Robinson Crusoe has exactly 8 hours per day to spend gathering coconuts or catching fish.He can catch 4 fish per hour or he can pick 8 coconuts per hour.His utility function is U(F, C)= FC, where F is his consumption of fish and C is his consumption of coconuts.If he allocates his time in the best possible way between catching fish and picking coconuts, his consumption will be the same as it would be if he could buy fish and coconuts in a competitive market where the price of coconuts is $1, his income is
A)$96 and the price of fish is $4.
B)$64 and the price of fish is $.25.
C)$32 and the price of fish is $4.
D)$64 and the price of fish is $2.
E)$48 and the price of fish is $.25.

Question

Quizplus · Accepted Answer

Robinson's optimal allocation is determined by maximizing his utility function U(F, C) = FC subject to his time constraint. He can spend his 8 hours catching fish or gathering coconuts. If the price of coconuts is $1 and the price of fish is $2, then his income of $64 allows him to purchase 32 coconuts and 16 fish, which matches his production possibility of 32 coconuts and 16 fish when he allocates his time optimally.

Robinson Crusoe Has Exactly 8 Hours Per Day to Spend