Y7 Robinson's technology for gathering coconuts (x) is represented by x = Lx, where Lx is hours

Y7

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Robinson's technology for gathering coconuts (x) is represented by x = Lx, where Lx is hours of labor devoted to gathering coconuts per day and x denotes coconuts gathered per day. His technology for catching fish (y) is represented by y= Ly, where Ly is hours of labor devoted to fishing per day and y denotes pounds of fish captured per day. Robinson has already decided he will allocate 10 hours a day between these two activities. a. Write down the production possibilities frontier (PPF) for this economy. Carefully plot the production possibilities frontier in this economy. Plot y on the vertical axis and x on the horizontal axis. Robinson has preferences between coconut and fish represented by the utility function U(x,y)=1 3lnx+2 3lny b. Calculate the Pareto efficient allocation in this simple production economy. Plot this Pareto efficient allocation in the PPF you drew above and draw the indifference curve that passes through that point. c. Derive the Walrasian equilibrium in this economy. Find Robinson's equilibrium production (and consumption) of coconuts and of fish, the equilibrium hourly wage, the equilibrium prices of fish and coconuts, the amount of labor devoted to fishing, the amount of labor devoted to gathering coconuts, and the firms' profits. Measure all prices, budgets and profits in units of y, that is, in terms of pounds of fish. Robinson's technology for gathering coconuts (x) is represented by x = Lx, where Lx is hours of labor devoted to gathering coconuts per day and x denotes coconuts gathered per day. His technology for catching fish (y) is represented by y= Ly, where Ly is hours of labor devoted to fishing per day and y denotes pounds of fish captured per day. Robinson has already decided he will allocate 10 hours a day between these two activities. a. Write down the production possibilities frontier (PPF) for this economy. Carefully plot the production possibilities frontier in this economy. Plot y on the vertical axis and x on the horizontal axis. Robinson has preferences between coconut and fish represented by the utility function U(x,y)=1 3lnx+2 3lny b. Calculate the Pareto efficient allocation in this simple production economy. Plot this Pareto efficient allocation in the PPF you drew above and draw the indifference curve that passes through that point. c. Derive the Walrasian equilibrium in this economy. Find Robinson's equilibrium production (and consumption) of coconuts and of fish, the equilibrium hourly wage, the equilibrium prices of fish and coconuts, the amount of labor devoted to fishing, the amount of labor devoted to gathering coconuts, and the firms' profits. Measure all prices, budgets and profits in units of y, that is, in terms of pounds of fish.