Question

A consumer with strictly convex preferences chooses an interior optimal bundle A as the solution to the budget constrained, utility maximization problem. If the price of one of the goods increases subsequently and we compensate the consumer with just enough income to reach the same utility level (but no higher) achieved with bundle A prior to the price increase, then bundle A must also be affordable (in the budget set) after the price increase with the additional income compensation. True or False?

Answer 1

Here the consumer chooses bundle A before the price increase which has a specific amount of utility to such a consumer. After the price or one good increases, we are compensating the consumer the extra amount of money required in his budget to afford the bundle of goods which provide the same utility as bundle A before such an increase in the price of the good. So we are compensating the consumer to receive an equal level of utility as he was deriving from bundle A, prior to such increase. So we can say that if bundle A still holds the same amount of utility as prior to the price increase to such a consumer, then the utility for bundle A prior to price increase and after a price increase will be same, i.e., if the utility derived from bundle A does not change with an increase in price of the consumer, though it may have become costlier, but we will compensate the customer to afford the extra cost, but the utility derived from bundle A should be the same.

We get the level of utility derived from the indifference curve, higher indifference curves mean higher utility and lower indifference curves imply lower utility. And we have the budget line which cuts through the indifference curve representing the affordable goods. Here, the budget constraint has been solved by us providing the customer with an extra amount of income so that he can get the same utility as he was deriving before.

The utility derived from bundle A as it remains the same for the consumer, though the prices changed, and the optimum point may have also changed due to more choices, but if the consumer still prefers bundle A and has the same amount of utility as it had earlier, then the consumer can choose bundle A. The consumer is not allowed to choose any combination higher than bundle A prior to price change. So if bundle A has the same utility he can choose.

Usually, price change leads to a change in the budget line and the goods that can be affordable. As the consumer is getting compensation for the price, he can choose bundle A if it has the same level of utility. Due to the substitution effect, a consumer chooses a different bundle when the price of one product increases from among the bundle, and follows the budget line so as to cope with such an increase in the price of the commodity. But as we can see that the consumer is getting the compensation, assuming the utility of bundle A to be constant, the increase in the price of one good, and the extra income to afford the level of utility derived, it is true that the consumer can choose bundle A as the utility holds constant and it did not change with an increase in price, since the extra price is getting born. So it is true, that the consumer can still choose bundle A since utility holds constant even after price change and the extra price is compensated.