You can prepare your answers using word processing programs, e.g., MS Word. It is also fine to submit a properly scanned handwritten solution. The homework should be submitted as one single PDF file. If you choose to submit a scanned version, it is your responsibility to make sure that the document is legible and not too large. The solutions will be discussed in class on 18/22 February 2019.
1. International risk sharing: efficiency In the lecture, we have argued that with complete markets and commitment, the market equilibrium resulting from individual optimization is Pareto efficient. To confirm this claim, solve for the social planner’s solution for our two-country two-period setup and compare the social planner’s solution to the market equilibrium. Each period, the social planner maximizes a social welfare function – a weighted average of the welfare of the two countries – subject to the world resource constraint. Let the social welfare function be γu(c) + (1 − γ)u(c ∗ ), γ ∈ (0, 1) a) Write down the optimization problem of the social planner b) Derive the first order conditions c) Does the planner’s solution have the same implication for cross-country consumption allocation as in the lecture (p.27)? Interpret your result.
2. International risk sharing: efficiency In the lecture, we have argued that with complete markets and commitment, the market equilibrium resulting from individual optimization is Pareto efficient. To confirm this claim, solve for the social planner’s solution for our two-country two-period setup and compare the social planner’s solution to the market equilibrium. Each period, the social planner maximizes a social welfare function – a weighted average of the welfare of the two countries – subject to the world resource constraint. Let the social welfare function be γu(c) + (1 − γ)u(c ∗ ), γ ∈ (0, 1) a) Write down the optimization problem of the social planner b) Derive the first order conditions c) Does the planner’s solution have the same implication for cross-country consumption allocation as in the lecture (p.27)? Interpret your result
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