The demand for a good is $x = 20 - 2p$, where $x$ is the quantity demanded at price $p$ (in ₹). Find the elasticity of demand at $p = 4$ and at $p = 6$, and state whether demand is elastic or inelastic at each price.

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Accepted Answer

**Set up.** Demand as a function of price is $x = 20 - 2p$, so
$$\frac{dx}{dp} = -2.$$

The elasticity of demand is
$$\eta = -\frac{p}{x}\cdot\frac{dx}{dp} = -\frac{p}{x}\,(-2) = \frac{2p}{x} = \frac{2p}{20 - 2p}.$$

**At $p = 4$:** demand $x = 20 - 2(4) = 12$, so
$$\eta = \frac{2(4)}{12} = \frac{8}{12} = \frac{2}{3} \approx 0.67.$$
Since $\eta < 1$, demand is **inelastic** at $p = 4$ — a change in price causes a proportionally smaller change in quantity.

**At $p = 6$:** demand $x = 20 - 2(6) = 8$, so
$$\eta = \frac{2(6)}{8} = \frac{12}{8} = 1.5.$$
Since $\eta > 1$, demand is **elastic** at $p = 6$ — a change in price causes a proportionally larger change in quantity. …

Q.The demand for a good is $x = 20 - 2p$ , where $x$ is the quantity demanded at price $p$ (in ₹). Find the elasticity of demand at $p = 4$ and at $p = 6$ , and state whether demand is elastic or inelastic at each price.

Concept understanding — Elasticity of Demand

Q.The demand for a good is x=20−2px = 20 - 2px=20−2p, where xxx is the quantity demanded at price ppp (in ₹). Find the elasticity of demand at p=4p = 4p=4 and at p=6p = 6p=6, and state whether demand is elastic or inelastic at each price.

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Q.The demand for a good is $x = 20 - 2p$ , where $x$ is the quantity demanded at price $p$ (in ₹). Find the elasticity of demand at $p = 4$ and at $p = 6$ , and state whether demand is elastic or inelastic at each price.

Unlock everything free for 14 days