Economics Stack Exchange
Economics Stack Exchange

Questions tagged [steady-state]

32 questions
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Solow Model: Steady State v Balanced Growth Path

Okay, so I'm having real problems distinguishing between the Steady State concept and the balanced growth path in this model: $$ Y = K^\beta (AL)^{1-\beta} $$ I have been asked to derive the steady state values for capital per effective worker: $$…
James Baker
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Optimality of Zero Capital Taxation

The Chamley-Judd result of zero optimal capital taxation says that 0 capital taxation are required in order to maximize welfare at the steady state. The result is 30 years old. Still assuming that we only care about the steady state, what's the…
FooBar
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"If $\lambda$ is greater than than 1, the system explodes." Why does the system explode?

David Romer in his textbook Advanced Macroeconomics (Third Edition) writes regarding the speed of convergence of the Diamond model the following: (Pg. 83) Equation (2.60) [$k_{t+1}={1\over{(1+n)(1+g)}}{1\over{2+\rho}}(1-\alpha)k_t^\alpha$] gives…
Bensstats
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An Optimal Control Model: A Ridiculous Result for a Steady State

I was experimenting with a seemingly simple optimal control problem that generates a system of differential equations. When I calculate the values of the steady state of the system I get some very strange results I believe I did something wrong when…
Artem Kochnev
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Solution Method for Infinite-Horizon Maximization Problem

Full disclosure: this problem was part of a final exam that none of our class could really solve definitively. Below the general form is a specific utility function we worked with that I'll try to replicate my work for. Any help on the solution…
Kitsune Cavalry
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Multiple equilibria: which one to select?

There are two agents $i=1,2$. Consider the following programm \begin{align} &V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\ &V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}F_2(x(t),u(t),v(t))dt\\ s.t.~&\dot…
clueless
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Real Positive Eigenvalue, but Stable Dynamics

UPDATE I was not thinking straight anymore and got totally confused after working hours on my equations. The point is, I have an unstable system, but I force it on the stable path. After realizing that crucial point everything made perfect…
clueless
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Conjecture Steady State from limit properties

The question is related to this thread. I'd like to derive a unique steady state for an optimal control problem. Consider the following programm \begin{align} &V(x_0) := \max_u \int^\infty_0 e^{-\rho t}F(x(t),u(t))dt\\ s.t.~&\dot…
clueless
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Steady-state savings rate

I'm having trouble with the steady-state savings rate type of problems. Here is the problem I'm stuck on: The production is $Y = 0.5*K^{1/3}(AN)^{2/3}$. If savings is $s$%, what are the steady-state values of capital per unit of effective worker…
user40459
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Get empirical steady state moments for calibrating a DSGE model

I want to calibrate some parameters of my DSGE model so that in the steady state some variable ratios, that are present in data, are met. My question is, how do I get such ratios from time series correctly? For example, say I want to target the…
manifold
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Derive the Demographic Structure in the Steady State

I am reading a paper with following description on the demographics in their model: "... each (representative) agent lives for $T$ periods ... We assume that each individual has $e^{f}$ children at age $B$. Since we consider only steady states, we…
Alalalalaki
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Non-trivial steady state

Consider the growth model with inelastic labor supply, full depreciation, log utility and CRS technology with the Bellman equation be defined as follows: $$V(k)=\max(log(k^\alpha-k')+\beta V(k'))$$ st $$k\geq0\ \text{and}\ \theta…
Maybeline Lee
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Overlapping Generations model: Social Planner solution

Assume we have a model of OVG where there are 2 overlapping generations, youngs and olds, the agents are two period living. The utility function is logaritmic, and the production function is Cobb-Douglas. I have to show that the solution for the…
Chaos
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What conditions must we demand for the economy to be always on the saddle path?

Is it enough to assume that agents have perfect foresight, or have 'rational' expectations for the economy to always - except in few cases - be in the stable saddle path? With rational expectations, I think with shocks, there can be a temporary…
An old man in the sea.
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Prove the uniqueness of steady state

I have a difference equation $$ p_t^{1-\alpha}=\alpha\sigma \left(y-p_t-\frac{(\sigma p_{t-1}^\alpha+b)p_t^{1-\alpha}}{\alpha\sigma} \right) $$ where $\alpha \in [0,1]$ and everything else is $>0$. I need to prove that this equation has a…
Sher Afghan
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