An increase in income from $30,000 to $40,000 leads to a decrease in the quantity demanded from 50 to 40.The income elasticity of demand is:
A) 7/9
B) -7/9
C) 1
D) 9/7
E) -9/7

Question

Quizplus · Accepted Answer

The income elasticity of demand (Ey) is calculated as the percentage change in quantity demanded divided by the percentage change in income:
Ey = (%ΔQd / %ΔIncome)

Starting with the initial values:
Qd1 = 50
I1 = $30,000

And the final values:
Qd2 = 40
I2 = $40,000

The percentage changes can be calculated as:
%ΔQd = ((Qd2 - Qd1)/((Qd1+Qd2)/2)) * 100 = -20/45 * 100 = -44.44%
%ΔIncome = ((I2 - I1)/((I1+I2)/2)) * 100 = 100/35000 * 100 = 0.29%

Plugging these values into the formula for Ey:
Ey = (%ΔQd / %ΔIncome) = -44.44% / 0.29% = -153.63

Since the elasticity is negative, we know that these goods are inferior, meaning as income increases, people will buy less of them. Therefore, choices A, C, D, and E are all incorrect. The only choice left is B, which corresponds to the negative value we calculated.

An Increase in Income from $30,000 to $40,000 Leads to a Decrease