Robinson Crusoe economy Suppose that Robinson Crusoe produces and consumes sh (F) and coconuts (C ). Assume that he has decided to work a total of 200 hours a month and is indifferent as to whether he spends this time shing or gathering coconuts. Crusoe's production function for sh is given by F = 1M": and his production function for coconuts by C = 1,41? , where {"F and 5 denote the number of hours per month spent working by shing or collecting coconuts, respectively. His utility function for sh and coconuts is given by IMF, C) = VF C . (a) If Crusoe cannot trade with the rest of the world, how will he choose to allocate his labor between shing and collecting coconuts? What will the optimal levels of F and C be? (b) Given your answers to part (a), what will Crusoe's utility be? What will be the RPT (of sh for coconuts)? (c) Now suppose that trade is opened and Crusoe can trade sh and coconuts at a price ratio of :F = 2. If he continues to produce the quantities of sh and coconuts from part (a), C what will he choose to consume once given the opportunity to trade? What will his new level of utility be? ((1) How would your answer to part (c) change if Crusoe adjusts his production to take advantage of the world prices? (e) Graph your results for parts (a)(d)