Final answer:
The quantity demanded of bananas decreased by 50% when the price doubled from $1 to $2, and this indicates that the demand for bananas is inelastic with an elasticity of -0.5.
Step-by-step explanation:
When the price of bananas increased from $1 to $2 a pound due to rain ruining the crop in Central America, and the total revenue remained unchanged, we can determine the percentage change in quantity demanded and the elasticity of demand for bananas. If growers sold fewer bananas at the higher price but maintained the same total revenue, this indicates that the demand for bananas is inelastic.
To calculate the percentage change in quantity demanded, we can use the formula for elasticity:
Elasticity (E) = (% Change in Quantity Demanded) / (% Change in Price).
In this situation, Price rises from $1 to $2, which is a 100% increase. Assuming constant revenue, if the price doubles, the quantity must have halved for revenue (Price x Quantity) to remain the same. Thus, the percentage change in quantity demanded is -50%. The negative sign indicates a reduction in quantity demanded.
Substituting these values into the elasticity formula gives us E = (-50%) / (100%), which simplifies to -0.5. Since the absolute value of elasticity is less than 1, the demand is characterized as inelastic, meaning the quantity demanded is relatively unresponsive to price changes.