Question

Assume that the price and income elasticities of demand for luxury cars are E_P = –0.52 and E_Y = 3.2 respectively. In the coming year, car prices are expected to decrease by 1.66 percent and income increases by 10.4 percent. Based on this information, sales of cars are expected to increase by_____%.

Answer 1

The price elasticity is $E_P = \frac{\% \Delta Q}{\% \Delta P}$ , ie the percentage change in quantity for a unit percent increase in price. We have $\frac{\% \Delta Q}{-1.66} = - 0.52$ or $\% \Delta Q = - 0.52 * (-1.66)$ or $\% \Delta Q_P = 0.8632$ , meaning that for the given decrease in price, the quantity would increase by 0.8632%.

The income elasticity is
0ܠ Ev= %AY
, ie the percentage change in quantity for a unit percent increase in income. We have $\frac{\% \Delta Q}{10.4} = 3.2$ or $\% \Delta Q = 3.2*10.4$ or $\% \Delta Q_I = 33.28$ , meaning that for the given increase in income, the quantity would increase by 33.28%.

The total change in sales of cars would be $\% \Delta Q_P + \% \Delta Q_I = 0.8632 + 33.28$ or $\% \Delta Q_P + \% \Delta Q_I = \underline{34.1432} \; \%$ .