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Price elasticity of supply determinants

Explore what makes supply more or less elastic in this video.

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  • blobby green style avatar for user hcasper595
    The market demand curve for good Y is given as Y=8Py*-2 , where Y is market quantity demanded for good Y and Y P is price of good Y in dollar.
    what is the value of own price elasticity demand for good y
    (0 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user daniella
      To find the own price elasticity of demand (PED) for good Y, we can use the following formula:

      PED = change in quantity demanded/change in price

      Given the demand function for good Y is Y = 8Py^-2, we need to differentiate the demand function with respect to price (P_y) to find the derivative which will give us the rate of change of quantity demanded with respect to price, which is essentially the percentage change.

      Taking the derivative with respect to Py:

      dY/dPy = 16Py^-3

      Now, to find the percentage change in quantity demanded and price, we use:

      % change in quantity demanded = (dy/y) x 100
      % change in price = (dPy/Py) x 100

      Now, let's find the value of PED:

      PED = -16Py^-3 / 8Py^-2
      PED = (-16/8)Py^-3+2
      PED = -2Py^-1

      So, the own price elasticity of demand for good Y is -2Py^-1
      (1 vote)

Video transcript

- [Instructor] In several videos we have talked already about the price elasticity of supply. In this video, we're going to dig a little bit deeper, and we're going to think about what factors might make a supply curve, or supply schedule, or portions of it, to be more elastic or inelastic. So we'll think about the determinants of the price elasticity of supply. And to help us think about that, I've drawn two different supply curves. And so, remember, price elasticity is thinking about how sensitive is the quantity, or the price elasticity of supply, we're thinking about how sensitive is a percent change in quantity supplied to a percent change in price. So, for example, if we were to go from this price, to this price, it's a pretty significant percent change in price. It looks like about a 50% change in price. But if we look at this supply curve, where it's getting pretty vertical, it's not quite vertical yet, but it's getting pretty steep, our percent change in quantity is going from here to here, so it's not as dramatic. So these parts of the curve that are relatively steep, as they're approaching more and more vertical, we would consider those to be relatively inelastic. If you had a perfectly vertical, or portions of this curve that were perfectly vertical, at those portions you would say that you have perfect inelasticity. And then, if on the other hand, in this example, if we were to change our price from say, this to this, that's a relatively small percent change in price, but notice it could result in a fairly large percent change in quantity supplied, we're going from this to this. So, when we are more horizontal, or the flatter our supply curve is, that would be, we're talking about relative elasticity, or we are much more elastic here than we are there. So, elastic. And if you were perfectly horizontal, then you would have a perfectly elastic part of our supply curve, or our supply schedule. Now what would cause, what are the factors that would make us get more inelastic, or more elastic? Well let's think about a situation, let's say we are in this world. Let's say we are in the world, starting at this price, where this is our quantity. Imagine that the factories that produce whatever good we're talking about here, they're already at full production. And to make more production would take a lot of time, or there might not even be the resources to have more production. Maybe the people who make the factories are doing other things right now. Maybe you have other resources, other inputs, into your production that there's just not more of. Maybe oil, as much oil in the world is being produced, and that's an input into our production. And so in that world, even if the price is, even if the price goes dramatically up, people might want to produce a lot more quantity, but they just can't, they don't have more factories, or they don't more inputs to produce them. So, the quantity might go up a little bit, they might run the factory, they might run the factories in overtime, or the people who are trained to do that skill, and maybe there just aren't a lot more people who can do that skill, they're working overtime, but they can't produce a lot more. And so, a couple of things that we can glean from that example is, this inelasticity of supply tends to happen in the short run, when in the short run, you're not gonna be able to build a new factory in the short run. You're going to be able to find more sources of let's say oil in the short run. You're not going to be able to train a lot more people to produce a lot more, in the short run. So if we're talking about a supply curve that's describing more of a short run time frame, then it tends to be more inelastic, and then the other thing is, and we already talked about this is, there's not available resources, or not a lot of available resources, not a lot of available, available resources. Once again, your factory's operating full-out. You've hired everyone who can produce that thing you're producing, or some natural resource that you need as an input, to make this good, well, the world is already producing as much as they could. Well, let's then go to the other situation. What would cause elasticity? Well, this could be a world where in the long run, it might be easier to get more resources. In the long run, you can build more factories. You can find and hire and train more people. So, the longer run that we are talking about, that tends to lead to a more elastic supply curve, in the longer run, and then another notion here, is that you aren't capacity constrained, or maybe I should say, aren't resource constrained. Aren't resource constrained. So, maybe our factories are running nowhere near capacity. So even a small increase of price, where it's like, "Hey, I'm gonna just make my factories run "a little bit more." Or there might be a lot of people who can help produce who have the skills to do, to produce that good, so as the price goes up, more and more people are going to start producing that good. Or it might be using resources where there's no shortage of it. Where, as the price even goes up incrementally, people will just use more and more of that resource to provide more and more of that good.