Question

4. A consumer can buy either Food or Luxuries. Assume the consumer has wellbehaved preferences. The government is considering providing an in-kind transfer of Food. (For example, the government could issue a debit card that can only be used to buy Food up to a certain dollar value.) Show that the consumer: cannot be worse off from the in-kind transfer; and that the consumer might be better off with a transfer of money of equal value than with the in-kind transfer of Food.

Answer 1

The consumer´s decisions without tranfers are as follow:

The straight line represents the restriction, X is the quantity of food and L is luxury. The consumer maximizes its utility in U1 that is the utility curve above the restriction line (for the insasiability pinciple). In this situation, the basket chosen is A.

If the government adds an in-kind transfer of Food, the new restriction is the light blue line, and the utility that maximizes the new restriction is U2 at the point B. Now the consumer is better because he/she can consume more of both goods with the new restriction.

But if the transfer is of money, the hole restriction will shift to the right. In this situation the consumer is even better than with the in-kind transfer because he/she can reach a higher utility curve that was out of the restriction before.

So as we can see, at the initial situation the consumer consumes X1. With the in-kind transfer its consumption increases to X2 and luxurious increases too. With the transfer of money the consumer chooses less food than before (X3) but more luxurious reaching the highest utility.

Usually, with wellbehaved utilities, a transfer of money is preferred to a in-kind transfer because money let you adjust better your chooses by letting you using the money to consum any good. That way the consumer do not have restrictions in the use of the transfer.