Final answer:
The price elasticity of demand for pistachios when the price increases from $20 to $24 per ton, using the midpoint method, is calculated to be -0.48, indicating inelastic demand.
Step-by-step explanation:
When calculating the price elasticity of demand using the midpoint method, we examine the percentage change in quantity demanded in response to a percentage change in price to measure how sensitive the quantity demanded is to a change in price. Considering the demand for pistachios has changed from $20 to $24 per ton, let's assume the quantity demanded has decreased from 2400 to 2200 tons.
First, calculate the percentage change in price using the midpoint formula:
Percentage change in price = ((New Price - Old Price) / ((New Price + Old Price) / 2)) × 100
= ((24 - 20) / ((24 + 20) / 2)) × 100
= (4 / 22) × 100
= 18.18%
Next, calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = ((New Quantity - Old Quantity) / ((New Quantity + Old Quantity) / 2)) × 100
= ((2200 - 2400) / ((2200 + 2400) / 2)) × 100
= (-200 / 2300) × 100
= -8.70%
Finally, divide the percentage change in quantity demanded by the percentage change in price to get the elasticity of demand:
Price Elasticity of Demand = (Percentage change in quantity demanded) / (Percentage change in price)
= (-8.70%) / (18.18%)
= -0.48
This indicates that the demand curve for pistachios is inelastic in this price range, as the absolute value of the elasticity is less than one (|0.48| < 1). A price increase leads to a smaller percentage decrease in quantity demanded, which is characteristic of inelastic demand.