Background Info In paid - What is the cost per registration

Background Info In paid search, for a given search word, the ads for multiple companies may be displayed Ads shown in higher positions on the page result in a greater number of clicks Companies pay a certain $ amount each time a customer clicks on their ad A higher $ per click amount paid by a company gives the company a higher position on the page "Impressions" are driven by the number of searches users make -- it is identically the same as the instances that an online advertisement is displayed The number of impressions is driven by the number of searches made by people --and thus is the same regardless of what position we are in A "Click" is an instance of someone clicking on an advertisement Only a fraction of impressions results in clicks An "tration" is an instance of someone signing up to become a customer Only a fraction of clicks results in registrations

Scenario You are currently in position 2 of a paid search term, the click-through rate (customer clicks per impression) is 1% and the cost per click is $1.50 You can get into position 1 by paying $2.50 per click. In position 1, you expect a click-though rate of 1.5% In position 3 you would pay $0.50 cost per click, and have a click-though rate of 0.5% Conversion rate (registrations per click) once someone clicks is 10% in all 3 positions Our total Revenue per registration (before search costs) is $30 Our goal is to maximize the Total $ profit

Questions

A) What is the cost per registration in position 2?

B) What is the cost per registration in position 1?

C) Which of the 3 positions do you want to be in to maximize total profit?

D) At what click through rate in position 1 are you indifferent between positions 1 and 2?

E) What is the cost per registration of the registrations you gain by moving from position 3 to position 2

Please show all your analysis, and specify any assumptions you make.