Okay, let's talk now about income elasticity. Now, is income elasticity some kind of price elasticity? It isn't, right, so you ask well what's it going to do in a price in course. Well, we have the data right here, we just looked at price elasticity, cross price elasticity. And I think it's very easy and would be interesting for you if I explain income elasticity and it can tell you a lot about your product and how maybe the perceptions of it are changing over time. So let's just dive in and do this. The definition is virtually the same as the definition that you've seen before. Except, look at the denominator here, we don't have price there. We don't have our price, we don't have a competitor's price, we have income. And in particular, often this is, it's estimated using something called disposable income. You can often get that data from a government or some other source. And disposable income is the money people have left over after they pay things like rent and food. So that's data that's available. So if you look here, I've broken down this definition like I've broken down all the other definitions. By putting the delta Q divided by delta whatever, in this case, income out front. And that is because I can go back to our regression, remember we have disposable income in our regression model, and it's sitting there. Now it is interesting, one thing I'll point out about this estimated coefficient is it's negative. And right off the bat, one of the things we can say is that chuck is not viewed perhaps as the highest quality cut of beef. Because as people income goes up, what happens? It appears that they're buying less chuck. Maybe they're not buying beef at all, or maybe they're just buying more expensive cuts of beef, as chuck is a relatively inexpensive cut of beef. So it's negative, and it is significant, so people really do kind of move away from the cut as the income goes up. How do I calculate the income elasticity? Same way I did all the other ones, I take that coefficient on income, I plug it in here, and then I use the means of the data. That's the mean of the income data, right, and there is our Q mean that we've seen before and I calculate that as- 4.6. It means that a 10% increase in disposable income leads to a decrease in consumption of chuck by 46%. That is a pretty powerful effect, right, so, the data is pretty striking on that dimension. Now, generally here's the way these things are interpreted, if you have an elasticity that's less than zero, that's a called an inferior good. In this case it's- 4.6, it's actually let's called a substantially inferior good, that's a big negative income elasticity. Zero means it's sticky and a good example of this might be gasoline for your car. As the price, as your income goes up or income goes down. At least in the short-term it really doesn't affect how much gas you're going to consume. because you've gotta drive back and forth to work, right, you gotta buy the stuff. And you don't use a lot of extra gas if you suddenly get more money. You're probably going to spend the money on something else. Elasticity between zero and one are kind of like necessities. A lot of things you buy at the grocery store could come into this category, buy a snack product. If you have more income, maybe you buy a little bit more of that fancy cheese. You don't buy a whole lot more of the fancy cheese, but you might buy a little more, right. And a lot of products kind of fit into that category. And then elasticities greater than one are called luxuries. So Cartier think of the big luxury brands, what happens is up to a certain amount of income people just don't consume those items. And then once they get to a certain point they use, maybe a fair amount of their disposable income on those more luxurious items. So a company that's in the luxury good business would probably want to track their income elasticity over time to try to figure out, how are my perceptions changing? Am I being viewed as more of a luxury good or is my income elasticity starting to drop? What's going on there? Can I tease out any of the dynamics of the market? They would be interested in information like that. So, technically, income elasticity is not directly related to price, but it is an interesting matrix we can get from the same data, and certainly tells people in marketing good and useful things about their product.