Equilibrium, Welfare, Multi-Period Models Flashcards
Equivalent market clearing definition under endowments and payoff matrix X
\sum_i X_s\cdot \theta ^i=\sum_i X_s\cdot \rho^i
Rational expectations
price equals market clearing price. (Auctioneer).
Pareto efficiency
no other feasible allocation such that all equally well off and at least one strictly better off (state, individual pair)
When is social planner pareto
strictly positive weights
when is CE a social planner?
exists some “weakly” positive weights, provided complete markets.
Condition for second welfare theorem
convex choice set and convex preferences, and non-satiation
When is Radner constrained efficient?
Only one consumption good in each state, or quasi-linear preferences, or no trade. Requires symmetry of preferences, though.
Write the inter-temporal budget constraint which holds under complete markets (with endowments)
c_0^i+\sum_s q_s c_s^i = w_0^i + p_0\cdot e_0^i + \sum s q_s p_s \cdot e_s
Derive Euler equation from complete market FOC (for asset with payoff X_a,s, price q_a)
v_c^i=\beta E_0[X_a,s/q_a v_c^i]
Does Euler depend on complete markets?
No. Show this.
Does the agent reoptimize in the complete markets dynamic specification?
No, since the policy is time-consistent since it is state contingent, and the problem does not change in each state tuple.
