Consider an individual earning $1000 per month who also receives $100 per month in food stamps (they can only be exchanged, legally, for food). The individual's preferences are defined over expenditures on food and expenditures on all other goods.
a. Draw the individual's budget constraint before and after the food stamp grant. Place food on the horizontal axis and "all other goods" on the vertical axis. Clearly label and identify all of the relevant parts of the budget constraint, including intercepts, etc. What is the price of food?
b. Show that if the individual consumes more than $100 in food after receiving the stamps, he is indifferent between receiving the stamps and a $100 cash grant.
c. Show that if he consumes exactly $100 in food after receiving the stamps he is almost certainly worse off than if he had been given $100 in cash.
d. Given your analysis in part c, what is the justification for a subsidy program like food stamps?
e. Show that it is also possible that the government can give the consumer a cash grant of less than $100 (thus lowering the cost to the government) and the individual will be no worse off than under the food stamp program.
f. If it is illegal to sell food stamps, what does your analysis indicate about the potential existence of a black market in food stamps? Indicate graphically an acceptable price that your consumer would accept for his food stamps, and that someone would be willing to pay for them. Also indicate his new optimal bundle and the amount of food stamps that he would sell. Would you allow the sale of food stamps? Why?