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Let the initial endowment be y0 = 500, ?1 = 1650. The utility function of the...

Let the initial endowment be y0 = 500, ?1 = 1650. The utility function of the agent is

given by ? = log(?0?1). Suppose that the production possibility frontier (PPF) is defined by

? =5000−0.00004*(P0)^3 +1650 for P0 =(0,500).

Assume that the interest rate is 10%

(i) Derive the opportunity set (capital market line)

(ii) Derive the optimal consumption bundle (?0*, ?1*)

(iii) Calculate the marginal rate of return.

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