Define elasticity | inelastic demand | elastic demand |Unit elasticity | short run v long run elasticty | Mid-point formula

Define Elasticity

E = (Change in price ÷ Price) ÷ (Change in quantity ÷ Quantity)

Where:

change in price equals (Price 1 - Price 0) and change in quantity equals (Quantity 1 - Quantity 0)

An example

Suppose we have the following:

Price            QTY
------------|---------|
$10                 6
$12                 4
$14                 2

 

Suppose we wish to know the elasticity from going from price $12 to $14.

We have the following:

Price 0 = $12
Price 1 = $14

Price = $12 (see below for which price to use)

Quantity 0 = 4
Quantity 1 = 2

Quantity = $4

(Change in price ÷ Price) = ($14 - $12)÷12 = .16666
(Change in quantity ÷ Quantity) = (4-2)/4 = .5

E = .1666 ÷ .5 = .32

 

Mid point formula

Suppose we have the following:

Price            QTY
------------|---------|
$10                 6
$12                 4
$14                 2

Students often pose the question which price or quantity do we use for the denominator? If the difference in price is not very big, it does not typically matter too much. However, one method to overcome this problem is the mid point formula.

The midpoint formula says the Price you use as the denominator is equal to (Price 1 + Price 0) ÷ 2 - it is called the mid point formula because it finds a point half way between the two prices. The same logic applies for quantity.

Using the above example, we would instead have:

Price = ($12 + $14) ÷ 2 = $13
quantity = (4+2) ÷ 2 = $3

(Change in price ÷ Price) = ($14 - $12)÷13 = .15
(Change in quantity ÷ Quantity) = (4-2)/3 = .6666

E = .15 ÷ .66 = .22

Because the change in quantity is quite drastic (it increases by 100%) the elasticity estimates differ quite drastically from above.

Inelastic demand, Elastic demand, Unit elasticity. 

Inelastic demand is when E < 1. This means that the percent change in quantity is less than the percent change in price. In this case, if a firm increases price they would be able to increase their revenue.

Elastic demand is when E > 1. This means that the percent change in quantity is larger than the percent change in price. In this case, if a firm decreases price they would be able to increase revenue.

Unit elasticity is when E = 1. This means that the percent change in quantity is the same as the percent change in price. In this case, an increase or decrease in price will result in the same revenue.

 

Is the price elasticity of supply usually larger in the short run or long run? 

Elasticity tends to be larger in the long run than the short run.

Elasticity being "larger" means that the amount firms produce responds more to a change in price.

The logic is that in in the long run, firms can increase the productive capacity (i.e install more machinery, hire more workers) and new firms can enter the market-place.

In the short run, it is difficult for firms to increase their productive capacity and it takes time for new firms to enter the market-place. Therefore, elasticity tends to be larger in the long-run compared with the short run.

 

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