Here, I'll draw all those same axes, price and quantity.

A firm has a choice.

Firm says, if I offer a price,

let's just pick a price out.

We'll, call this price P_0.

At this price, the firm says,

"Why don't we try this price?"

They do these things, and they do these marketing tricks.

They know that along that price line,

consumers are actually going to be distributed

along something that looks kind of like the normal distribution.

The normal distribution says that,

they don't know for sure how many people were going to buy the product.

They say, if we quote a price here,

I know that it's very unlikely that only this amount will be sold.

It's very unlikely that this amount will be sold.

As we get over here,

we see that the amount that we think is the best estimate of what

will be sold would be the peak of that normal distribution.

Now, it's up to the firm to sort of tinker around with prices and say,

well, at different possible prices,

how much will people actually want to purchase?

They know that if they lower the price to say P_1,

that along that possible price,

the distribution, consumer purchases will probably look something like this.

Again, it's still a normal distribution.

It's just that the mean of that distribution has shifted to the right.

Along that price vector,

there's a small probability that this amount will be purchased.

There's a higher probability that this amount will be purchased and as well out here,

but the most likely amount is right here,

the center of that distribution.

Not to belabor the point too much longer,

but we could do one more possible price.

At this lower price,

the distribution for consumers would look something like this.

Again, for us, the mean of that,

that is the most likely amount of sales, would be right here.

So, from the first of view,

for different possible prices,

they can discover this sort of this locus of

expected sales points and this we would call our demand curve.

Now, how did they find these?

Well, they hire statisticians,

they have people who go out and look at the data, they look at their sales,

they do gimmick tricks,

they'll mail out certain discount cards.

So, some people will have a discount of $0.20,

another one with a discount of two dollars,

and another one with a discount of four dollars,

and then get an idea of how much does a lower price really spur more purchases?

They'll get an idea of how they can actually figure out what this distribution

of consumption patterns is all about for the prices for their product.

So, what we see then,

is that we'll end up with a product that we'll call a market demand curve.

The market demand curve is basically

the summation of all of the demands of the individual consumers.

Some people really like this product.

As price goes up, they don't cut back their purchases very much at all.

Some people, the product's okay.

If the price goes up, they'll cut back a little more.

From the point of view of the firm,

the firm aggregates those by thinking about

those probability functions and understanding for different possible prices,

what's their expected amount of sales.

For us, that locus of those expectation points gives

us what we estimate to be the demand curve.

In this course, we'll use these expected value operators,

understanding that actually there's a little uncertainty there.

The firm doesn't know for sure how many people

are going buy it if they quote a price of P_0

but they have a pretty good idea of the distribution to consumers and

say the expected sales at that price P_0.

They know the expected sales if they raise the price to some higher level P_1.

They know the expected sales, they've put it down.

We are gathering those expected amounts and putting them

down as this representation of what we expect the demand curve to be.