Suppose low-income people have preferences for nonfood consumption (NF) and for food consumption (F). In the absence of any income transfer programs, a person’s budget constraint is given by
NF + PFF = I
Where PF is the price of food relative to nonfood items and NF and I are measured in terms of nonfood prices (that is, dollars).
a. Graph the initial utility-maximizing situation for this low-income person.
b. Suppose now that a food stamp program is introduced that requires low-income people to pay C (measured in terms of nonfood prices) in order to receive food stamps sufficient to buy F* units of food (presumably PFF* > C). Show this person’s budget constraint if he or she participates in the food stamp program.
c. Show graphically the factors that will determine whether the person chooses to participate in the program. Show graphically what it will cost the government to finance benefits for the typical food stamp recipient.
d. Show also that some people might reach a higher utility level if this amount were simply given with no strings attached.