a) [Word limit 400] Suppose Robinson Crusoe produces Coconut (C) and Fish (F) using only labour...

 

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a) [Word limit 400] Suppose Robinson Crusoe produces Coconut (C) and Fish (F) using only labour and the production functions are: C=10VLC andF=0LF LC and LF represent labour devoted to the production of coconut and fish, respectively, and 0>0 is a constant. Suppose labour supply is fixed at L = 400, and the utility function of Crusoe is U = vCF. i)Suppose 0 = 1. Derive Crusoe's production possibility frontier for coconut and fish production. [4 Marks] ii)Now make no assumptions on the value of 0. What would be the equilibrium price ratio and equilibrium quantities of coconut and fish? [6 Marks] iii)How do the equilibrium quantities and price ratio change when 0 increases? Explain the intuition behind your mathematical results. [4 Marks] iv)Assume now 0 > 4. Also assume that Crusoe would like to trade with Friday. Suppose Friday's price ratio is pC/Pf = 1. How much would Crusoe want to consume and how much would Crusoe want to produce (each good)? Find the consumption and production bundle. For what values of 0 will Crusoe want to export coconut to Friday? How about Fishes? [6 Marks] If you would like this question split let me know and I will do split it. However I am pretty sure this should be considered one question as it is in parts! a) [Word limit 400] Suppose Robinson Crusoe produces Coconut (C) and Fish (F) using only labour and the production functions are: C=10VLC andF=0LF LC and LF represent labour devoted to the production of coconut and fish, respectively, and 0>0 is a constant. Suppose labour supply is fixed at L = 400, and the utility function of Crusoe is U = vCF. i)Suppose 0 = 1. Derive Crusoe's production possibility frontier for coconut and fish production. [4 Marks] ii)Now make no assumptions on the value of 0. What would be the equilibrium price ratio and equilibrium quantities of coconut and fish? [6 Marks] iii)How do the equilibrium quantities and price ratio change when 0 increases? Explain the intuition behind your mathematical results. [4 Marks] iv)Assume now 0 > 4. Also assume that Crusoe would like to trade with Friday. Suppose Friday's price ratio is pC/Pf = 1. How much would Crusoe want to consume and how much would Crusoe want to produce (each good)? Find the consumption and production bundle. For what values of 0 will Crusoe want to export coconut to Friday? How about Fishes? [6 Marks] If you would like this question split let me know and I will do split it. However I am pretty sure this should be considered one question as it is in parts!