A drop in a town's average monthly incomes from $2000 to $1000 causes sales of canned meat to rise from 10 000 to 15 000 cans.The numerical value of the income elasticity of this item is:
A)-1.0
B)1.0
C)-0.6
D)0.6
E)1.67

Question

Quizplus · Accepted Answer

The income elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in income. Here, the quantity demanded of canned meat increases from 10,000 to 15,000 cans, a 50% increase. The average monthly income drops from $2000 to $1000, a 50% decrease. Thus, the income elasticity = (50% / -50%) = -1. However, the correct calculation for elasticity should consider the midpoint formula for percentage changes, which adjusts the calculation to account for the starting point. Using the midpoint formula, the percentage change in quantity demanded = [(15,000 - 10,000) / ((15,000 + 10,000)/2)] = 5,000 / 12,500 = 0.4 or 40%, and the percentage change in income = [($1000 - $2000) / (($1000 + $2000)/2)] = -$1000 / $1500 = -2/3 or -66.67%. The income elasticity of demand = 40% / -66.67% = -0.6.

A Drop in a Town's Average Monthly Incomes from $2000