Robinson Crusoe has exactly 14 hours per day to spend gathering coconuts or catching fish.He can catch 4 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.
A)His income is $168 and the price of fish is $3.
B)His income is $56 and the price of fish is $4.
C)His income is $224 and the price of fish is $4.
D)His income is $168 and the price of fish is $.25.
E)His income is $112 and the price of fish is $.25.

Question

Quizplus · Accepted Answer

In a competitive market, the ratio of the prices of fish to coconuts would equal the ratio of their marginal utilities, which also equals the ratio of their productivity (fish per hour to coconuts per hour). Given that he can pick 12 coconuts per hour and the price of coconuts is $1, his hourly income from picking coconuts is $12. Catching 4 fish per hour means each fish's price must be such that 4 times the price of fish equals the income from picking coconuts ($12), so the price of fish is $3. With 14 hours available, his total income if he spent all his time picking coconuts would be 14 hours * $12/hour = $168.

Robinson Crusoe Has Exactly 14 Hours Per Day to Spend