Question

If the price of leeks falls by $2 per pound, then the demand for leeks will rise by 10 pounds. Therefore we can conclude that the demand for leeks is elastic.

Answer 1

Elasticity of demand can be defined as the percent change in quantity due to the percentage change in price of the good or service. It can be determined using the following formula

$\large E = \frac{\% \triangle Q}{\% \triangle P}$

Given, price of the leeks fall by $ 2 per pound then the quantity demanded increases by 10 pounds.

Let us assume the price of the leek was $ 10 per pound and the quantity demanded was 100 pounds.

After the decrease in price the quantity demanded is 110 pounds and price is $ 8 per pound. We can determine the price elasticity using the mid point method

$\LARGE E = \frac{\frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2}}}{\frac{P_2-P_1}{\frac{P_2+P_1}{2}}}$

$\large \implies E = \frac{(Q_2-Q_1)(P_2+P_1)}{(Q_2+Q_1)(P_2-P_1)}$

$\large \implies E = \frac{(110-100)(8+10)}{(110+100)(8-10)}$

$\large \implies E = \frac{(10)(18)}{(210)(-2)}$

$\large \implies E = \frac{180}{-420}= - 0.4286 \ Inelastic (\because <1)$

Since the price elasticity of demand is less than 1 therefore the price elasticity is inelastic.

Now assume when before the change in price P1 = $ 10

Q1 = 20 pounds

P2 = $8 and Q2 = 30

$\large \implies E = \frac{(30-20)(8+10)}{(30+20)(8-10)}$

$\large \implies E = \frac{(10)(18)}{(50)(-2)}$

$\large \implies E = \frac{180}{-100} = - 1.8\ Elastic (\because > 1)$

Now in this case it is elastic. In previous case it was inelastic.

We cannot conclude on the basis of magnitude of change in price and quantity because it depends on the percent change in quantity and price of the good.

Percent change in quantity and percent change in price determines the elasticity of demand that is whether it will be elastic,inelastic or unitary elastic. Without this we cannot conclude that whether it is elastic or inelastic.

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