Robinson Crusoe has exactly 10 hours per day to spend gathering coconuts or catching fish.He can catch 3 fish per hour or he can pick 6 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 $60 and the price of fish is $2.
B)His income is $60 and the price of fish is $.33.
C)His income is $90 and the price of fish is $3.
D)His income is $30 and the price of fish is $3.
E)His income is $45 and the price of fish is $.33.

Question

Quizplus · Accepted Answer

In a competitive market, the ratio of the prices of goods will equal the ratio of the marginal utilities. Given that Robinson can gather 6 coconuts or catch 3 fish per hour, and the price of coconuts is $1, he effectively earns $6 per hour picking coconuts. Over 10 hours, his income is $60. Since he can catch 3 fish per hour, and given his income and the price of coconuts, the price of fish must be such that he could also choose to spend his time fishing without changing his income. Thus, if he spent an hour fishing instead of coconut gathering, he would forego $6, catching 3 fish in the process. Therefore, each fish must be worth $2 to equate the opportunity cost of not gathering coconuts.

Robinson Crusoe Has Exactly 10 Hours Per Day to Spend