Problem
Hom Tanks has exactly 12 hours per day to spend gathering coconuts or catching fish. He can catch 3 fish per hour or he can pick 15 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.
What is the price of fish and what is his income (at competitive equilibrium prices)?