Now advertising doesn't guarantee success.

So if we decide to pay out for

advertising, let's model it as not guaranteeing a high level of sales,

rather it acts to increase the probability of this good outcome.

Now if you think about marketing agencies around the world, one hopes as a client if

you pay them money to do some advertising campaign for you, one hopes it works

either to increase demand, that demand generation form of advertising.

Or maybe your goal is just to perhaps raise your brand awareness.

But you hope that the advertising campaign would be successful.

Now one likes to think, most of the time, advertising campaigns are successful but

clearly not every advertising campaign did reach those particular goals either

of demand generation or increasing brand awareness.

So in our problem, let's assume that if we decide to

undertake some advertising this will increase the probability of success.

Here, a high level of sales.

So without advertising, we model the probability of success of 0.6.

Let's increase this to 0.9 in the event where we take some advertising.

Of course, if we are increasing the probability of the good outcome,

we must be decreasing the probability of the bad outcome.

So, the risk now of having a low level of sales was originally not 0.4,

but that would be revised down to 0.1.

So our question is very straight forward, to advertise or not to advertise?

This is the decision we will need to make.

Well, we just need to make it slightly more realistic and

we know that advertising typically cost some money to undertake.

Let's assume the cost of this advertising campaign will be 100,000 pounds.

And we have to pay this 100,000 pounds

regardless of whether we end up with a high or low level of sales.

Now, here we may think about sort of conventional forms of advertising maybe in

the print media, maybe online advertising, or billboards posted around a city.

Of course some advertising could be free

if we think about word of mouth advertising.

Remember, if you have a good or bad experience with some product,

you're likely to tell your friends, family, associates about that.

About whether to recommend buying the product, or to perhaps avoid it.

But here we'll stick with conventional advertising which costs money.

So with all of this, we now want to depict it in a decision tree.

So on the screen is our decision tree for this problem.

So how do we read this?

Well, you read a decision tree from left to right and

think of this as the time order in which events takes place.

You will see on the far left that we have a square depicted.

So in a decision tree, a square is going to represent a decision node.

So when you're effectively standing at that square, you have a decision to make.

Now here we've kept it very simplified and we have a binary decision,

either to advertise and hence pay for the advertising or not to advertise.

So, we see some branches stemming out from that decision node.

These branches then lead to a couple of circles.

Now these depict so-called chance nodes.

So this is where we leave things down to chance, fate, destiny,

call it what you will.

But here is something about which we have no control.

We do have control of whether we advertise or

not, this is our conscious decision at the start of the game.

But what happens there after regardless of our advertising decision

is beyond our control.

So this is the uncertainty being modeled.

And note here how the square comes before the circles.

As in, we need to make the decision at the start of the game before we know

whether these sales turn out to be high or low.

You also see the probabilities of high sales and low sales in those different

states in the world where we've chosen to advertise or not advertise, depicted.

And at the very end of these branches, one sees the payoffs that would accrue to us.

So note in the arguably the best scenario, we didn't pay for advertising but

we did get those high sales anyway.

We make 300,000 pounds profit.

Whereas if we had high sales but I had to pay advertising,

then we would have to deduct the cost of the advertising from our payoff.

And hence we would only make 200,000 pounds.

But a profit, nonetheless.

So the question, to advertise or not to advertise?

How are we going to solve this problem?

Well, here we can appeal to something called the expected monetary value.

So remember, a few weeks ago we introduced the concept of an expectation,

a probability-weighted average.

And that's how we're going to solve this decision tree.

Namely, we'll consider each possible routes,

namely the advertise and not advertise routes.

And work out the expected monetary value in each situation.

So, all we do is do probabilities times payoffs and

sum them over the respective branches along one route of our tree.

So, for example, if we decided to advertise, we have a 0.9

probability of high sales times the payoff of 200,000 pounds +

0.1 probability of low sales with the loss of 200,000 pounds.

The initial loss of 100,000 less the advertising costs.

So as an expectation, this would then give us 160,000 pounds.