The demand for good X is given by $Q_X = 400 - 4P_X + 3P_Y + 0.05I$, where $P_X$ and $P_Y$ are the prices (in £) of X and a related good Y respectively, and $I$ is consumer income in £. Currently $P_X = 20$, $P_Y = 10$ and $I = 2000$.

Calculate (i) the own‑price elasticity of demand for X, (ii) the cross‑price elasticity with respect to $P_Y$, and (iii) the income elasticity of demand for X, all evaluated at the given values. Give your answers to two decimal places.

Question

The demand for good X is given by $Q_X = 400 - 4P_X + 3P_Y + 0.05I$, where $P_X$ and $P_Y$ are the prices (in £) of X and a related good Y respectively, and $I$ is consumer income in £. Currently $P_X = 20$, $P_Y = 10$ and $I = 2000$.

Calculate (i) the own‑price elasticity of demand for X, (ii) the cross‑price elasticity with respect to $P_Y$, and (iii) the income elasticity of demand for X, all evaluated at the given values. Give your answers to two decimal places.

Accepted Answer

Own‑price elasticity ≈ -0.18 (inelastic); cross‑price elasticity ≈ 0.07 (weak substitute); income elasticity ≈ 0.22 (normal good).

Gce Model Questions Vol1 2018 Economics Question 18

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