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 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 with first simplicity let's just think of s really just how much total sales will I get in a given hour so let me just write it over here total revenue total revenue well if 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 is going to be is going to be the quantity pretty straightforward if I sell if I sell 10 things at $5 I am going to 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's just let me just make a little table right over here so if I'll make one column price one column quantity and then let's make one column total revenue total total revenue all right so let's look at a couple of scenarios here well we could actually look at some of these points that we already have defined at Point a over here price is nine so I'll do the point a is color price is nine quantity is to nine dollars times two burgers nine dollars per burger times two burgers per hour your total revenue is going to be eighteen and you can see it visually right over here this height this height right over here is nine and this width right over here is two and your total revenue is going to be the area 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 well let me do a couple of them just to just to really make it clear for us let's try point B so at point B when our price is 8 and our quantity is 4 for burgers per hour a 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 this 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 let's go to a point that I haven't actually graphed here actually well let me just actually I'll go through all the points just for fun so now at Point C we have 550 550 is the price the quantity is 9 9 times 5 59 times 5 is $45 and then you have another 450 so that is 49 49 50 so once again it's going to be the area 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 we're increasing the total revenue let's see if this keeps happening so if we go to point D if we go to point D L do in that same color we have 450 450 and we are selling 11 units so 11 times 450 to see this going to be 44 plus 550 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 do 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 actually actually let's do the last one F just to feel a sense of completion so one dollar 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 at 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 let's just plot total revenue with respect to quantity so let's try it out so if you 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 but we don't have price on this axis right over here but what our quantity is 2 our total revenue is 18 so it's going to be something like something like there then when our quantity is 4 our total revenue is 32 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 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 11 it's also at that same point right over there and then when our quantity is 16 our total revenue is 32 16 so 32 right there and then finally when our quantity is 18 our total revenue is 18 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 to this is this is a concave downwards parabola right over here and you can see there was actually some point in which you can maximize your total revenue and if you really try it all the points here you would see that that maximum point is if you tried if you tried this point right over here right at price v and quantity 10 at price v and quantity 10 in that hour you would sell $50 so this is the maximum point right over there 50 $50 now the whole reason why I'm talking 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 in the demand curve but there is an interesting relationship in that very first video and we actually use 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 at this part of the curve and orange for any change when you do a change in your 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 the the or I should say the absolute for every one down we move in price we're moving to up in quantity but that one 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 elastic elastic or you could say that it's price elasticity for demand is greater than one you get larger changes in percent quantity for a given change in percent price now these parts of the curve down here these parts of the curve down here we saw is the opposites happening you move one down one unit down in price you move two units to the right and quantity but over here price is much lower so this is a much larger chain 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 in elastic 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 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 - there's a couple of boundary cases on the map that make it a little bit you can't make it absolutely true but while we are elastic while we are elastic at the elastic points of our demand curve a decrease in price price goes down total revenue was going up 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 then when you are at unit unit elasticity unit elasticity what was happening and unit elasticity you are right at this point right over here right at this point over here and roughly and roughly when you do a price cut and I'm going to say this is roughly true your total revenue total revenue stays constant constant but just right at that point right when you're going through that unit elasticity point and then finally when you are in elastic inelastic when large percent changes in price result in not so large percent changes in quantity demanded then a price change going down then a price change going down 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 over here at this point if given percent change in 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 percent quantity so when you when you made your when you made your rectangles a little bit shorter you didn't you weren't able to compensate by growing the width as much and so you actually had a lower area lower total revenue