For which of the following goods will a decrease in income most likely lead to a consumer spending a lower proportion of her income on the good?
A)A good for which income elasticity of demand equals +1.5
B)A good for which income elasticity of demand equals −1.5
C)A good for which income elasticity of demand equals +0.5
Accoding to the author the answer is A
I belive is C because it has the lowest absolute value less than 1
If income elasticity lies between 0 and 1, as income increases, a consumer spends a lower proportion of her income on the product, and as income decreases, she spends a higher proportion of her income on the product. So C is wrong. If income elasticity is greater than 1, as income increases, a consumer spends a higher proportion of her income on the product, and as income decreases, she spends a lower proportion of her income on the product. The correct answer is A.
Let choice A be good A, choice B be good B, and choice C be good C.
So first up “decrease in income…” “…spending lower…”
=> same direction, positive income elasticity, eliminate B
Now,
Income Elasticity = % Change in Q Demanded / % Change in Income
Choice A => a 1% Income increase would lead to 1.5% increase in Qd
=> a 1% Income decrease would lead to 1.5% decrease in Qd
Choice C = > a 1% Income increase would lead to 0.5% increase in Qd
=> a 1% Income decrease would lead to 0.5% decrease in Qd
So clearly, Choice A is more responsive/sensitive to a decrease in income. This results in a bigger decrease in quantity of A consumed relative to quantity of C , for a given fall in income (holding all else the same of course). Therefore, A is likely to represent a lower proportion of total income post the fall in income.
Suppose both goods A and C have the same prices (say $20) and are consumed in equal amounts. If the consumer initally earned $80 and spent it equally between A and C ($40 each), she would buy 2 units of A (@ $20 per unit) and 2 units of C (@ $20 per unit).
Now if income falls to $60 = > % change in income = (60-80) / [(60+80)/2] = -0.2857 => 29% fall in income
She will now buy 1.5 x 29 = 43.5 % less of A (since a 1% income decrease leads to a 1.5% Qd decrease in A, a 29% income decrease leads to a percentage decrease in Qd of 1.5 times 29)
Qd for A after fall in income = 2 - 0.435 x 2 = 2 x(1-0.435) =1.13 (let’s assume the quantity is continuous like kg) and spend on A is = $20 x 1.13 = $22.6
For C, she will buy 0.5 x 29 = 14.5% less of C after income falls. i.e. : She buys 2 x (1-0.145) = 1.71 and total spend on C is = $20 x 1.71 = $34.2
Proportion of $60 income spent on A = 22.6/60 = 37.7%
Proportion of $60 income spent on C = 34.2/60 = 57 %
Therefore, she spends a lower proportion of income on A