Robinson Crusoe has exactly 8 hours per day to spend gathering coconuts or catching fish.He can catch 2 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)$64 and the price of fish is $4.
B)$64 and the price of fish is $.50.
C)$16 and the price of fish is $2.
D)$80 and the price of fish is $2.
E)$40 and the price of fish is $.50.

Question

Quizplus · Accepted Answer

In a competitive market, Robinson Crusoe would allocate his resources (time, in this case) to equalize the marginal utility per dollar spent on each good. Given his utility function and the productivity rates (2 fish per hour, 8 coconuts per hour), we can determine the optimal allocation by comparing the prices and his productivity. Since he can gather 8 coconuts per hour at a price of $1 each, he effectively earns $8 per hour picking coconuts. Catching 2 fish per hour, the price of fish must be set so that his hourly earnings from fishing would also be $8 to make him indifferent between the two activities. Therefore, the price of fish must be $4 (since 2 fish * $4 = $8). With 8 hours available, his total income would be 8 hours * $8/hour = $64, making option A correct.

Robinson Crusoe Has Exactly 8 Hours Per Day to Spend