Question

Suppose the price elasticity of demand for heating oil is 0.1 in the short run and 0.9 in the long run. if the price of heating oil rises from $1.20 to $1.80 per gallon, the quantity of heating oil demanded will by % in the short run and by % in the long run. the change is in the long run because people can respond easily to the change in the price of heating oil.

Answer 1

The answer is given below

Step-by-step explanation:

a) In the short run, the price elasticity of demand for heating oil is 0.1. Using midpoint method, the price elasticity of demand (Ed) is given as:

`E_d=(\% \ change \ in\ quantity)/(\% \ change \ in\ price) =(\%\Delta Q)/(\%\Delta P) \\But \ \%\Delta Q=(Q_2-Q_1)/((Q_2+Q_1)/2) \ and \ \ \%\Delta P=(P_2-P_1)/((P_2+P_1)/2) \\Given\ P_1=\$1.2 ,P_2=\$1.8\\\%\Delta P=(P_2-P_1)/((P_2+P_1)/2) *100\%=(1.8-1.2)/((1.8+1.2)/2) *100\%=40%\\\\E_d=(\%\Delta Q)/(\%\Delta P)\\0.1=(\%\Delta Q)/(40\%)\\\%\Delta Q=0.1*40\%=4\%\\\%\Delta Q=4\%`

b) In the long run, the price elasticity of demand for heating oil is 0.1. Using midpoint method, the price elasticity of demand (Ed) is given as:

`E_d=(\% \ change \ in\ quantity)/(\% \ change \ in\ price) =(\%\Delta Q)/(\%\Delta P) \\But \ \%\Delta Q=(Q_2-Q_1)/((Q_2+Q_1)/2) \ and \ \ \%\Delta P=(P_2-P_1)/((P_2+P_1)/2) \\Given\ P_1=\$1.2 ,P_2=\$1.8\\\%\Delta P=(P_2-P_1)/((P_2+P_1)/2) *100\%=(1.8-1.2)/((1.8+1.2)/2) *100\%=40\%\\E_d=(\%\Delta Q)/(\%\Delta P)\\0.9=(\%\Delta Q)/(40\%)\\\%\Delta Q=0.9*40\%=36\%\\\%\Delta Q=36\%`

the quantity of heating oil demanded will by 4% in the short run and by 36% in the long run. the change is 36% in the long run because people can respond easily to the change in the price of heating oil.