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ECOS3022

S1 2024

Quiz

1. (1 point)Write down the Lagrangian function for the following maximization problem.

2. Consider a contingent claim economy with two consumers(A and B),two states tomor- row and one good in each state.Agents have the following utility functions:

As for endowments,

(a) (1 point)Write down the state-by-state budgent constraints for A and B. Use and to denote the units of contingent claims consumers buy for each state s.

(b) (1 point)State the utility maximization problem for A and B without the use of and mentioned above.

(c) (3 points)Derive consumers'demand functions with the Lagrangian method.

(d) (3 points)Find the market equilibrium for this contingent claim economy.

(e) (1 point)Verify that the equilibrium allocation is Pareto efficient.