Video transcript
So we're going back toour little burger stand where we had our demand curvein terms of burgers per hour. And now, I want tothink about something from the perspectiveof our burger stand. And think about,at any given point on this demand curve, how muchrevenue would we get per hour. And when I talk about revenue,for simplicity, let's just think that's really justhow much total sales will I get in a given hour. So let me just writeover here total revenue. Well, the totalrevenue is going to be how much I get per burger timesthe number of burgers I get. So the amount that Iget per burger is price. So it's going tobe equal to price. And then the total numberof burgers in that hour is going to be the quantity. Pretty straightforward. If I sell 10 thingsat $5, I am going to get $50 of revenue,$50 of sales in that hour. Now, let's think aboutwhat the total revenue will look like at differentpoints along this curve right over here. And actually, let me justmake a table right over here. So I'll make one columnprice, one column quantity. And then let's make onecolumn total revenue. So let's look at acouple scenarios here. Well, we could actuallylook at some of these points that we already have defined. At point A overhere, price is 9. So I'll do it inpoint A's color. Prices is 9. Quantity is 2. $9 times2 burgers, $9 per burger times 2 burgers per hour. Your total revenueis going to be $18. And you can see itvisually right over here. This height rightover here is 9. And this width rightover here is 2. And your totalrevenue 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 isthe area right over there. Now, let's go to point--let me do a couple of them just to really makeit clear for us. Let's try to pointB. So at point B when our price is 8 and ourquantity is 4, 4 per hour. Our total revenue isgoing to be 8 times 4 which is $32 per hour. And once again, youcan see that visually. The height here is 8. And the width here-- so theheight of this rectangle is 8. And the width is 4. The total revenue isgoing to be the area. It's going to be the heighttimes the width just like that. Now, let's go to a point that Ihaven't actually graphed here. Actually, let mejust-- actually, I'll go through all thepoints 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 tobe the area of this rectangle. Area of that rectangleright over there. So you might already benoticing something interesting. As we lower the price, at leastin this part of our demand curve, as we lower theprice, we are actually increasing not justthe quantity were increasing the total revenue. Let's see if thiskeeps happening. So if we go to point D, I'lldo 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 goingto be 44 plus 5.50. Once again, that is 49.50. So that this rectangle isgoing to have the same area as that pink one that wejust did for scenario C. And I'll actually justdo one more down here, just to see what happens. Because this is interesting. Now we lower the price. And it looks like thingsdidn't change much. And now, let's go-- let'sjust do one more point actually for the sake of time. Point E. And I encourageyou to try other ones. Try F on your own. Point E, my priceis $2 per burger. My quantity is 16burgers per hour. I sell a total of 32 burgers. Now actually, let'sjust do the last one, F, just to feel asense of completion. So $1 per burger. I sell 18 burgers per hour. My total revenue, when youmultiply them, is $18 per hour. And once again, that's thearea of this rectangle, this short and fatrectangle right over here. And E was the area--the total revenue in E was the area of thatright over there. And you could graphthese just to get a sense of how totalrevenue actually changes with respectto price or quantity. Lets plot the total revenuewith respect to quantity. So let's try it out. So if you-- let me plot it out. So this is going tobe total revenue. And this axis right overhere is going to be quantity. And we're going to, onceagain, 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 is2, and our price is 9. Well, we don't have price onthis axis right over here. But when our quantity is2, our total revenues 18. So it's going to besomething like there. Then, when our quantity is4, 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, whenit's 11, it's also at that same pointright over there. And then, when we are quantityis 16, our total revenues 32. 16. So 32. Right there. And then finally, whenour quantity is 18, our total revenue is 18. And what you see isthat it's plotting out a curve that looks like this. And if you remembersome of your algebra 2, this is a concave downwardsparabola right over here. And you can seethere was actually some point at which you couldmaximize your total revenue. And if you really triedall the points here, you would see thatmaximum point is if you tried this pointright over here, right at price 5 and quantity 10. At price 5 and quantity 10, inthat hour, you would sell $50. So this is the maximumpoint right over there $50. Now, the whole reason whyI'm talk think about this. I could have talked about thisindependently of any discussion of elasticity just to see howtotal revenue relates to price and quantity at differentpoints on the demand curve. But there is aninteresting relationship. In that very firstvideo, and we actually used this exactdemand curve for it. When we exploredelasticity, we saw that up here at thispart of the curve-- let me do this ina different color. At this point of the curve inorange for any change-- when you do a change in your pricesince the prices are pretty high, that is a muchlower percent change in price than the impactthat you get on quantity. Because over here, althoughthey look like they're close. Or I should say the absolute. For every 1 that downwe move in price, we're moving 2 up quantity. But that 1 down in price is avery small percentage of price because our pricesare high here. And it's a very large percentageof quantity right over here. So you get huge changesin percent quantity for very small changes in pricein this part of the curve. So this part of thecurve is elastic. Or you could say that itsprice elasticity for demand is greater than 1. You get larger changesin percent quantity for a given changein percent price. Now, these parts of thecurve down here, we saw is the opposite's happening. You move 1 down, 1unit down in price, you move 2 units tothe right in quantity. But over here, priceis a much lower. So this is a much largerpercentage change in price. And this is a much smallerpercentage change in quantity. So you get largepercentage changes in price for small percentagechange in quantity. That means that here, youare relatively inelastic. And then right over here,right at this point, right in this region,right over here, we saw that wehad unit-- we were unit elastic right over there. So there's an interestingrelationship going on. While we were, sowhile we were elastic, this part right overhere, 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 boundarycases on the math that make it a little bit, youcan't make it absolutely true. But while we are elastic, atthe elastic points of our demand curve, a decrease in price. Price goes down. Total revenue was going up. You do a price cut on thispart of the demand curve, you get more revenue. Then, when you are at unitelasticity, what was happening? At unit elasticity, you wereright at this point right over here. Right at this point over here. And roughly, whenyou do a price cut-- and I'm going to saythis is roughly true-- your total revenuestays constant. But just right atthat point, right when you're going throughthat unit elasticity point. And then finally, when you areinelastic when a large percent changes in price result andnot so large percent change is in quantity demanded, thena price change going down resulted in lower total revenue. Resulted in totalrevenue going down. And this should, hopefully,make a little bit of intuitive sense. Because over here, thispoint, if given percent change in price, you weregetting a larger percent change in quantity. So the percent inprice went down. Your percent inquantity grew even more. So you made up anydecrease in height with a increase in width. So your area increased. Down here, your decreasein percent price wasn't made up for adecrease in quantity. So when you made yourrectangles little bit shorter, you didn't, we weren'table to compensate by growing the width as much. And so you actually had a lowerarea, lower total revenue.
