What we would like to do is calculate something called willingness to pay.

And willingness to pay is how much,

at most, a consumer is willing to pay for the next item we're selling them.

So, imagine the following sales process, the consumer comes and

I'm going to tell them, the first item costs $10.70 and

the second item is going to cost $9 and the third item is going to cost $7.

Will the consumer still willing to buy all of these products?

On the table on the right-hand side, you can see this calculation in quantities

of half items, and generally, you can do that for whole number of items,

half items, quarter items, etc., depending on the type of the product.

What we can see on the right-hand side is that for a different quantity of items

sold, I'm calculating the price of the next item to be sold.

For example, if I already sold one item for the next half item,

the consumer will be willing to pay between $10.14 to $9.59,

which is basically the prices on the demand curve.

And then, the prices, let's say, of the next half item between three items, so

3.5 items is going to be $7.92 to a price of $7.37.

We can take these numbers and try to calculate an average

price the consumer will be willing to pay for this additional half item.

The way to do that is to calculate the surface below the demand curve or

the graph, because basically, it gives us kind of the average price

that the consumer will be willing to pay for each fractional part of the item.

So, lets take a look at two examples.

If I never sold any item to the consumer, I know that for

the first fractional item, the consumer is willing to pay a price of $11.26, and

when the consumer reaches half an item,

they will be willing to pay at most $10.70 for this additional fraction.

And if we do this average price, which is basically the trapezoid

surface below the curve, we will get a willingness to pay of $5.49.

We can do this same analysis for items between three and three and a half Items.

And we will see that for a quantity between three and three and

a half items, the willingness to pay will be $3.82.

Now, we know how much a consumer is willing to pay for each additional item,

the question is what is the profit we're making?

In order to understand the profit,

we need to look at the cost as well, which is the fourth column on the table, and

compare it to the willingness to pay which is the third column on the table.

If we do the calculation,

basically we will take the willingness to pay minus the cost.

And we'll get the profit we will make for

each additional half item we're selling to the consumer.

So, for the first half item, we will get $4.49.

For the second half item, we'll get $4.29, and then,

that means for that one first item, that is first half plus the second half,

we will get a profit of $4.49 plus $4.29.

Now, if we're looking how much we will make for

the fourth item we're selling, which means between three to four items,

then we will be getting the willingness to pay between 3 to 3.5.

The profit is 2.82, and

the profit between 3.5 and 4, and the profit is 2.54.

And that sum will be the profit for the fourth item that we're selling.

What we can do is we can calculate the total profit we will be making for

each bundle, or each quantity of products we will be selling.

So, we can do it for up to one item, up to two items, up to three items, etc.

And all the way going down to up to nine items.

And what you will notice is that at the ninth half item at the end,

actually it's the 18th half item, but

it's the ninth item we're selling, the profit is becoming negative.

That is the willingness to pay of the consumer

is less than the cost it is costing us to actually produce the product.

It means that it's not worthwhile for me, and I'm not making a profit from sending

an additional item to the consumer, and I would probably like to stop.

So, how can we use all of this to increase our profit?

What we can do is we can sell something called a bundle.

And a bundle is basically a take it or leave it offer to the consumer.

In a bundle, we're telling this consumer, you can buy this quantity of

items at this fixed price, or you can get nothing, and it's your choice.