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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 ...
• 31.9k
Accepted

"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 ...
• 1,206
Accepted

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 ...
• 9,157

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-...
• 31.9k

"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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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 ...
• 31.9k
Accepted

• 43.4k

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 $K$.
• 26.6k
Accepted

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: $$\frac{d}{dt} Y = \frac{d}{dt} C \cdot X = C \cdot \frac{dX}{dt} = C \cdot \... • 15.9k 3 votes Solution Method for Infinite-Horizon Maximization Problem Your first question, if it's literally correct, is easy: The only way for u' to be positive for c=0 is for p=1. if p =1 then sign(\phi)=sign(\theta) so that the product is positive. But, since ... • 2,590 3 votes Multiple equilibria: which one to select? I'm not sure I follow the logic on that equation having infinitely many solutions and steady states. In any case, in what follows are some guidelines for equilibrium selection. It depends a lot on ... • 10.4k 3 votes Accepted Constant to the power of t in steady state If the variables are constant, everything in the equation is time-invariant, while a^t will still grow or fall over time (unless a=1). This is a contradiction and no steady state exists, unless a=... • 479 3 votes Accepted Derive the Demographic Structure in the Steady State I don't know the paper nor the notation, so I am just guessing here. I gues N(a,t) is the number of agents of age a at time period t. Let's follow the number of age B accross generations:$$ \...
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$\delta = 0.02$ 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 ...
• 15.9k
Accepted

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 ...
• 26.6k

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 $A$...
• 26.6k
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 ...