Question

Rain spoils the strawberry crop, the price rises from \(\$ 4\) to \(\$ 6\) a box, and the quantity demanded decreases from 1,000 to 600 boxes a week. a. Calculate the price elasticity of demand over this price range. b. Describe the demand for strawberries.

Short answer

The price elasticity of demand is -0.8. The demand for strawberries is inelastic.

Step-by-step solution

- Identify and Write Down Initial Values

The initial price is \( P_1 = 4 \) dollars and the initial quantity demanded is \( Q_1 = 1000 \) boxes. The new price is \( P_2 = 6 \) dollars and the new quantity demanded is \( Q_2 = 600 \) boxes.

- Calculate the Percentage Change in Price

The formula for percentage change in price is: \[ \frac{P_2 - P_1}{P_1} \] Substituting the values: \[\frac{6 - 4}{4} \times 100 = 50\% \]

- Calculate the Percentage Change in Quantity Demanded

The formula for percentage change in quantity demanded is: \[ \frac{Q_2 - Q_1}{Q_1} \] Substituting the values: \[\frac{600 - 1000}{1000} \times 100 = -40\% \]

- Calculate the Price Elasticity of Demand

The price elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in price: \[ E_d = \frac{-40\%}{50\%} = -0.8 \]

- Interpret the Price Elasticity of Demand

A price elasticity of demand of -0.8 indicates that for each 1% increase in price, the quantity demanded decreases by 0.8%. Since the absolute value is less than 1, the demand for strawberries is inelastic.

- Describe the Demand for Strawberries

The inelastic demand means that consumers do not significantly reduce their quantity demanded in response to price increases. Therefore, even as the price increases, the decrease in quantity demanded is proportionally smaller.

Key concepts

Percentage Change in Price

Understanding the percentage change in price helps in the calculation of price elasticity. It shows how much the price of a product has changed over a specific period. The formula used is: \( \frac{P_2 - P_1}{P_1} \times 100 \). In the case of strawberries, the price went from 4 dollars to 6 dollars. The calculation looks like this: \( \frac{6 - 4}{4} \times 100 = 50\% \) increase in price. This means that the price of strawberries increased by 50%.

Percentage Change in Quantity Demanded

Percentage change in quantity demanded measures how much the quantity demanded of a product changes in response to a price change. The formula for this is: \( \frac{Q_2 - Q_1}{Q_1} \times 100 \). For strawberries, with the quantity demanded changing from 1,000 to 600 boxes, the calculation is: \(\frac{600 - 1000}{1000} \times 100 = -40\% \). This shows a 40% decrease in the number of boxes demanded when the price increased.

Inelastic Demand

The concept of inelastic demand indicates that the quantity demanded doesn't significantly change with price variations. In our example, the price elasticity of demand is calculated as: \( E_d = \frac{-40\%}{50\%} = -0.8 \). An absolute value less than 1 signifies inelastic demand. Hence, a price rise of 1% results in only a 0.8% decrease in quantity demanded. For strawberries, this means consumers don't drastically reduce their purchases even when prices go up. This suggests some necessities or preferences in consumption behavior that make the demand less sensitive to price changes.