15 votes
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Solow Model: Steady State v Balanced Growth Path

This is when the attempt at accuracy creates confusion and misunderstanding. Back in the day, growth models were not incorporating technological progress, and led to a long-run equilibrium ...
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10 votes
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"If $\lambda$ is greater than than 1, the system explodes." Why does the system explode?

Eq. (2.64) can be written as (at first order) $$ k_{t+1} - k^* = \lambda (k_t - k^*) \tag{1a} $$ Define the quantity $\kappa_t$ as $$ \kappa_t \stackrel{\rm def}{=} k_t - k^* \tag{2} $$ So that ...
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  • 1,206
9 votes
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Optimality of Zero Capital Taxation

There is quite a bit of work being done in that area. One very recent example is Straub and Werning's working paper "Positive Long Run Capital Taxation: Chamley-Juff Revisited." The point seems to be ...
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  • 9,157
6 votes

Optimality of Zero Capital Taxation

Ljungqvist and Sargent (2004). Recursive macroeconomic theory 2n ed. (ch. 15) present and review the issue. In the Concluding Remarks section, they mention two environments, where the "zero-optimal-...
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5 votes

"If $\lambda$ is greater than than 1, the system explodes." Why does the system explode?

A system is explosive if its coefficients are non-stationary. Stationary is an important property to have in dynamic models as it tells us that an equilibrium value is obtainable (which is important ...
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  • 7,715
5 votes

Solow Model: Steady State v Balanced Growth Path

Following the conversation with user @denesp at the comments of my previous answer, I have to clarify the following: the usual graphical device we use related to the basic Solow growth model (see for ...
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5 votes
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Prove the uniqueness of steady state

Rearranging the steady state equation $$ \overline{p}^{\alpha}=\alpha y\overline{p}^{\alpha-1}- \alpha\overline{p}^{\alpha}-\frac{a+1}{\sigma} $$ we get $$ (1 + \alpha)\overline{p}^{\alpha}=\alpha y\...
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4 votes
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Solow Growth Model. Steady State. Can someone explain please?

An axis is characterized not by the variable it measures, but by the unit of measurement. So an axis can measure any number of variables, as long as they are measured in the same measurement unit. In ...
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4 votes
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Solution Method for Infinite-Horizon Maximization Problem

Your first question (regarding constraints on the parameters) can be answered through first and second derivative analysis. In order to satisfy strictly increasing, we need $u'>0$ and to satisfy ...
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  • 1,548
4 votes

An Optimal Control Model: A Ridiculous Result for a Steady State

One general issue I see is that you try to include uncertainty in a framework developed for a deterministic setup. What you do is to use expected income in the equation of motion for human capital. ...
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3 votes
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Log linearising EUler equation

As you say the first step is to take log of both sides after that you are just applying the rules for logarithms and rearrange. For example: $$\ln (XZ)=\ln X + \ln Z$$ $$\ln X/Z= \ln X - \ln Z$$ $$\...
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3 votes

Marginal Product of Capital in the Solow Model

According to your calculations MPK is not increasing in $K$. The Solow model assumes $0< \alpha < 1$, thus $\alpha - 1 < 0$ and $K^{\alpha - 1}$ is decreasing in $K$.
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3 votes
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Solow Model, Growth rate of K/L and Y/L in steady state

If $Y = C \cdot X$ where $C$ is constant and $\frac{\dot{X}}{X} = g$ then we can solve for $\frac{\dot{Y}}{Y}$ as follows: $$ \frac{d}{dt} Y = \frac{d}{dt} C \cdot X = C \cdot \frac{dX}{dt} = C \cdot \...
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  • 15.9k
3 votes

Solution Method for Infinite-Horizon Maximization Problem

Your first question, if it's literally correct, is easy: The only way for $u'$ to be positive for c=0 is for p=1. if p =1 then sign($\phi$)=sign($\theta$) so that the product is positive. But, since $...
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  • 2,590
3 votes

Multiple equilibria: which one to select?

I'm not sure I follow the logic on that equation having infinitely many solutions and steady states. In any case, in what follows are some guidelines for equilibrium selection. It depends a lot on ...
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  • 10.4k
3 votes
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Constant to the power of t in steady state

If the variables are constant, everything in the equation is time-invariant, while $a^t$ will still grow or fall over time (unless $a=1$). This is a contradiction and no steady state exists, unless $a=...
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  • 479
3 votes
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Derive the Demographic Structure in the Steady State

I don't know the paper nor the notation, so I am just guessing here. I gues $N(a,t)$ is the number of agents of age $a$ at time period $t$. Let's follow the number of age $B$ accross generations: $$ \...
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  • 8,642
3 votes

Steady-state savings rate

$\delta = 0.02$ is depreciation. $p = 0.02$ is population growth. $g = 0.03$ is technological growth. $s = 0.14$ is the savings rate. $Y=0.5\cdot K^{\frac{1}{3}}\left(AN\right)^{\frac{2}{3}}$ is the ...
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  • 15.9k
3 votes
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Steady state equilibrium in Solow model with a convex production function

You only provide partial information. E.g., this production function is unusual; is anything else unusual? Is depreciation still linear in $k$? Is the rate of population growth constant? etc. If ...
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  • 26.6k
2 votes

Real Positive Eigenvalue, but Stable Dynamics

If you have are trying to discretize the continuous time model $$ \dot{\textbf{x}} = A\textbf{x}, $$ then in discrete time you will have $$ \textbf{x}_{t+1} = B \textbf{x}_t $$ but $A\neq B$, since $A$...
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  • 26.6k
2 votes
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Evaluation around steady state for a specific DSGE Model

I found the error in my derivation: I mistakenly supposet that the steady state of $p_t+1$ equals $\bar{\rho}$. I did not recognize that p was different from $\rho$ because of the poor quality of my ...
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2 votes

Taylor Series Approximation around steady state in Solow

The steady-state value $k^*$ must be a fixed point : $(1+g)(1+n)k^* = s(k^*)^{\alpha} +(1 - \delta) k^*$ Taking the difference between this equation and the dynamic one : $(1+g)(1+n)(k_{t+1} - k^*) ...
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  • 170
2 votes

Solow model, time and steady state

In the model with technological progress the capital per effective worker remains constant, implies that capital per worker grows at the rate of exogenous rate of technological progress. See Barro and ...
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2 votes

What does steady state mean?

Usually the term steady state is derived from the Solow Model and its derivatives that seek to explain long-term economic growth. The steady state is a state in which the growth rate of the economy is ...
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  • 1,262
2 votes

Would a zero-growth economy with zero-growth population still have the same GDP?

Smith pointed out that as wealth was growing in any nation, the rate of profit would tend to fall and investment opportunities would diminish. Source The first half of the sentence makes it ...
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  • 26.6k
2 votes
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Non-trivial steady state

Let's guess that the value function is of the form $a + b \ln(k)$. Then substituting for $V(k) = a + b \ln(k)$ in the Bellman equation gives: $$ a + b \ln(k) = \max_{k'}\left(\ln(k^\alpha - k') + \...
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  • 8,642
1 vote
Accepted

Difference between long run coefficient and non stochastic steady state coefficient ARDL model

yes, the term that you showed for the ALDR non-stochastic steady state: $$\frac{ \beta_1 + \beta_2 }{1- \rho_1 -\rho_2}$$ is long-run multiplier or sometimes also called long run equilibrium ...
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  • 43.4k
1 vote
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Overlapping Generations model: Social Planner solution

Start by writing the Lagrangian (as it sounds like you have already done): $$L=\sum_{t=0}^{\infty} \{\beta^t(\ln C_t^y + \ln C_t^o) + \lambda_t (C_t^y +\frac{C_t^o}{1+n} +k_{t+1}(n+1)-k_t-f(k_t))\}.$$...
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  • 595
1 vote
Accepted

Solow model golden rule with my exact answer

Let production function $$F(K_t,L_t)=K_t^aL_t^{1-a}$$ $$max[c^*=f(k^*)-(δ+n)k^*]$$ with respect to $k^*$ Then $MPK=a(k^*)^{a-1}$ So $k_G= (\frac{a}{(δ+n)})^{1/1-a}$ which is golden rule level of ...
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