I want to talk a little bit now about price elasticity. And the reason we're covering this particular metric in the course is because it's a very common metric to describe how sensitive a company's, or even an industry's, quantity sold is to price. And that the standard way it's used. As a metric to say okay if we change price how sensitive is our own demand to that price change? If you've taken a course in microeconomics, you almost certainly at some point saw someone describing what a price elasticity is. Now, we are going to really look at three different types of price elasticities over these next few videos. The first that I'm going to talk about now is the standard price elasticity metric, but we're also going to look at cross-price elasticities, and something called an income elasticity. Now, a price elasticity is just, is defined as the percentage change in quantity divided by the percentage change in price. And if you just look at that definitionally, you'll see, well that's a measure of how sensitive quantity demand is to a change in price. And the price that goes in the denominator there is my price, the price that I'm charging for my particular product service. A cross price elasticity is different in a fairly fundamental way. And that is that we're measuring the sensitivity of my demand to changes in someone else's price, okay? So how does the quantity that I sell react to the price changes that maybe one of my competitors, or maybe another complimentary product may be setting in the marketplace. That's going to be a very useful metric as well. And finally I'm going to look at income elasticity. Income elasticity is a measure of how sensitive quantity demand is for my product to changes in the disposable income, sometimes is income sometimes is disposable income of my consumer target population. If you don't know what the term disposable income is, it's not overly important but generally it's defined as the amount of money that people have left over after paying basic necessities like food and rent. Okay. That becomes interesting because depending on the particular income elasticity, that gives me an idea of whether my product is really perceived as a luxury good, a necessity, more of basic kind of item. And by looking at how that changes over time, it can also tell me something about how the market perceives the positioning of my product. So to do this I'm going to use some data, and I'm not going to put the data up on the screen. Although I can describe the data to you, it's some data on beef and chicken sales. So beef and chicken, it was collected by the US Department of Agriculture. It's monthly data, and it contains information on how much beef was sold. The average price of the beef, how much chicken is sold, the average price of the chicken and it also has disposable income in it as well. So which they got from another source but included in the database. Now this is the point that if you haven't reviewed the regression material in the course recently and perhaps you don't feel like have a good grasp on that, you may want to re-review it at this point because I'm going to make use of what's called a multiple regression in order to calculate the price elasticities and this is a very common way of doing. Okay, so there is my linear model. Don't let that scare anybody! If that scares you, just go back and look at the regression video, and I think in a few minutes you'd be comfortable with this again. And what's in this regression model? Well, it's generally what's called a demand model, so you have how much beef is sold over here? That's what's called my dependent variable. And then I have a series of independent variables, these are the things that we believe might impact beef sales. That's why they are in the model. The first one X1 here is defined as my own price and that's pretty straight forward, right? What I'm charging for the beef that affects how much I'm selling of the beef. The second is the price of a related good and in this case, chicken. We might believe that the price of chicken might impact beef sales one way or the other, that's why it's in the model. And then we have a measure of disposable income. So, what's that going to answer is when people have more money, do they buy more or less of this particular cut of beef? And finally what's called a trend variable. And that was covered in the regression model, it's simply a very simple time trend variable. Just to account for the fact that it might be the case that beef sales are growing or shrinking over time for reasons unrelated to price. So we need to put that in there. So now we are going to perform a linear regression. We are going to estimate the model. Okay and we did some initial analysis on the beef prices and this is a chuck roast in particular. And we did some initial analysis with the chicken to make sure that the data was suitable to put it into the model. Here is the estimated model. The model is reproduced down below, but what you see are the estimated coefficients. Those beta coefficients, those coefficients measure how sensitive the dependent variable, in this case the quantity sold of this chuck, this beef, Is to the particular variables in the model. That's the way you interpret it. So there it is for chuck, and it's negative and you would expect it to be negative. That just means the demand curve is downward sloping. The higher price I charge, or the less people buy. I've got a chicken price, also a negative coefficient and income and trend. And if I look over here on the right hand side, if you recall from the regression video, that we can look at the t statistics to determine what is significant and what isn't. And chuck price is significant. Income is significant. And trend is significant. Chicken price is kind of marginally significant, not overly significant. Okay. Now, what can we do with this? We can calculate the price elasticities, cross price elasticities, and income elasticities. In this video I'm just going to look at the price elasticities and then I can also take that information and use the estimated model as a demand function. Okay, more about that later. And then I could also compute the optimal price of this cut of beef under different scenarios. But right now, I mean we're going to do all this, but right now I'm going to focus on price elasticity. So remember the definition of price elasticity. Percentage change in quantity divided by percentage change in price. It can be written as that. Delta just means change in Q divided by Q, that's the percentage change. Delta P divided by P, and rearranging that gives us this definition right here. What's nice about that is I know this, the change in Q divided by the change in P. And I know that, because that is coming from the regression model, that's the estimated coefficient, this -50.16. I can then use that estimated coefficient and multiply that by P over Q right? From the definition, and I get the P and the Q out of the means of the data. So the mean price and the mean quantity of chuck sales. If I compute the mean across all the data the average for chuck for any given month, it's 107.54 and that's an index number that relates to the number of pounds that are sold and the average price is $2.47 per pound. So I can then put that back into the model -50.16, insert those means. That gives me -1.15 and how is that interpreted? At its most basic level the way that's interpreted is a 10% change in price will be associated with approximately 11.5% change in quantity. Or you could say a 1% change in price will lead to a 1.15% change in quantity. That's the basic definition and the way to calculate an elasticity. And I will talk more about the interpretation of this and what else you can do with it, at a later time.