25.1 There are 200 pounds of food that must be allocated between two sailors marooned on an island. The utility function of the first sailor is given by utility = VFi, where FY is the quantity of food consumed by the first sailor. For the second sailor, utility (as a function of his food consumption) is given by utility = jV¥2.

a. If the food is allocated equally between the sailors, how much utility will each receive?

b. How should food be allocated between the sailors to ensure equality of utility?

c. How should food be allocated so as to maximize the sum of the sailors' utilities?

d. Suppose sailor 2 requires a utility level of at least 5 to remain alive. How should food be allocated so as to maximize the sum of utilities subject to the constraint that sailor 2 re ceive that minimum level of utility?

e. Suppose both sailors agree on a social welfare function of the form W= U\

/2U\

/2

. How should food be allocated between the sailors so as to maximize social welfare?