Questions tagged [steady-state]

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Proving the existence of a steady state

I am trying to prove the existence of at least one stable steady state in a situation where I am given properties of the production function but not an explicit functional form. I have the following (...
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35 views

Log-linearization about steady state

I am working on a Solow model where: $$ y_{t} = k_{t}^{\alpha}(Z_{t})^{1-\alpha} $$ $$ y^{*} = (\frac{s}{n+\delta})^{\frac{\alpha}{1-\alpha}} Z $$ $$ k^{*} = (\frac{s}{n+\delta})^{\frac{1}{1-\alpha}}...
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1answer
64 views

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-...
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2answers
182 views

What does steady state mean?

I am reading a book on business cycle models, and it keep using the word "steady state". It never defined what that actually means. Obviously it is the idea that some key variables reach constant ...
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1answer
157 views

Solow model golden rule with my exact answer

In a perfectly competitive Solow economy with physical capital accumulation, population growth and a Cobb-Douglas production function, show that the “golden rule” steady-state would be reached if at ...
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2answers
141 views

“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+...
7
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1answer
128 views

An Optimal Control Model: A Rediculous 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 ...
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1answer
377 views

Taylor Series Approximation around steady state in Solow

In my Advanced Macro script, the professor says take TSA1 of the following equation: $(1+g)(1+n)k_{t+1} = sk^\alpha_{t+1} + (1-\delta)k_t$ where $g$ is technological progress, $n$ population growth, ...
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2answers
345 views

Solow model, time and steady state

Suppose we have a Solow model: $$ Y(t)=C(t)+I(t) $$ $$ I(t)=sY(t) $$ $$ \dot K=I(t)-δK(t) $$ With a given Cobb-Douglas: $$ Y(t)=Z(t)K^aL^{1-a} $$ $$ y(t)=Y(t)/L(t) $$ $$ k(t)=K(t)/L(t) $$ $$ y=...
3
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1answer
141 views

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, ...
1
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1answer
270 views

How to determine the Steady State of this model?

Consider the system of two equations: $$y_t=\beta\mathbb{E}_t[y_{t+1}+\gamma\cdot z_{t+1}]$$ $$x_t=\rho x_{t+1}+y_t$$ $$z_t=(z_0-Z_t)e^{-at}+z_T$$ Determine the steady state. The solution manual ...
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1answer
124 views

Evaluation around steady state for a specific DSGE Model

The following equations are taken from Ravenna, walsh: "Optimal Monetary Policy with Unemployment and Sticky Prices" (2011). (i)$$\frac{Z_{t}}{\mu_{t}} = w_t + \frac{\kappa}{q_{t}} - (1-\rho)E_{t}(\...
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3answers
541 views

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 ...
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1answer
498 views

Solow Growth Model. Steady State. Can someone explain please?

my lecturer is doing a rather poor job explaining what he's written down, so I'm wondering if someone would be able to explain the following graph for me? This is a part of the Solow-Swann Growth ...
3
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1answer
197 views

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 $&...
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2answers
2k views

Marginal Product of Capital in the Solow Model

In the classic form of the Solow Model: $$ Y=K^\alpha (AL)^{1-\alpha } $$ Describe circumstances in which the marginal product of capital could rise over time, at least for a temporary period. I've ...
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1answer
1k views

Solow Model, Growth rate of K/L and Y/L in steady state

I have been given the following setup: $$ Y=K^\theta (AL)^{1-\theta }$$ Where Y = Output, K = Capital, L = Labour and A = Productivity. $$ \frac{\dot{L}}{L} = n $$ $$ \frac{\dot{A}}{A} = g $$ The ...
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2answers
10k views

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 ...
3
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1answer
73 views

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^{-\...
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0answers
113 views

Log linearization

Consider some time series data $X=\{x_t:t\in[0,\infty)\}$. Define a steady state by \begin{align} x\in X:x_{t+1} - x_t = 0 \end{align} and the log deviation from steady state with \begin{align} \hat ...
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2answers
172 views

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}...
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2answers
94 views

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 ...
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2answers
196 views

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 ...