(a) Define cross elasticity of demand. (b) The table below shows the response of quantity demanded to changes in price for three pairs of commodities. Use t...

(a) Cross elasticity of demand measures the responsiveness of the quantity demanded of one commodity to a change in the price of another commodity. It is given by \[E_c=\dfrac{\%\ \text{change in quantity demanded of good B}}{\%\ \text{change in price of good A}}.\] A positive value indicates substitutes, a negative value indicates complements, and a value near zero indicates unrelated goods.

(b) Reading the price change of the first commodity against the quantity change of its paired commodity:

Bread (price) and Yam (quantity): \(\%\Delta P=\dfrac{20-15}{15}\times100=33.3\%\); \(\%\Delta Q=\dfrac{200-150}{150}\times100=33.3\%\); \[E_c=\dfrac{33.3}{33.3}=+1.\] The positive sign shows the two are substitutes.

Beef (price) and Fish (quantity): \(\%\Delta P=\dfrac{40-25}{25}\times100=60\%\); \(\%\Delta Q=\dfrac{3{,}000-1{,}000}{1{,}000}\times100=200\%\); \[E_c=\dfrac{200}{60}=+3.33.\] The positive value shows the two are substitutes.

Butter (price) and Margarine (quantity): \(\%\Delta P=\dfrac{50-100}{100}\times100=-50\%\); \(\%\Delta Q=\dfrac{400-250}{250}\times100=60\%\); \[E_c=\dfrac{60}{-50}=-1.2.\] The negative sign shows the two behave as complements in this data.