Robinson produces and consumes fish (F) and coconuts (C) using the technology F2 + C2 = 200. His preferences can be represented by the utility…

Robinson produces and consumes fish (F) and coconuts (C) using the technologyF2 + C2 = 200.a. His preferences can be represented by the utility function U = FC. He does not trade with anyone. What quantitiesof fish and coconuts will he produce and consume? Show your logic and calculations clearly.b. Graph this equilibrium and label it “A.” Put F on the x-axis.c.Suppose Robinson begins to trade and finds that the com petitive price ratio for fish and coconuts is pf / pc = 2. Hecontinues to produce the same quantities of fish and coconuts as before (point A). What is his new “budgetconstraint” under the trading regime?d.Add the constraint to the graph, labeling its intercepts clearly.e.What quantities of fish and coconut will he consume in this particular trading regime? Show your logic clearly andall your calculations.f.Show this equilibrium on the graph and label it “B.”g.Now Robinson realizes that his decision to produce the quantities at point A after beginning to trade was a mistake.He can improve his welfare by adjusting his production of fish and coconuts. Compute the economically efficientquantities of fish and coconuts for production. Show your logic clearly.h.Label this equilibrium point “C” in the graph. (Don’t bother computing his new “budget constraint” andequilibrium consumption.)