final Flashcards
(15 cards)
What is the objective of the static consumption-leisure model?
Maximize utility subject to the budget constraint
What is the budget constraint in the static consumption-leisure model?
c = w h
What is the Lagrangian for the static consumption-leisure model?
ℒ = u(c, h) + λ (w h - c)
What are the first-order conditions (FOCs) for the static consumption-leisure model?
∂ℒ/∂c = u_c - λ = 0; ∂ℒ/∂h = u_h + λw = 0
What is the optimality condition derived from the FOCs in the static consumption-leisure model?
u_h/u_c = -w
What does MRS equal in the context of the static consumption-leisure model?
MRS = wage
How does the central planner’s version of the static consumption-leisure model differ?
Same as above if the planner controls c and h, no externalities or distortions
What is the objective of the intertemporal consumption-savings model?
Maximize u(c_1) + βu(c_2)
What is the budget constraint for the intertemporal consumption-savings model?
c_1 + c_2/(1 + r) = y_1 + y_2/(1 + r)
What is the Lagrangian for the intertemporal consumption-savings model?
ℒ = u(c_1) + βu(c_2) + λ(y_1 + y_2/(1 + r) - c_1 - c_2/(1 + r))
What are the first-order conditions (FOCs) for the intertemporal consumption-savings model?
∂ℒ/∂c_1 = u’(c_1) - λ = 0; ∂ℒ/∂c_2 = βu’(c_2) - λ/(1 + r) = 0
What is the Euler equation derived from the FOCs in the intertemporal consumption-savings model?
u’(c_1) = β(1 + r)u’(c_2)
What does the optimality condition in the intertemporal consumption-savings model represent?
Present marginal utility = discounted future marginal utility
What is the resource constraint for the central planner in the intertemporal consumption-savings model?
c_1 + c_2/(1 + r) = y_1 + y_2/(1 + r)
What will the planner choose in the intertemporal consumption-savings model?
c_1 and c_2 to satisfy the same Euler equation
