In equilibrium a consumer was buying 5 units of good A and some of good B. His
income was Rs 100 and the prices were P A = Rs 8 and P B = Rs 5. The price of good A
falls to Rs 5. By how much does his income need to be compensated so that he is able to
buy the (old) bundle at the original equilibrium?
Solution:
The budget constraint is as follows: I = PAA + PBB
Where: I = Income level
PA = Price of Good A
PB = Price of Good B
A = Quantity of Good A
B = Quantity of Good B
First derive the units of good B in the old bundle:
I = PAA + PBB
100 = 8(5) + 5(B)
100 = 40 + 5B
100 – 40 = 5B
60 = 5B
B = "\\frac{50}{5} = 12"
B = 12
Unit of good B consumed in the old bundle = 12 units
Now calculate by how much does his income need to be compensated so that he is able to buy the (old) bundle at the original equilibrium:
Calculate the new income following the fall of good A price to Rs.5:
I = PAA + PBB
I = 5(5) + 5(12)
I = 25 + 60
I = 85
New income = Rs.85
Deduct new income from the old income to derive the amount to be compensated
100 – 85 = 15
His income needs to be compensated by Rs.15 so that he is able to purchase the old bundle at the original equilibrium.
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