So, price elasticity is one kind of pricing metric that can be used to

help optimize prices.

But there are other types of price elasticities

that can tell us very useful things, and I want to turn to one of them right now, and

that's the cross-price elasticity.

Now, the definition will look a little bit familiar, but it has a bit of a twist.

So, if we look at the definition,

it's percent change in quantity divided by the percent change in price.

The difference here is that this percent change in price is not my price.

It's the price of, maybe, one of my competitors, or

another product that competes in the same space that I do.

So, cross-price elasticity is fundamentally asking the question,

when somebody else changes their price, what happens to my demand?

You might imagine that is a very interesting thing that

managers often want to know.

And it can tell us a lot of things about the nature of competition,

in whatever market we're working in.

So, I've rewritten the answer.

Percentage change of quantity divided by percentage change in price.

Remember that that can be rewritten as just delta Q over delta P,

that's the change, multiplied by P over Q.

Looks very similar to price elasticities.

Now, where do we get this information?

We're going to go back to that regression output that we were looking at earlier.

But this time, instead of grabbing the estimated coefficient on the chuck price,

which is our known price, right?

We're selling chuck.

We are going to look at the estimated coefficient for

chicken, because it is possible that as the price of chicken varies,

that our demand could be affected by that.

Now, recall something that I said earlier, that in this regression,

I'm showing you real data here, and the chicken price is not quite significant.

So, you would normally want to see something like 1.96 or greater for

that t-statistic.

But I'm going to use this information anyway,

because I want to show you how to calculate a cross-price elasticity.

So, I take that estimated coefficient, and then I use the definition.

So, that estimated coefficient is what?

That is the delta Q divided by delta P, right?

The change in chuck quantity relative to the price change in chicken.

So, I use that coefficient, then I multiply it by P over Q, okay?

And those come from where?

Remember, those come from the mean of the data.

Okay, so, this is the price of chicken and our chuck quantity.

We get the means of the data, and then we can put that in, and

what comes out the other end of that is -0.84.

So what does negative mean in a cross-price elasticity?

It means that when their price goes up, what do you think happens to our demand?

When their price goes up, our quantity goes down.

And that means that somehow, they're almost compliments to each other,

which may be a little counterintuitive to you.

But think about that.

For some products, let's say the price of Parmesan cheese went up.

What might happen to the sales of spaghetti sauce?