Suppose low-income people have preferences for non-food 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 PFF is the price of food relative to non-food items and NF and I are measured in terms of non-food prices ($ dollars).
(a) Graph the initial utility-maximizing situation for this low-income person.
(b) Suppose now that a food stamp program a introduced that requires low-income people to pay C (measured in terms of non-food price) in order to receive food stamps sufficient to by F* units of food (presumably PFF > C). Show this person's budget constraint 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.