Why elasticity is not constant

And we're going to assume that this curve meets the law of demand, which means as price goes down, quantity demanded goes up. So let's think. 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. So let's think about it. It would be roughly about this size. And I'm just trying to get the general shape of this curve. I'm not going to go into the deep mathematics or the calculus of it.

But remember, our quantity is only at 1. So our curve up here would look something like this. It would actually have to be quite steep. Now let's think about what the curve would look over here.

It's going to be roughly a tenth of a movement. So at this point in the graph, it would look something like this. It would flatten out a good bit, just like that. 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.

But since the price and quantity are the same, the absolute movements are also going to be the same. So at that point, our curve should look something like that. It should have a slope of 1. Economics Glossary. Economic Indicators. Fiscal Policy. Comparative Advantage. The Supply Curve. Price Elasticity. Marginal Revenue. Output Decision. Price Floor. Price Ceiling. Negative Externalities. Positive Externalities. Price Gouging. Sunk Costs. Game Theory Introduction.

Nash Equilibrium. Extensive Form. A percent change is just an absolute change i. Thus, a percent change in quantity demanded is just the absolute change in quantity demanded divided by quantity demanded.

Similarly, a percent change in price is just the absolute change in price divided by price. Simple arithmetic then tells us that price elasticity of demand is equal to the absolute change in quantity demanded divided by the absolute change in price, all times the ratio of price to quantity. The first term in that expression is just the reciprocal of the slope of the demand curve, so the price elasticity of demand is equal to the reciprocal of the slope of the demand curve times the ratio of price to quantity.

Technically, if price elasticity of demand is represented by an absolute value, then it is equal to the absolute value of the quantity defined here.

This comparison highlights the fact that it's important to specify the range of prices over which elasticity is calculated. Elasticity is not constant even when the slope of the demand curve is constant and represented by straight lines. It is possible, however, for a demand curve to have constant price elasticity of demand, but these types of demand curves will not be straight lines and will thus not have constant slopes.

Using similar logic, the price elasticity of supply is equal to the reciprocal of the slope of the supply curve times the ratio of price to quantity supplied. In this case, however, there is no complication regarding arithmetic sign, since both the slope of the supply curve and the price elasticity of supply are greater than or equal to zero.

Other elasticities, such as the income elasticity of demand, don't have straightforward relationships with the slopes of the supply and demand curves. If one were to graph the relationship between price and income with price on the vertical axis and income on the horizontal axis , however, an analogous relationship would exist between the income elasticity of demand and the slope of that graph.

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