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 PA = Rs 8 and PB = 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?
According to the given information, units of B consumed by the consumer would be:
"M=PA(QA)+PB(QB)\\\\\n\n100=8(5)+5(QB)\\\\\n\n100-40=5(QB)\\\\\n\n\\frac{60}{5}=QB\\\\\n\n12=QB"
Therefore, original bundle consumed by the consumer would be (5,12)
Here, it is given that the price of good A falls to Rs 5 and consumer wants to consume the same bundle as earlier. Therefore, using the given information, new income to consume original bundle would be:
"M=PA(QA)+PB(QB)\\\\\n\nM=5(5)+5(12)\\\\\n\nM=25+60\\\\\n\nM=85"
Therefore, he needs to compensate Rs 15 (Rs100 - Rs85) from his income so that he is able to buy the (old) bundle at the original equilibrium.
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