Elasticities Of Demand And Supply Practice Test

The price elasticity of demand for a straight-line demand curve is:

lower at higher prices. higher at higher prices. 1 at all prices. the same at all prices but not 1.

Correct Answer:

higher at higher prices.

Explanation:

On a straight-line demand curve, the price elasticity of demand is not the same everywhere along the curve. It changes with price and quantity because elasticity depends on the ratio P to Q. For a linear demand like Q = a − bP, the elasticity in magnitude is |E| = |dQ/dP| × (P/Q) = b × P/(a − bP). As price rises, quantity falls, so the denominator (a − bP) shrinks while the numerator P grows. This makes the fraction P/(a − bP) increase, and thus |E| increases. Near the price where quantity nears zero, elasticity becomes very large; at the midpoint of the line, elasticity equals 1; at lower prices, elasticity is less than 1. So elasticity is higher at higher prices.

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