Ryan's preferences for food and gasoline each week can be described by the utility function U(F,G) = FG2, where F is pounds of food and G is gallons of gas. For this utility function, MUF = G2 and MUG + 2FG.His monthly income is $1,200, the price of food is $4 per pound, and the price of gas is $4 per gallon. The government gives him $1,200 per month in food stamps.
a. What is the formula for his MRSFG? Do his preferences have the declining MRS property?
b. What bundle of food and gasoline would he choose without the food stamp program?
c. Draw his budget set (the set of affordable bundles) with the food stamp program.
d. What is his best choice with the food stamp program in place?
e. Suppose the government wants to give him a cash grant instead that would get him to consume 40 pounds of food per week. How much more would that program cost the government than the food stamp program?