In the previous video,

we introduced the concept of price-per-click and

click-through-rate. Once we know both

of these quantities, we can calculate the

average price per display. This is simply

the average amount that an advertiser pays when

a user is shown their ad. We can compute this by

multiplying the price-per-click with the click-through-rate. Let’s go through an example

to see how this works. Suppose we have 10 users who

search for “best LTE network”. Google decides to display

Verizon’s ad to all of them. We know that the

click-through-rate for Verizon and for the “best LTE network”

query is 0.2, so only two users click on the ad. Verizon must now pay

the price-per-click for each of these users. Since there were two clicks

and each click costs $25, Verizon must pay a

total of $50 to Google. If we consider how much Verizon

paid to Google on average, per user, or equivalently how

much Verizon paid per display of the ad, we just

divide the total amount of $50 for the 10

users who saw the ad. Doing this, we see that the

average price per display was $5. We could have obtained this

amount in a simpler way. In particular, as we defined

in the previous slide, this turns out to be exactly

the same as the price-per-click multiplied by the

click-through-rate. For our data then, to obtain

the average price per display we simply need to multiply

the price-per-click table and the click-through-rate

tables together. The last piece of

data that we need before we can define

our problem is we need to know how

popular the queries are. Obviously, Google does

not control how many times a search query will be

searched because the users are the ones who submit the queries. However, Google does

have an estimate of the number of

times, on average, the query will be

requested over a given day. For the example that we

have been building so far, let’s suppose that we expect

to see “4G LTE” 140 times, “largest LTE” 80 times, and

“best LTE network” 80 times, as well. We’re now ready to start

modeling this problem. The problem that we

will consider is this. How many times should Google

display each ad for each query, so as to maximize

their total revenue? In the next video,

we will formulate this as a linear

optimization problem.