Questions tagged [recursive-macroeconomics]

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Proof monotonicity on Blackwell sufficient conditions

I need to prove monotonicity assumption on Blackwell’s sufficient conditions for a contraction, that is: Given the operator T defined as $(Tf)(x) = sup [F(x,y)+bf(y)]$ I need to show that $f\leq g\...
4
votes
0answers
154 views

Eating a Cake with Uncertain Preferences

I've been playing around with a lot of cake eating problems and have been messing with how uncertainty could enter the model. One thing that I'm thinking about is whether we can solve a cake eating ...
3
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38 views

Deriving the Euler equation from a Continuous Time Dynamic Programming Problem (HJB)

Solving for the Euler equation in discrete time is farily straight forward with the use of the Benveniste Scheinkman theorem. However for the following standard Ramsey model: $$\max \int_{0}^{\infty}e^...
3
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34 views

Optimization problem of the firm

I have been reading an Economics working paper and trying to derive the first-order conditions of a seemingly complicated optimization problem. The optimization problem with choice variables $P_{t}^{R}...
3
votes
0answers
34 views

Epstein zin and resolution of uncertainty

I'm reading Simon Gilchrist's notes here. I understood everything until and including page 14, where it reads $$\frac{W_h^{1-\rho} + W_l^{1-\rho}}{2} \geq \frac{c_h^{1-\rho} + c_l^{1-\rho}}{2} $$ and ...
1
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52 views

Can the Bellman Equation be used for Finite time problems?

Its known that the Bellman equation in recursive macroeconomics is used for the following problems: $$\sum_{t=1}^\infty\beta^tU(c_t)$$ $$s.t. c_t+k_{t+1}=f(k_t)$$ $$k_0>0$$ Im wondering if we can ...
0
votes
0answers
8 views

log-linearize a forward looking variable (P/D) with recursive expression

I can solve the model in dynare but I need your help with the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, ...
0
votes
0answers
65 views

How does one find values of constants in a value function?

Problem: suppose I have the following maximization problem: \begin{align} &\max_{(c_t)_{t \geq 0}}E_0\left[\sum^{\infty}_{t=0}\beta^{t}\ln c_t\right]\\[2mm] \text{s.t.} \quad & k_{t+1}=A^{1-\...