Serving the Quantitative Finance Community

User avatar
Topic Author
Posts: 155
Joined: March 16th, 2004, 3:14 am

Business Advertising Problem

September 11th, 2006, 1:18 am

Recently I placed an advertisement for my business ( on a tuition specific directory ( I was given the choice of either buying a deluxe ad ($123.70/year), a standard ad ($99.00/year) or an economy ad ($49.50/year). The site also provided the following basic details about the search algorithm.[Without going into mathematical details of the algorithm, we would like to describe the way the algorithm sorts student search results in real world terms:The names of the tutors matching student search results are written on cards and placed in a deck. Each tutor on Economy membership level gets one card, on Standard level - 3 cards, and on Deluxe level - 10 cards. The deck is then shuffled, the names of the tutors are randomly chosen from the deck and presented to the user performing the search. Once the name of a tutor is displayed, other cards with the same name (if any) are removed from the deck.Thus, any tutor on Deluxe level will have 10 times more chance of being first in the search results list than a tutor on Economy level. A tutor on Standard level will have 3 times more chance of being first than a tutor on Economy level.Despite that, any tutor regardless of membership level will have a chance to be on top of search results list.]My question is, what information would I need (e.g. site traffic, advertising elasticity of demand etc) to determine if each of the individual membership levels are appropriately priced relative to the probabilities associated with each membership level?
User avatar
Posts: 6433
Joined: July 23rd, 2001, 3:46 pm

Business Advertising Problem

September 14th, 2006, 4:44 pm

In the simplest model, the price of the ads should be proportional to the number of cards. That would be the case if there were a very large number of tutors of all membership levels, the list presented to each student were short, the student chose at random from the list and you can handle any number of inquiries at a fixed profit. To determine the absolute value of the ads you need to know also the number of students who come to the site.If the first four assumptions hold, then if any ad were a good deal, the deluxe would be the best deal. Therefore if you buy a standard or economy ad, you must think at least one of the four things isn't true.Suppose, for example, there are d, s and e other tutors with deluxe, standard and economy ads and the other three assumptions are true: two tutors are presented per student, the student chooses at random and each inquiry is worth a fixed amount to you. The chance of you getting an inquiry for each student who does a search is:x / (10*d + 3*s + e + x) + 10*d*x /[(10*d + 3*s + e + x)*(10*d + 3*s + e + x - 10)] + 3*s*x/[(10*d + 3*s + e + x)*(10*d + 3*s + e + x - 3)] + e*x/[(10*d + 3*s + e + x)*(10*d + 3*s + e + x - 1)]where x is 10 if you choose deluxe, 3 if you choose standard and 1 if you choose economy. Under these assumptions, the closest I can come to making these correctly priced is if there is one deluxe and one standard ad out, in which case if the economy is fairly priced at $49.50, the standard should sell for $100.05 and the deluxe for $153.77.
User avatar
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

Business Advertising Problem

September 18th, 2006, 12:57 am

The relative values of the Deluxe, Standard, and Economy depends on the total population of tutors, the specificity of students' searches, and the predilection of students to pick the first tutor listed over the second, third, etc. If the population of tutors is very large and the students do low-specificity searches, then they will get very long lists of candidates. Under such conditions, Deluxe level tutors will dominate the first pages and the relative value of the ad will track the number of cards given (i.e., 10:3:1). If, on the other hand, there is a very small number of total tutors or the students use very specific searches, then the number of tutors returned by a search may be very small. With a small number of candidates, tutors of all ad levels will make the first page of hits and only the tendency of the student to take the top of the list will determine the relative value.You might try doing a search to see how many tutors are similar to you. If the number seems large, then spring for the deluxe level. If your searches show that you're competing with only a few tutors, then buy the economy ad. I suppose there may be a set of conditions in which the standard ad is optimal, but I'd bet it's a very small window in the parameter space.