Mathematical relationship between elasticity and total revenue

Total revenue and elasticity (video) | Khan Academy

mathematical relationship between elasticity and total revenue

Is the relationship between elasticity of demand and total revenue always true? What is the relationship between total expenditure and price elasticity of. In economics, the total revenue test is a means for determining whether demand is elastic or Mathematical explanation[edit]. The mathematical link between them comes from the formula of the price elasticity of demand: E d = − ((Q 2 − Q 1). What you'll learn to do: explain the relationship between a firm's price elasticity of demand and total revenue. Price elasticity of demand describes how changes.

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, for simplicity, let's just think that's really just how much total sales will I get in a given hour. So let me just write 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. So 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.

Now, let's think about what the total revenue will look like at different points along this curve right over here.

The Relationship Between Price Elasticity & Total Revenue |

And actually, let me just make a table right over here. So I'll make one column price, one column quantity. And then let's make one column total revenue. So let's look at a couple scenarios here.

Well, we could actually look at some of these points that we already have defined. At point A over here, price is 9. So I'll do it in point A's color. And you can see it visually right over here.

The Relationship Between Price Elasticity & Total Revenue

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.

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And the width is the quantity. So that total revenue is the area right over there.

mathematical relationship between elasticity and total revenue

Now, let's go to point-- let me do a couple of them just to really make it clear for us. Let's try to point B. So at point B when our price is 8 and our quantity is 4, 4 per hour. And 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. The quantity is 9. And you have another 4. So that is So once again, it's going to be the area of this rectangle. 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 were 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 color.

  • Total revenue and elasticity
  • Total revenue test

And we are selling 11 units. So 11 times 4. Let's see, this is going to be 44 plus 5. Once again, that is So that this rectangle is going to have the same area as that pink one that we just did for scenario C. And I'll actually just do one more down here, just to see what happens.

Relationship between elasticity and total revenue

Because this is interesting. Now we lower the price. And it looks like things didn't change much. And now, let's go-- let's just do one more point actually for the sake of time. And I encourage you to try other ones. Try F on your own. My quantity is 16 burgers per hour.

Total revenue test - Wikipedia

I sell a total of 32 burgers. Now actually, let's just do the last one, F, just to feel a sense of completion. I sell 18 burgers per hour. And once again, that's the area of this rectangle, this short and fat rectangle right over here.

mathematical relationship between elasticity and total revenue

And E was the area-- the total revenue in 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. Lets plot the total revenue with respect to quantity. So let's try it out. So if you-- let me plot it out.

mathematical relationship between elasticity and total revenue

So this is going to be total revenue. And this axis right over here is going to be quantity. And we're going to, once again, go from-- let's see. The price for oatmeal goes up, and consumers buy less of the product. They may start buying other cereal products, or they might switch to the grocery store's generic brand of oatmeal.

Factors That Affect Elasticity The factors that affect the price elasticity of any product include: As in the case of rising prices for oatmeal, consumers can shift their purchases to similar products if they are readily available.

Coca-Cola and Pepsi are products that can be easily substituted for each other when prices change. This is an example of elastic demand. If the alternatives are limited, the demand is less elastic. Necessities are products that people must have regardless of the price. Everyone has to drink water, so if the water company raises prices, people continue to consume and pay for it.

Luxuries are optional; they aren't necessary to live. Large-screen HDTVs are nice to have, but if the prices go up, consumers can put off buying them. Share of the consumer's income: Products that consume a high proportion of a family's income are sensitive to price increases.

A car is a good example. Increases in car prices can cause a family to delay purchasing a new car. They keep their old car longer and make the necessary repairs. However, if a grocery store increases the price of toothpicks, consumers still buy them because the price isn't a big piece of their income. Short-term versus long-term timing: Gasoline is an excellent example of a product that prices inelastic in the short term but elastic in the long term.

When gas prices go up, the consumer still has to buy gas to get to work. However, if gas prices stay high for the long term, consumers make changes.