The Robinson Crusoe Economy: Robinson Crusoe has decided that he will spend exactly 8 hours a day gathering food. He can either spend his time gathering coconuts or catching fish. He can catch 1 fish per hour and he can gather 2 coconuts per hour.

(a) On a graph, show Robinsons production possibility frontier between fish and coconuts per day (put coconuts on the vertical axis). Write an equation for the line segment that is Robinsons production possibilities frontier.

(b) Robinsons utility function is U(F, C) = F C, where F is his daily fish consumption and C is his daily coconuts consumption. On your graph from part (a), sketch the indifference curve that gives Robinson a utility of 4 and also sketch the indifference curve that gives him a utility of 8.

(c) How many fish will Robinson choose to catch per day? How many coconuts will he collect? (Hint: Robinson will choose a bundle that maximizes his utility subject to the constraint that the bundle lies in his production possibility set. But for this technology, his production possibility set looks just like a budget constraint.)

(d) Suppose Robinson is not isolated on an island in the Pacific, but is retired and lives next to a grocery store where he can buy either fish or coconuts. If fish costs $1 per fish, how much would coconuts have to cost in order that he would choose to consume twice as many coconuts as fish? Suppose that a social planner decided she wanted Robinson to consume 4 fish and 8 coconuts per day. She could do this by setting the price of fish equal to $1, and the price of coconuts equal to p C and giving Robinson a daily income of m. Determine the values of p C and m .

Notes: Thank you for helping and please give me the details and explaination because i want to understand all of it. I appreciate.