After this, we can try and find out by how much one campaign is having more impact on smoker's quitting as compared to other campaign. This will be useful to allocate funds to the different campaign in order to increase the impact on smokers so that they quit smoking. Thus will give us a functional form useful for our optimization problem.

b) Per unit price of two types of advertising is required because we have a budget constraint. The fund given to us is fixed which is $100,000. So, in order to set up our optimization problem it is required to know the per unit cost of each advertising methods.

c) Considering a utility function as the utility of advertising on the smoker's quitting we can maximize this utility function subject to our budget constraint.

d)

The utility function gives a indifference curve which is drawn by pencil. This is convex in nature. The bold linear line is the budget constraint. The point of intersection of these two lines gives the OPTIMAL ALLOCATION.

X axis and Y axis contains quantity of funds allocated to each of the two advertising campaigns.

PS: APOLOGIES FOR THE BAD LOOKING GRAPH in question d. If there are more doubts, please comment. I will like to clarify.