Assume a person consumes only two goods, food (F) and the other goods (X). This person's budget constraint can be written as
PF+X=I
Where P is the relative price of food.
1. Describe why the budget constraint for this person can be written in this way and graph the constraint. Also demonstrate this person's utility-maximizing choices for F and X.
2. Assume that the government provides a food subsidy to this person that allows him or her to consume all the food desired at half price. Discuss how would that shift this person's budget constraint? Discuss how would it affect food and non-food purchases?
3. Assume 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. Demonstrate graphically the maximum amount C could be in order to get this person to buy the card.
4. 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?