(a) Define cross elasticity of demand. (b) The table below shows the response of quantity...

Explanation

(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 y

or

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

changeQX xPY=50x15=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

iiiLet 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