Constant unit elasticity

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Constant unit elasticity발음듣기

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We've already talked about linear demand functions that actually have changing price elasticity as we go down the curve.발음듣기

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And we've shown the extremes.발음듣기

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We've shown things that are perfectly inelastic and things that are perfectly elastic.발음듣기

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What I want to do in this video - and it'll be a quick little video - is think about can we construct a demand curve, or at least understand what it looks like, that has a constant elasticity across the curve?발음듣기

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And just for fun, let's make it a constant elasticity of 1.발음듣기

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So it has constant unit elasticity of demand.발음듣기

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So let's think about how we can create that.발음듣기

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And hopefully, it will give us a bit more intuition on how this elasticity business even works.발음듣기

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So let's draw our axes.발음듣기

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So there you go, that is price.발음듣기

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And that right there is quantity.발음듣기

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And let me put quantity.발음듣기

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Now let's put some numbers there that'll just help us draw this demand curve that has unit elasticity at every point, at every price, in every quantity.발음듣기

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So I'm just going to put some numbers here.발음듣기

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So let's say that that right over there is 10.발음듣기

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So that's $10 or whatever we're doing.발음듣기

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And then this is 10 units per time period, 10 units per week, or 10 units per month, or whatever else.발음듣기

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Now, we want the absolute value of the elasticity of demand to be equal to 1 at all points.발음듣기

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And we're going to assume that this curve meets the law of demand, which means as price goes down, quantity demanded goes up.발음듣기

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So let's think.발음듣기

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This is going to be a downward sloping, so really we're going to say that the elasticity of demand is going to be equal to negative 1.발음듣기

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If we have a 1% decrease in price, we're going to have a 1% increase in quantity, and vice versa.발음듣기

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So let's think about it.발음듣기

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If we're up here, where the price is near $10, and maybe where the quantity is closer to $1, let's think about what a 10% movement in price would look like, a 10% movement down.발음듣기

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It would be roughly about this size.발음듣기

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A 10% movement would be roughly there.발음듣기

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And I'm just trying to get the general shape of this curve.발음듣기

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I'm not going to go into the deep mathematics or the calculus of it.발음듣기

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So that is a 10% price movement down.발음듣기

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And we also want to 10% quantity movement up.발음듣기

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But remember, our quantity is only at 1.발음듣기

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So a 10% quantity movement up would only be 10% of 1.발음듣기

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So if we're moving 10% in price downwards, this is a 10% upwards in quantity.발음듣기

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So our curve up here would look something like this.발음듣기

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It would actually have to be quite steep.발음듣기

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Now let's think about what the curve would look over here.발음듣기

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Once again, we want 10% for both of them, because we want the price elasticity of demand to be 1 throughout the curve.발음듣기

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So if we go over here, a 10% movement in price - so let's say we're down here, where price is close to 1 - a 10% movement in price is going to be very small.발음듣기

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So a 10% movement in price is going to be like that.발음듣기

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It's going to be roughly a tenth of a movement.발음듣기

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So that's a 10% movement in price.발음듣기

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But a 10% movement in quantity demanded over here, it's going to be much larger.발음듣기

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It's going to look something like that, because the quantity is approaching 10, so 10% of that is about 1 unit just like that.발음듣기

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So at this point in the graph, it would look something like this.발음듣기

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It would flatten out a good bit, just like that.발음듣기

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And then when the price and the quantity is about the same, so let's say this point right over here, where the price and the quantity is about the same - so let's say that that is 2, this is 3, this is 2, this is 3 right over here - your percent movements are going to be the same.발음듣기

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But since the price and quantity are the same, the absolute movements are also going to be the same.발음듣기

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So at that point, our curve should look something like that.발음듣기

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It should have a slope of 1.발음듣기

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And so if you connect the dots, you get the general shape of a demand curve that has a price elasticity of demand at negative 1 throughout the curve, or whose absolute value of the price elasticity of demand is 1.발음듣기

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So let's just do that.발음듣기

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So the curve would look something like - I'll just draw a dotted line; it's easier to do - so it'll look something like that.발음듣기

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It'll keep getting steeper as we get the quantity closer to 0, and it'll keep flattening out as the quantity grows and grows and grows.발음듣기

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Anyway, hopefully you found that interesting.발음듣기

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