Splurge

You are in charge of test marketing for Splurge. It is your job to determine the soft drink preferences of people in Austin, Seattle and Washington. Each month (one turn) you may conduct a survey of consumers in one of the cities. You set the price of Splurge and then a market research consultant conducts a survey of a random sample of the city's population. The consultant will collect data on whatever variables you request: the average amount of money people spend on soft drinks, the average number of cans of Splurge they drink, or the number of cans they drink of your competitor's product, for example.

The catch is that it costs money and time to do surveys and you a limited amount of both. The cost of a survey is $1,000 times the number of variables you request. If you survey Seattle and request data on total drink expenditure and Splurge consumption, it will cost $1,000 x 2 or $2,000. Be sure not to spend more than your budget. Also, you have at most 18 months to conduct the study. (That is, the game will end after 18 turns; however you can start over an play again as many times as you want.)

Enter the price of Splurge, select the city to survey, and indicate what variables you'd like to collect. When you're happy with your settings, click the "Conduct the survey" button to see how things turn out.

The game will be most interesting if you try to imagine you're doing this for real. This is exactly the sort of decision faced by many companies every day; for example, the inspiration for this game was the introduction of the soft drink "Surge" by Coke. The cost of an ad campaign can be tens of millions of dollars or more, and there is no room for errors like producing an extra campaign when it isn't necessary, or using an ineffective campaign.

Splurge has a single competitor, brand X. People within each city have identical preferences over Splurge and brand X but preferences may not be the same across different cities. You may assume that preferences may be represented by a utility function of the form below:

U(s,x) = (s - b)^a x^1-a

In this expression, s is the quantity of Splurge consumed, x is the quantity of the competing product consumed, and a and b are constants. The budget constraint faced by consumers has the form:

Ps * s + Px * x = E

where Ps is the price of Splurge, Px is the price of brand X, and E is total expenditure on soft drinks. (You may assume that E is not affected by anything you do.)

The catch is that the numerical values of a and b are unknown and are not necessarily the same across different cities. In order to determine whether people in the three cities have identical preferences you will need to calculate each city's a and b. If the values of a and b are identical in two cities, people in those cities have identical preferences. This task is complicated, however, by the fact that total expenditure, E, and the price of brand X, Px, may also vary across cities. Be sure you don't confuse differences in budget constraints with differences in preferences.

Splurge