Question

3. Suppose the price elasticity of demand for heating oil is 0.2 in the short run and 0.7 in the long run.

a. If the price of heating oil rises from $1.80 to $2.20 per gallon, what happens to the quantity of heating oil demanded in the short run? In the long run? (Use the midpoint method in your calculations.)
b. Why might this elasticity depend on the time horizon?

Answer 1

Price elasticity of demand (PED) for heating oil in short run = 0.2

Price elasticity of demand (PED) for heating oil in long run = 0.7

Midpoint formula for elasticity of demand is written as:

$PED = \frac{\%\triangle Quantity Demanded}{\%\triangle Price}$

Where;

$\%\triangle Q_d = \frac{Q_2 -Q_1}{\frac{Q_1+Q_2}{2}}$

$\%\triangle P = \frac{P_2 -P_1}{\frac{P_1+P_2}{2}}$

a.

If the price of heating oil rises from $1.80 to $2.20 per gallon then quantity of heating oil demanded in the short run will be:

$PED = \frac{\%\triangle Q_d}{\frac{P_2 -P_1}{\frac{P_1+P_2}{2}}}$

$0.2= \frac{\%\triangle Q_d}{\frac{2.20 -1.80}{\frac{1.80+2.20}{2}}}$

$0.2= \frac{\%\triangle Q_d}{\frac{0.4}{2}}$

$\%\triangle Q_d = (0.2\times0.4) \div2=0.04$

This means the quantity of heating oil demanded will decrease by 4% in short run.

Now, the impact of increase in price on quantity of heating oil demanded in the long run will be:

$0.7= \frac{\%\triangle Q_d}{\frac{2.20 -1.80}{\frac{1.80+2.20}{2}}}$

$0.7= \frac{\%\triangle Q_d}{\frac{0.4}{2}}$

$\%\triangle Q_d = (0.7\times0.4) \div2=0.14$

It is determined that the quantity of heating oil demanded will decrease by 14% in long run.

b.

Elasticity depends on the time horizon because there is a possibility of substitutes for heating oil in the market. It is likely that people might be prefer other source of heating oil in future in case of rise in its prices.