Complete Markets

Question 1

Envelope theorem in indirect utility

Answer 1

v_w(w,p)=lambda^* (more generally, for solutions of first order, changing state variables does not interact with optimal solution)

Question 2

Definition of homothetic preferences

Answer 2

x\succeqx’ \iff lambdax\succeq\lambda x’ for all positive lambda

Question 3

Equivalent characterization of homotheticity

Answer 3

u(f(lambda x))=u(lambda^af(x))

Question 4

FOC of complete markets

Answer 4

pi(s)*v_w^i=lambda q_s

Question 5

Across States complete markets condition

Answer 5

v^i_w(s)/v&i_w(s’)=\pi(s’)q_s/\pi(s)q_s’

Question 6

The point of the Giants example

Answer 6

marginal utility is not just level–value of dollar

Question 7

Good markets equilibrium definition

Answer 7

1) Agents maximize utility given their BC and transfers; 2) Allocations are feasible; 3) Net transfers are zero (within state).

Question 8

Contingent Commodities

Answer 8

State-dependent good consumption–only available in complete markets for Radner. First welfare theorem applies, hence, have efficiency.