Question

4. (25 pts) Robinson Crusoe is trying to survive by either gathering coconuts (C) or fish (F). The technologies available for these two production pro- cesses are given by: C = Lc and F = 3LF where Lc is the amount of labor (time) used for gathering coconuts and LF is the amount of labor (time) used for gathering fish. The total time (L) is 10 hours per day, i.e. Lc+LF = L = 10. Robinson Crusoe's preferences are given by the utility function, U(C; F) = C*F. (a) Construct the production possibility frontier (PPF) and show it on a graph. (5 pts) (b) Find the marginal rate of transformation (MRT) and MRS between coconuts and fish. (5 pts) (c) Find the optimal combination of fish and coconuts and the optimal allocation of time. Show the competitive equilibrium on the graph. (10 pts) (d) Give an interpretation for the MRS and MRT. What is the relation- ship between MRS and MRT at the optimal allocation of consump- tion? (5 pts)

Answer 1

CEL L . F=3LF =) Les § het LF = 10 et F =10. BC +5 =30 PPE

b) Marginal rate of trans primation = 3- MRS. = 5a

Optimal combination of hish and Fisha coconuts Pcoconuts F=30 30+30=30 GC=30 IC=5 F =15 . MRS is the late at which for the other consumer substitute one good MRT is the rate at which one case Moss of one good can be produced by producing less of the other Attimal allocation. A consumption avel to MRS

F =15 d) MRS is the late at which for the other consumeer substitutes one good MRT is the rate at which one spo moss a one good can be produced by producing less of the other B At optimal allocation of consumption , MRT is equal to MRS,