There are 200 pounds of food on an island that must be allocated between 2 maroo

Question

There are 200 pounds of food on an island that must be allocated between 2 marooned sailors. The utility function of the first sailor is given by
Utility= ?( F1)
Where F1 is the quantity of food consumed by the first sailor. For the second sailor utility (as a function of food consumption) is given by
Utility= 1/2 ?( )F2

C. suppose the second sailor requires a utility level of at least 5 to remain alive. How should food be allocateds so as to maximize the sum of the utilities subject to the restraint that the second sailor receives the minimum level of utility?

D. What other criteria might you use to allocate the availiable food between the sailors.

Explanation / Answer

a) 200 total, split into 2 parts evenly - 100, 100 1st person U=sqrt(100) = 10 2nd person U = .5sqrt(100) = .5(10) = 5 b no if food is given equally then the utility is uneven, 1st person has higher utility than 2nds person you should give the 2nd person more food for more equal utilities

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