Total revenue and elasticity

So we're going back to our little burger stand where we had our demand curve in terms of burgers per hour. And now, I want to think about something from the perspective of our burger stand. And think about, at any given point on this demand curve, how much revenue would we get per hour. And when I talk about revenue, for simplicity, let's just think that's really just how much total sales will I get in a given hour. So let me just write over here total revenue. Well, the total revenue is going to be how much I get per burger times the number of burgers I get. So the amount that I get per burger is price. So it's going to be equal to price. And then the total number of burgers in that hour is going to be the quantity. Pretty straightforward. If I sell 10 things at $5, I am going to get $50 of revenue, $50 of sales in that hour. Now, let's think about what the total revenue will look like at different points along this curve right over here. And actually, let me just make a table right over here. So I'll make one column price, one column quantity. And then let's make one column total revenue. So let's look at a couple scenarios here. Well, we could actually look at some of these points that we already have defined. At point A over here, price is 9. So I'll do it in point A's color. Prices is 9. Quantity is 2. $9 times 2 burgers, $9 per burger times 2 burgers per hour. Your total revenue is going to be $18. And you can see it visually right over here. This height right over here is 9. And this width right over here is 2. And your total revenue is going to be the area of this rectangle. Because the height is the price. And the width is the quantity. So that total revenue is the area right over there. Now, let's go to point-- let me do a couple of them just to really make it clear for us. Let's try to point B. So at point B when our price is 8 and our quantity is 4, 4 per hour. Our total revenue is going to be 8 times 4 which is $32 per hour. And once again, you can see that visually. The height here is 8. And the width here-- so the height of this rectangle is 8. And the width is 4. The total revenue is going to be the area. It's going to be the height times the width just like that. Now, let's go to a point that I haven't actually graphed here. Actually, let me just-- actually, I'll go through all the points just for fun. So now at point C, we have 5.50. 5.50 is a price. The quantity is 9. 9 times 5.50. 9 times 5 is $45. And you have another 4.50. So that is 49.50. So once again, it's going to be the area of this rectangle. Area of that rectangle right over there. So you might already be noticing something interesting. As we lower the price, at least in this part of our demand curve, as we lower the price, we are actually increasing not just the quantity were increasing the total revenue. Let's see if this keeps happening. So if we go to point D, I'll do it in that same color. We have 4.50. And we are selling 11 units. So 11 times 4.50. Let's see, this is going to be 44 plus 5.50. Once again, that is 49.50. So that this rectangle is going to have the same area as that pink one that we just did for scenario C. And I'll actually just do one more down here, just to see what happens. Because this is interesting. Now we lower the price. And it looks like things didn't change much. And now, let's go-- let's just do one more point actually for the sake of time. Point E. And I encourage you to try other ones. Try F on your own. Point E, my price is $2 per burger. My quantity is 16 burgers per hour. I sell a total of 32 burgers. Now actually, let's just do the last one, F, just to feel a sense of completion. So $1 per burger. I sell 18 burgers per hour. My total revenue, when you multiply them, is $18 per hour. And once again, that's the area of this rectangle, this short and fat rectangle right over here. And E was the area-- the total revenue in E was the area of that right over there. And you could graph these just to get a sense of how total revenue actually changes with respect to price or quantity. Lets plot the total revenue with respect to quantity. So let's try it out. So if you-- let me plot it out. So this is going to be total revenue. And this axis right over here is going to be quantity. And we're going to, once again, go from-- let's see. This is 0. This is 5. This is 10. This is 15. And this is 20 right over here. And then total revenue. Let's see, it gets as high-- it gets pretty close to 50. So let's go. This is 10 20, 30, 40, and 50. So that's 50, 40, 30, 20, and 10. So when our quantity is 2, and our price is 9. Well, we don't have price on this axis right over here. But when our quantity is 2, our total revenues 18. So it's going to be something like there. Then, when our quantity is 4, our total revenue is 32. Right about there. Then, when our quantity is 9, our total revenue is almost 50. So right over there. And then, when it's 11, it's also at that same point right over there. And then, when we are quantity is 16, our total revenues 32. 16. So 32. Right there. And then finally, when our quantity is 18, our total revenue is 18. And what you see is that it's plotting out a curve that looks like this. And if you remember some of your algebra 2, this is a concave downwards parabola right over here. And you can see there was actually some point at which you could maximize your total revenue. And if you really tried all the points here, you would see that maximum point is if you tried this point right over here, right at price 5 and quantity 10. At price 5 and quantity 10, in that hour, you would sell $50. So this is the maximum point right over there $50. Now, the whole reason why I'm talk think about this. I could have talked about this independently of any discussion of elasticity just to see how total revenue relates to price and quantity at different points on the demand curve. But there is an interesting relationship. In that very first video, and we actually used this exact demand curve for it. When we explored elasticity, we saw that up here at this part of the curve-- let me do this in a different color. At this point of the curve in orange for any change-- when you do a change in your price since the prices are pretty high, that is a much lower percent change in price than the impact that you get on quantity. Because over here, although they look like they're close. Or I should say the absolute. For every 1 that down we move in price, we're moving 2 up quantity. But that 1 down in price is a very small percentage of price because our prices are high here. And it's a very large percentage of quantity right over here. So you get huge changes in percent quantity for very small changes in price in this part of the curve. So this part of the curve is elastic. Or you could say that its price elasticity for demand is greater than 1. You get larger changes in percent quantity for a given change in percent price. Now, these parts of the curve down here, we saw is the opposite's happening. You move 1 down, 1 unit down in price, you move 2 units to the right in quantity. But over here, price is a much lower. So this is a much larger percentage change in price. And this is a much smaller percentage change in quantity. So you get large percentage changes in price for small percentage change in quantity. That means that here, you are relatively inelastic. And then right over here, right at this point, right in this region, right over here, we saw that we had unit-- we were unit elastic right over there. So there's an interesting relationship going on. While we were, so while we were elastic, this part right over here, when we lowered price in this region. While we were elastic, when we lowered price, we got increases in revenue. So let me write this down. And this is generally, too, there's a couple of boundary cases on the math that make it a little bit, you can't make it absolutely true. But while we are elastic, at the elastic points of our demand curve, a decrease in price. Price goes down. Total revenue was going up. You do a price cut on this part of the demand curve, you get more revenue. Then, when you are at unit elasticity, what was happening? At unit elasticity, you were right at this point right over here. Right at this point over here. And roughly, when you do a price cut-- and I'm going to say this is roughly true-- your total revenue stays constant. But just right at that point, right when you're going through that unit elasticity point. And then finally, when you are inelastic when a large percent changes in price result and not so large percent change is in quantity demanded, then a price change going down resulted in lower total revenue. Resulted in total revenue going down. And this should, hopefully, make a little bit of intuitive sense. Because over here, this point, if given percent change in price, you were getting a larger percent change in quantity. So the percent in price went down. Your percent in quantity grew even more. So you made up any decrease in height with a increase in width. So your area increased. Down here, your decrease in percent price wasn't made up for a decrease in quantity. So when you made your rectangles little bit shorter, you didn't, we weren't able to compensate by growing the width as much. And so you actually had a lower area, lower total revenue.