Question

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?

Answer 1

Solution:

The budget constraint is as follows: I = P_AA + P_BB

Where: I = Income level

           P_A = Price of Good A

           P_B = 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 = P_AA + P_BB

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 = P_AA + P_BB

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.