(a)Cross elasticity of demand is the degree of responsiveness of demand for a commodity to changes in the price of another commodity. It is the proportionate change in the quantity of goods (x) demanded over the proportionate change in the price of another goods (y) demanded.
= % change in quantity demanded of commodity x
,% change in price of commodity yor
change \(\frac{QX} {QX} \times \frac{PY} {DPY}\)
b(i) Cross elasticities of demand for bread and yam
Let X = Yam, Y = Bread
New demand = 200kg,
Initial demand = 150kg
Change in demand = 200 -150 = 50kg
Initial price = N15,
New price = N20
Change in price = 20 - 15 = N5
\(\frac{200-150} {150}\) x 100 = 33.3%
\(\frac{20 -15} {15}\) x 100 = 33.3%
or
change QX x PY = 50 x 15 = 750 = 1
Py Qx 5 150 750
(ii) Beef and fish: Let x = fish, y = Beef
Initial demand = 1000kg,
New demand = 3000kg
Change in demand = 3000 - 1000 = 2000kg
Initial price = N25
New price = N40
Change in price = N40 - N25 = N15
Cross elasticity = change in \(\frac{Qx}{Qx} \times \frac{Py}{Py}\)
\(\frac{2000}{1000} \times \frac{25}{15}\)
= \(\frac{10}{3}\) = 3.3
or
\(\frac{3000-1000} {1000}\) x 100= \(\frac{200}{60}\) = 3.3
\(\frac{40-20} {25}\) x 100
iii Let x = Margarine,
y = Butter
Initial demand = 250kg
New demand = 400kg
Change in demand = 400 - 250 = 150kg
Initial price = N100
New price = N150
Change in price = N150 - N100 = N50
Cross elasticity = \(\frac{-QX}{QX}\)
\(\frac{PY}{PY}\)
= \(\frac{150}{50} \times \frac{100}{50}\) = \(\frac{6}{5}\) = 1.2
or
\(\frac{400 - 250}{250}\) x 100
= \(\frac{60}{50}\) = 1.2
\(\frac{150 - 100}{100}\) x 100 =50