Suppose the price of tea increases while the demand for coffee increases. The most plausible explanation is
Tea and coffee are substitute goods
The relationship between two goods is judged by cross elasticity of demand, \(E_{xy} = \dfrac{\Delta Q_x / Q_x}{\Delta P_y / P_y}\). It is positive for substitutes, negative for complements and zero for unrelated goods.
Step 1 — The price of tea rises, so \(\Delta P_y \gt 0\).
Step 2 — The demand for coffee rises, so \(\Delta Q_x \gt 0\), giving \(E_{xy} \gt 0\).
Step 3 — A positive cross elasticity means consumers switch from the dearer tea to coffee, which marks the two as substitute goods.
Complementary goods would show a fall in coffee demand when tea becomes dearer. Whether coffee is inferior concerns its response to income, not to the price of tea. Zero price elasticity of coffee concerns coffee’s own price and does not explain a change caused by the price of tea.
Tea and coffee are substitute goods option is correct.
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