Questions: 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 1.80 to 2.20 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 oil. easily to the change in the price of heating

To solve this problem, we need to calculate the percentage change in the quantity demanded of heating oil in both the short run and the long run, given the price elasticity of demand and the change in price.

1. Calculate the percentage change in price:

   The initial price of heating oil is $1.80, and the new price is $2.20. The percentage change in price is calculated as follows:

   \[ \text{Percentage change in price} = \left(\frac{\text{New Price} - \text{Old Price}}{\text{Old Price}}\right) \times 100 \]

   \[ = \left(\frac{2.20 - 1.80}{1.80}\right) \times 100 = \left(\frac{0.40}{1.80}\right) \times 100 \approx 22.22\% \]

2. Calculate the change in quantity demanded in the short run:

   The price elasticity of demand in the short run is 0.1. The formula for the percentage change in quantity demanded is:

   \[ \text{Percentage change in quantity demanded} = \text{Price elasticity of demand} \times \text{Percentage change in price} \]

   \[ = 0.1 \times 22.22\% = 2.22\% \]

   Therefore, in the short run, the quantity of heating oil demanded will decrease by approximately 2.22%.

3. Calculate the change in quantity demanded in the long run:

   The price elasticity of demand in the long run is 0.9. Using the same formula:

   \[ \text{Percentage change in quantity demanded} = 0.9 \times 22.22\% = 20.00\% \]

   Therefore, in the long run, the quantity of heating oil demanded will decrease by approximately 20.00%.

4. Explanation of the long-run change:

   The change is larger in the long run because people can respond more easily to the change in the price of heating oil. In the long run, consumers have more time to adjust their behavior, such as by improving home insulation, switching to alternative energy sources, or making other lifestyle changes that reduce their reliance on heating oil.

Summary:

• In the short run, the quantity of heating oil demanded will decrease by approximately 2.22%.
• In the long run, the quantity of heating oil demanded will decrease by approximately 20.00%.
• The change is larger in the long run because people can respond more easily to the change in the price of heating oil.