Robinson Crusoe has exactly 12 hours per day to spend gathering coconuts or catching fish.He can catch 3 fish per hour or he can pick 12 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)$144 and the price of fish is $4.
B)$144 and the price of fish is $.33.
C)$36 and the price of fish is $3.
D)$180 and the price of fish is $3.
E)$90 and the price of fish is $.33.

Question

Quizplus · Accepted Answer

In a competitive market, Robinson would allocate his resources (time, in this case) where the marginal rate of substitution (MRS) equals the price ratio of the two goods. Given that he can catch 3 fish per hour or gather 12 coconuts per hour, the opportunity cost of 1 fish is 4 coconuts. This implies that in equilibrium, the price ratio of fish to coconuts should be 4:1. Since the price of coconuts is $1, the price of fish should be $4 to make him indifferent between spending an hour catching fish or gathering coconuts. With 12 hours of work and the ability to gather 12 coconuts per hour, he could gather 144 coconuts a day if he spent all his time on that activity. Since coconuts are priced at $1 each, his income would be equivalent to $144 if he sold all the coconuts he gathered.

Robinson Crusoe Has Exactly 12 Hours Per Day to Spend