to calculate the cross elasticity of demand between commodity W and commodity X.

Question

ScanSolve AI Tutor · Accepted Answer

The question asks to calculate the cross elasticity of demand between commodity W and commodity X.
From the table, we have the following data points:

The formula for arc cross elasticity of demand ( $XED_{X,W}$ ) is:

XED_{X,W} = \frac{\frac{Q_{X2} - Q_{X1}}{(Q_{X2} + Q_{X1})/2}}{\frac{P_{W2} - P_{W1}}{(P_{W2} + P_{W1})/2}}

Calculate the percentage change in quantity demanded of X.
Change in quantity demanded of X:
$\Delta Q_X = Q_{X2} - Q_{X1} = 300 \text{ kg} - 500 \text{ kg} = -200 \text{ kg}$
Average quantity demanded of X:
$\text{Average } Q_X = \frac{Q_{X2} + Q_{X1}}{2} = \frac{300 \text{ kg} + 500 \text{ kg}}{2} = \frac{800 \text{ kg}}{2} = 400 \text{ kg}$
Percentage change in quantity demanded of X:
$\% \Delta Q_X = \frac{-200 \text{ kg}}{400 \text{ kg}} = -0.5$
Calculate the percentage change in the price of W.
Change in price of W:
$\Delta P_W = P_{W2} - P_{W1} = \text{N}30 - \text{N}20 = \text{N}10$
Average price of W:
$\text{Average } P_W = \frac{P_{W2} + P_{W1}}{2} = \frac{\text{N}30 + \text{N}20}{2} = \frac{\text{N}50}{2} = \text{N}25$
Percentage change in price of W:
$\% \Delta P_W = \frac{\text{N}10}{\text{N}25} = 0.4$
Calculate the cross elasticity of demand.
$XED_{X,W} = \frac{\% \Delta Q_X}{\% \Delta P_W} = \frac{-0.5}{0.4}$ $XED_{X,W} = -1.25$
The cross elasticity of demand between W and X is $-1.25$ . Since the value is negative, commodities W and X are complementary goods.

To calculate the cross elasticity of demand between commodity W and commodity X.