Chapter 18: Problem 6

A 5 percent increase in the price of sugar causes the quantity demanded to fall by 15 pereent. The demand for sugar is (101) a) perfectly clastic d) inclastic b) elastic e) perfectly inelastic c) unit elastic

Short Answer

Expert verified

The demand for sugar is elastic, as the calculated price elasticity of demand (PED) is -3, and the absolute value of -3 is greater than 1 (\( |PED| > 1 \)). The correct answer is (b) elastic.

Step by step solution

Understand the Price Elasticity of Demand formula

The formula for price elasticity of demand (PED) is: \[ PED = \frac{\% \, change \, in \, quantity \, demanded}{\% \, change \, in \, price} \] A positive PED value indicates normal goods, while a negative value indicates inferior goods.

Plug in the given percentages

In the given problem, the price of sugar increases by 5% and the quantity demanded falls by 15%. Plug these values into the PED formula: \[ PED = \frac{-15\%}{5\%} \]

Calculate PED

Divide -15% by 5% to find the value of the price elasticity of demand: \[ PED = -3 \]

Determine the category of elasticity

Based on the PED value, we can now determine the category of elasticity for sugar: - If PED = 0, the demand is perfectly inelastic. - If 0 < |PED| < 1, the demand is inelastic. - If |PED| = 1, the demand is unit elastic. - If |PED| > 1, the demand is elastic. - If |PED| = ∞, the demand is perfectly elastic. Our calculated PED is -3, which has an absolute value greater than 1. Therefore, the demand for sugar is elastic. So, the correct answer is (b) elastic.

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