Robinson Crusoe has exactly 12 hours per day to spend gathering coconuts or catching fish.He can catch 2 fish per hour or he can pick 4 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) $48 and the price of fish is $2.
B) $48 and the price of fish is $.50.
C) $24 and the price of fish is $2.
D) $72 and the price of fish is $2.
E) $36 and the price of fish is $.50.

In a competitive market, Robinson would allocate his resources (time, in this case) to equalize the marginal utility per dollar spent on each good. Given he can catch 2 fish per hour or gather 4 coconuts per hour, and the price of coconuts is $1, the opportunity cost of catching 1 fish is 2 coconuts. If the price of coconuts is $1, then the price of fish must be $2 to reflect this opportunity cost. With 12 hours and the ability to gather 4 coconuts per hour, he could gather 48 coconuts if he spent all his time on that activity. Since the price of coconuts is $1, his income if he sold all coconuts would be $48, which is the same amount he has to spend in the competitive market scenario.