Price elasticity
More on Total Revenue and Elasticity Clarification on the relationship between total revenue and elasticity
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- 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:
- this is my price axis,
- that is my quantity demanded 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 quantity that is 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 Q1.
- We already know that the total revenue is the area of this rectangle right over here -
- this is the total revenue, it's just the price times the quantity.
- If I'm selling two burgers an hour 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 in this part of the curve,
- that the price elasticity of demand is greater than one (>1), so we are elastic.
- So absolute value of the elasticity of demand is greater than one,
- which means for a 1% drop in price,
- you have greater than 1% increase in quantity.
- And that comes straight out of the expression or formula for what elasticity is
- Remember, elasticity is our % change in quantity over % change in price
- So if the absolute value of this is greater than 1
- that means this quantity is going to be larger than this quantity
- So if we have a 1% drop in price, the change in our quantity is going to be greater than 1%
- And so for this point right over here, if we lower this by 1%
- we're going to increase this by more than 1%
- So any reduction in our height will be more than made up for --
- this is generally the case -- will be more than made up for by increase in our width
- So total revenue will increase
- So when price drops -- so 1% drop in price and a larger than 1% increase in quantity
- means that total revenue will go up
- Now if we go down to this part of the curve
- Let's call this P2, and let's call that quantity 2
- And this area here will be total revenue 2
- Let's call that total revenue 1 here
- Price times the quantity
- We're going to assume that
- the absolute value of our price elasticity of demand is less than 1 at this point in the curve
- And all that is a fancy way of saying that for a 1% drop in price
- we get a less than 1% increase in quantity
- So if we have a 1% drop, we're lowering the height by 1%
- but we're not getting a 1% 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
- The area will get smaller. We're reducing our height more than we're expanding our width
- So in this situation, the total revenue will go down
- Remember this is a elastic situation
- So when it is elastic, a drop in price tends to make total revenue go up
- And when it is inelastic, 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 exactly a 1% increase in quantity demanded
- And so they'll kind of trade off; you won't get a noticeable change in revenue
- The reason why I say that is that many econ textbooks will tell you that
- you don't get a change in revenue, but if you look at the detailed math --
- 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% drop in price
- goes along with a 1% increase in quantity
- but if you look at the math, -- let's call this price 3, and call this quantity 3
- right over here, so total revenue 3, which is this area right over there
- is going to be equal to price 3 times quantity 3
- Now if we decrease price by 1%
- then this will become 0.99 times our price
- And if we increase our quantity by 1%, this'll become 1.01 times our quantity
- Now, let's think about what this number here is. This is what I'm saying
- The total revenue isn't exactly unchanged
- If you multiply 0.99 times 1.01, you don't get exactly 1
- Another way to think about it, .99 times 1.01 is going to be 1% less than 1.01
- and 1% of 1.01 is slightly larger than 1
- Or another way to think about it, this value is going to be 1% larger than .99
- and 1% of .99 is less than 1
- So it's not gonna get you to 1. You can calculate it
- .99 times 1.01 is very close to 1. This is going to be equal to 0.9999
- times P3 Q3, which is 0.9999 times total revenue 3
- But it is roughly unchanged. That's the general rule of thumb
- So when you're at unit elasticity
- then a decrease in price roughly says no change in total revenue
- So I just want to make sure that this makes sense. It really just comes from these areas
- If you're reducing the height less than you're increasing the width
- obviously the area is going to increase
- or most of the case, I should actually say. That depends on where you are
- If you're compensating whatever you reduce the height perfectly with the width
- then you're not going to have a change in revenue
- And if you decrease the height by more
- if you're taking more area from the top than you're adding on the width
- then you're going to have a total decrease in total revenue
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