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4 votes
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Calculating Time to Balanced Growth Path

a) Your calculations are correct, but in order for consumption to be positive, so for $$ c_t=\bigg(\frac{R}{(\beta R)^{\frac{1}{\gamma}}}-1\bigg)k_t > 0, $$ you will need to additional conditions. ...
Giskard's user avatar
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3 votes

Balanced growth path in the Hicks neutral technology and CES function

The problem is that, as in most cases for the Solow model, we don't know an explicit analytical solution of the differential equation for $k_t$, the so-called fundamental equation of growth, and in ...
BakerStreet's user avatar
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3 votes

Proving a result In Jones (1999) "Growth: With or Without Scale Effects"

We know that $g_A = \dot{A}/A$ and thus $g_A = \delta L_A A^{\phi-1}$. Take logs of both sides of $g_A = \delta L_A A^{\phi-1}$ and differentiating with respect to time gives us $$ \frac{\dot{g_A}}{...
1muflon1's user avatar
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3 votes
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Proving a result In Jones (1999) "Growth: With or Without Scale Effects"

There is more than one way to derive the formula for $g_A$ with constant growth: the following is a way I find conceptually simple. Starting from your $g_A=\delta L_A A^{\phi-1}$, differentiate with ...
Adam Bailey's user avatar
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3 votes
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Why are we using exp(.) as the functional form in the household maximization problem inside the RCK model?

I guess you already know that $\exp(-\rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor $$\exp(-\rho t)=\lim_{m \to \infty} \left(1+ \...
Patricio's user avatar
  • 721
2 votes

Balanced Growth Path (Qualifier Question)

(That one can use the log-difference approximation for the growth rates, can be glimpsed by the fact that while the model apparently is set in discrete time, the log-evolution of technology is ...
Alecos Papadopoulos's user avatar
2 votes
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Balanced growth path with specific technology

Assume there is a solution where $ Y, K, C$ all have constant growth rates. Impose that solution on Euler and you will have $Y/K$ is constant i.e growth rates of $Y$ and $K$ are same. Use the ...
erik's user avatar
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1 vote
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Balanced Growth Path in a 3-Sector Economy

It turns out there was a mistake in the problem statement. The question asked that we rank the sectors along the balanced growth path, but only meant that $k_t$, $c_t$, and $A_t$ should be in balanced ...
Joseph Basford's user avatar
1 vote
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In Solow model, on the balanced growth path, why aren't wages zero?

The condition $$ f(k^\ast) = \frac{n + g + \delta}{s} k^\ast. $$ is an equilibrium condition which only holds at the value of $k^\ast$. As such, you are not allowed to take derivatives of both sides ...
tdm's user avatar
  • 12k
1 vote

Solow model response function

The direction of $\frac{\partial c^{*}}{\partial n}$ is not ambiguous. An easy way to show this is taking derivative of $c^*=(1-s)f(k^*)$ so that $\frac{\partial c^{*}}{\partial n}=(1-s)f'\frac{\...
Alalalalaki's user avatar
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1 vote

Proving a result In Jones (1999) "Growth: With or Without Scale Effects"

He is just saying that there exists some exponent, reflecting either diminishing or increasing returns to scale, theta. Research can have nonlinear marginal returns. Given that, as theta increases ...
user28027's user avatar
1 vote
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Wage Growth Rate in the R&D Model

income is total profit plus wage income, and the two are fixed in proportions I.e. $y_t = w_t + \pi_t$ and $w_t = \alpha y_t$ and $\pi_t = (1-\alpha)y_t$, where $\alpha$ and $(1-\alpha)$ are the ...
Grada Gukovic's user avatar
1 vote
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Can saddle path not go through the origin in Ramsey model?

I guess you already went trough the algebra below, but just for context, the problem you're trying to solve is $$ \max_{c}\sum_{t=0}^{+\infty}\beta^t u(c_t) \\ \text{s.t.}~~ f(k_t) + (1- \delta)k_t =...
caverac's user avatar
  • 1,216
1 vote

Comparative Statics on Balanced Growth Path

The approach is not correct, because $\mu^{BGP}$ is a result of underlying structural parameters. So to say "when $\mu^{BGP}$ increases..." immediately begs the question why it increases, which ...
Alecos Papadopoulos's user avatar

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