Samantha purchases food (F) and other goods (Y) with the utility function U = FY. Her income is 12. The price of a food is 2 and the price of other goods 1.
a) How many units of food does she consume when she maximizes utility?
b) The government has recently completed a study suggesting that, for a healthy diet, every consumer should consume at least F = 8 units of food. The government is considering giving a consumer like Samantha a cash subsidy that would induce her to buy F = 8. How large would the cash subsidy need to be? Show her optimal basket with the cash subsidy on an optimal choice diagram with F on the horizontal axis and Y on the vertical axis.
c) As an alternative to the cash subsidy in part (b), the government is also considering giving consumers like Samantha food stamps, that is, vouchers with a cash value that can only be redeemed to purchase food. Verify that if the government gives her vouchers worth $16, she will choose F = 8. Illustrate her optimal choice on an optimal choice diagram. (You may use the same graph you drew in part (b).)