More on total revenue and elasticity

I want to do one more video on total revenue and price elasticity of demand just to make sure that you the relationship between the two is an intuitive one so let's draw an arbitrary demand curve so this is my price axis price axis that is my quantity demanded axis quantity axis and let me just draw an arbitrary demand curve right over here so let's say that is my demand curve and let's pick some price and quantities on this demand curve so let's say that the price is up here let's call that p1 and then the quantity demanded let's call that let's call that q1 let's call that q1 and we already know that the total revenue is the area of the of this rectangle right over here this is the total revenue it's just the price times the quantity if I'm telling if I'm selling two burgers an hour and for nine dollars a burger I'm going to make $18 per hour that's going to be this area right over here now let's assume let's assume in this part of the curve that that the price elasticity of demand is greater than 1 so we are elastic so let me write this so the price the elasticity of demand actually I should say the absolute value of the elasticity of demand it will be actually a negative number but the absolute value of the elasticity of demand is greater than 1 which means for a for a 1 percent 1 percent drop in price drop in price you have more you have a greater than greater than 1 percent increase increase in quantity in quantity and that comes straight out of the expression or our formula for what elasticity is remember elasticity is our percent change change in quantity over a percent change change in price so if this that if the absolute value of this is greater than 1 these move in opposite directions that's why it would be negative but if we say the absolute value of this is greater than 1 that means that this quantity is going to be larger than this quantity so if we have a 1% drop in price this the change in our quantity is going to be greater than 1% and so at for this point right over here if we lower this by 1% we're going to increase this buy more we're going to increase this by more than 1% so any drop in our any reduction in our height will be more than made up for and this is generally the case will be more than made up for by an increase in our width so total revenue will increase so when price drops so 1% drop in price would a larger than 1% increase in quantity means that total revenue total revenue will go up now if we go down here if we go down to this part of the curve and let's say that this let's call this let's call that p2 and let's call that quantity to quantity 2 and then this area right over here would be total revenue to total revenue 2 let's call that total revenue 1 over their price times the quantity now what's happening over here we're going to assume that our elast are price elasticity of demand the absolute value of it over here is less than 1 so the absolute value of our price elasticity of demand is less than 1 at this point in the curve and all that is is a fancy way of saying that for 1% drop drew 1 percent drop in price 1 percent drop in price we get less than a 1% drop 1 less than a 1% drop sorry what less than a 1% increase they move in opposite directions 1 percent increase increase in quantity so we're lowering the height if we if we have a 1% drop we're lowering that by 1 percent but we're not getting a 1 percent increase in our width so the width isn't going to be increasing that much so in general this is going to result in a lowering of this area this area will get smaller we're reducing our height more than we are expanding our width so in this situation in this situation total revenue total revenue would go down and remember this is an elastic situation so when it is elastic total revenue tends to go up and when it is inelastic in a lot I want to say when it's elastic a price a drop in price tends to make total revenue go up and when it is inelastic in elastic a drop in price tends to make total revenue go down and then you could imagine right when you're at unit elasticity someplace around there a 1% drop in price will result in a exactly a 1% increase in quantity demanded and so they will kind of trade off you won't get a you won't get a noticeable change you won't get a noticeable change in your revenue and the reason why I say that the reason why I say that is that actually some many econ textbooks will tell you that you don't get a change in revenue but if you actually will do a detailed look at the mats let me write it over here so the absolute value of the price elasticity of demand at that point is 1 which tells us that a 1% 1% drop in price will or it goes along with a 1% increase in quantity but if you look at the math so if the old area so let's call this let's call this price 3 and let's call this quantity 3 right over here and so total revenue 3 total revenue 3 let me do some new color which is this area right over there is going to be equal to price 3 times quantity 3 now if we increase price by or if we decrease price by 1% then this will become 0.99 times our price and if we increase our quantity by 1% then this will become one point zero one times our quantity now let's think about what this number right over here is this is why I'm saying it's not exactly the total revenues are going to be exactly unchanged if you multiply 0.99 0.99 times one point zero one you don't get exactly one you don't get exactly one another way to think about it point nine nine times point OH one is going to be 1% less than point 1.0 1 and 1% of 1.0 1 is slightly larger than 1 or another way to think about it this value is going to be one percent larger than 0.99 and one percent larger than 1% of 0.99 is less than 1 so it's not going to get you to one and you can see it with your calculator 0.99 times one point zero one get you two very close to one so this is going to be equal to this is going to be equal to zero point nine nine nine nine times p3 q3 which is equal to zero point nine nine nine nine times total revenue three times total revenue three but it is total revenue three but it is roughly roughly it roughly unchanged so we can that's kind of the general rule of thumb so when you are at unit elasticity unit eel s tested unit elasticity then a decrease in price roughly roughly says no change no approximately no change in total revenue so I just wanted to make sure that it makes sense it really just comes from these areas if you're reducing the height by less than you're increasing the width obviously the area is going to increase if you or most of the cases I should say it depends on where you are if you are if you're kind of compensating it whatever you reduce the height you are compensating perfectly with the increase in width then you're not going to have a change in revenue and if you decrease the the height by more if you're taking more area from the top then you're adding on the width then you're going to have a total decrease in total revenue