Question

Based on the following demand equation for cotton: Q =88.83−0.34Pc suppose that the average quantity consumed, Qc, is 63.2 million bales and the average price paid, Pc, is 74.5 cents per pound. What is the own-price elasticity of demand at the means? Interpret your result.

Answer 1

To find the own-price elasticity of demand using the provided demand equation and average values, one must insert these values into the elasticity formula and calculate the responsiveness of quantity demanded to price changes.

Step-by-step explanation:

To calculate the own-price elasticity of demand at the average quantity consumed (Qc = 63.2 million bales) and the average price paid (Pc = 74.5 cents per pound), we use the provided demand equation Q = 88.83 - 0.34Pc. The formula for elasticity is (dQ/dP) * (P/Q), where dQ/dP is the derivative of Q with respect to P, which in this case is -0.34.

Applying these values:

• dQ/dP = -0.34
• P = Pc = 74.5
• Q = Qc = 63.2

We plug them into the elasticity formula to get:

Elasticity = (-0.34) * (74.5/63.2)

This would provide us with the own-price elasticity at the given averages. The interpretation of the result would tell us how sensitive the quantity demanded of cotton is to changes in its price.