Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 33

Suppose a person consumes only two goods, food (F) and other goods (X). This person's budget constraint can be written as
PF + X = I
Where P is the relative price of food and X and I are measured in terms of prices of non-food items (that is, say inflation-adjusted dollars).
a. Explain why the budget constraint for this person can be written in this way and graph the constraint. Also show this person's utility-maximizing choices for F and X.
b. Suppose that the government provides a food subsidy to this person that allows him or her to consume all the food desired at half price. How would that shift this person's budget constraint? How would it affect food and non-food purchases?
c. Suppose now that the government requires that in order to buy food at half price this person must pay C dollars for a food credit card. Show graphically the maximum amount C could be in order to get this person to buy the card.
d. With C set at the amount described in the previous part, will this person consume more or less food than he or she did initially in part a?