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Problem 3 Consider a Robinson Crusoe economy with one consumer, endowed with one unit of labor (. The agent can work in the single firm producing the...

Fnal Problem 3- Advanced microeconomics - General Equilibrium
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Consider a Robinson Crusoe economy with one consumer, endowed with one unit of labor ( . The agent can work in the single firm producing the consumption good and L is the labor employed in production. The utility function of the agent is , where x is the amount of the consumption good and is the amount of leisure consumed.
Problem 3 Consider a Robinson Crusoe economy with one consumer, endowed with one unit of labor (. The agent can work in the single firm producing the consumption good and L is the labor employed in production. The utility function of the agent is , where x is the amount of the consumption good and is the amount of leisure consumed. a. Solve the firm problem & derive the demand of labor. b. Solve the consumer problem. Concentrate on the interior solution. c. Find the competitive equilibrium process (p&w) and the equilibrium labor supply&the output level. d. Is the equilibrium Pareto optimal? Prove e. Now assume that additionally the consumer initially receives 16 units of the consumption goods for free. How does this affect your answer in (c)?
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This question was asked on Jan 20, 2013.

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