Total Revenue and Elasticity Thinking about how total revenue and elasticity are related
Total Revenue and Elasticity
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- 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 persepective 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,
- let's just think about in terms of
- "How many total sales will I get in a given hour?"
- Let me just write it 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. 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.
- Actually, let me just make a little table right over here.
- So if I make one column price, one column quantity,
- and then let's make one column total revenue.
- Alright, so let's look at a couple of scenarios here.
- We could actually look at some of these points that
- we already have defined. At Point A here, price is $9
- - so I'll do it in Point A's colour - price is $9,
- quantity is 2. $9 x 2 burgers.
- $9 per burger x 2 burgers per hour - your total
- revenue is going to be $18. And you can see it
- visually right over here: this height, 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 make it really clear for us - let's try Point B.
- So, at Point B, when our price is $8, and
- our quantity is 4 - 4 burgers per hour - our total
- revenue is going to be $8 x 4 which is $32 per hour.
- 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 the price. The quantity is 9. $5.50 x 9.
- 9 x 5 = $45, and then you have another $4.50, so that
- is $49.50. So, once again, it's going to be the area
- of this rectangle, the 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 - I'll do it
- in that same colour - we have $4.50, and we are
- selling 11 units. 11 x $4.50, let's see this is going
- to be $44 plus $5.50. Once again, that is $49.50.
- So, this rectangle is going to have the same
- area as that pink one that we just did for scenario C.
- Now, I'll actually just do one more down here,
- just to see what happens, because this is interesting.
- Now we've lowered the price, and it looks like
- things didn't change much. And now let's go
- and just do one more Point, actually, for
- the sake of time - Point E. And I encourage you
- to do 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 [Should be: My total revenue is $32 per hour].
- 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 total 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 plot total revenue wih respect
- to quantity. So, let's try it out.
- So this is going to be total revenue, and this axis
- right over here is going to be quantity.
- And we're once again going to be from - let's see,
- this is zero, 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 right on this axis here -
- our quantity is 2, and our total revenue is $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 our quantity is 16, our total revenue is $32.
- 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 is actually some point
- at which you can maximise your total revenue, and
- if you really tried all the points here, you'd 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 [gain] $50. So this is the maximum point
- right over there, $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 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 colour -
- 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, the, or I should say, the absolute
- - for every 1 down we move in price, we're moving 2 up in 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
- at this part of the curve. So, this part of the curve is elastic.
- Or, you could say that its price elasticity for demand is >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 the opposites happening.
- You move 1 unit down in price, you move 2 units
- to the right in quantity, but over here, price is much
- lower, so this is a much larger change, 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 changes 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 elasticity right over there.
- So, there's an interesting relationship going on.
- 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 true - 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?
- Unit elasticity you are right at this point right over here,
- and roughly, when you do a price cut, and I'm going
- to say that this is roughly true - your total revenue stays constant.
- But just right at the point, right when you're going through
- that point, that unit elasticity point. And, finally,
- when you are inelastic, when large percent changes
- in price result in not so large percent changes in quantity demanded,
- then a price change going down,
- resulted in a lower total revenue - resulted in total
- revenue going down. And this should hopefully
- make a little bit of intuitive sense, because over here,
- at 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 an 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 made
- your rectangles a little bit shorter, you weren't able
- to compensate by growing the width as much - so, you
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