Answer:
The answer is given below
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:
[tex]E_d=\frac{\% \ change \ in\ quantity}{\% \ change \ in\ price} =\frac{\%\Delta Q}{\%\Delta P} \\But \ \%\Delta Q=\frac{Q_2-Q_1}{(Q_2+Q_1)/2} \ and \ \ \%\Delta P=\frac{P_2-P_1}{(P_2+P_1)/2} \\Given\ P_1=\$1.2 ,P_2=\$1.8\\\%\Delta P=\frac{P_2-P_1}{(P_2+P_1)/2} *100\%=\frac{1.8-1.2}{(1.8+1.2)/2} *100\%=40%\\\\E_d=\frac{\%\Delta Q}{\%\Delta P}\\0.1=\frac{\%\Delta Q}{40\%}\\\%\Delta Q=0.1*40\%=4\%\\\%\Delta Q=4\%[/tex]
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:
[tex]E_d=\frac{\% \ change \ in\ quantity}{\% \ change \ in\ price} =\frac{\%\Delta Q}{\%\Delta P} \\But \ \%\Delta Q=\frac{Q_2-Q_1}{(Q_2+Q_1)/2} \ and \ \ \%\Delta P=\frac{P_2-P_1}{(P_2+P_1)/2} \\Given\ P_1=\$1.2 ,P_2=\$1.8\\\%\Delta P=\frac{P_2-P_1}{(P_2+P_1)/2} *100\%=\frac{1.8-1.2}{(1.8+1.2)/2} *100\%=40\%\\E_d=\frac{\%\Delta Q}{\%\Delta P}\\0.9=\frac{\%\Delta Q}{40\%}\\\%\Delta Q=0.9*40\%=36\%\\\%\Delta Q=36\%[/tex]
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.
