# Tag Info

### Alpha interpretation in Solow growth model

I don't quite understand what you mean by "share that goes into capital", but the common interpretation is that $\alpha$ is the share of income/output spent on capital. You can show that the ...
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### Derivation of Solow Growth Model (Solow, 1956)

We have that: $$\dot K = s K^\alpha L_0^b e^{nbt}$$ Rewriting the differential equation gives: $$K^{-\alpha} \frac{dK}{dt} = s L_0^b e^{nbt}$$ Integrate both sides with respect to $t$ from $0$ to ...
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### What does "mass" mean in a Macroeconomic model?

In this example, "mass" means the same as "length". Let me try to explain it with a simple example. If you work in a continuous setting, you have an infinite number of agents, ...
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### How do you get to the formula L(t) = ln[L(0)] + nt on the Solow Model?

At any given time, $L(t) = L_0e^{nt}$ where $L_0$ is the amount of labor you start with, often normalized to 1, $n$ is the growth rate of labor, and $t$ is time. The idea here is that labor force ...
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### Economic growth in a DSGE model, despite mean-zero shocks

Yes, there are DSGE models that can be used for forecasting. These models typically have a particular kind of steady-state, which is, more precisely, called balanced growth path (BGP). On the BGP (in ...
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### Wages in Solow growth model with savings = 0

Let $$Q = F(K,L)$$ Assume a) $F(K,L)$ exhibits consant returns to scale. We need this to aggregate from the individual firms to the total. b) Price taking behavior and c) Profit maximizing ...
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### What happens to aggregate C, K, and Y when TFP increases permanently?

Take a look at the dynamics of the capital: $k_{t+1}=sA_ty_t+(1-\delta-n)k_t$. A sudden positive shock to TFP in period $t$ increases the capital stock of the next period $k_{t+1}$. So, there is no ...
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### If an economy has capital that is less than the golden rule level of capital, can we reach the golden rule without increasing the savings rate?

Yes the answer should be C. I have attached an image showing the variation with time of the variables $y$(per capita output), $c$(per capita consumption) and $i$(per capita investment). I am assuming ...
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### How is the Solow residual measured?

Below please find a portion of a lecture slide a professor of mine used last year. Please note that $\gamma_{\tilde{y}}$ denotes per-capita output growth, $\gamma_{\tilde{k}}$ denotes per-capita ...

### Alpha interpretation in Solow growth model

It represents two things: (1) the elasticity of output with respect to capital, and (2) capital's share of output. To show (1), just take the natural log of the production equation, and then take the ...

### Alpha interpretation in Solow growth model

Following Yorgos's alternative interpretation, (about $\alpha$ which shows the percentage change of $Y$ at $1\%$ change in $K$), one intuition may also be to log-linearize your production function. As ...
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### Why does a rise in the savings rate result in an increase in the capital stock intuitively?

The story in the other answer is not fundamentally wrong but incomplete and bit inaccurate. Saving does actually affect capital stock through investment in Solow model (assuming based on the Solow tag ...
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### Human Capital Vs TFP

Romer (1986): Increasing Returns to Long Run Growth Lucas (1988): On the Mechanics of Economic Development Romer (1990): Endogenous Technological Change Jones (1995): Time Series Tests of Endogenous ...
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### How do you get to the formula L(t) = ln[L(0)] + nt on the Solow Model?

Apparently equation (1.8) claims that the time derivative of the log of labor equals $n$ (some constant). So: $$\frac{\partial \log L}{\partial t}=n \qquad \forall t$$ It is straightforward to see ...
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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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### Steady state Solow model with exogenous technological change

To simplistically answer your question, use the following: $Y = K^\alpha (AL)^{1 - \alpha}$ In order to prove all three can be equal: We will assume that technological progress is labor augmenting (...
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### 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 ...
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^*) ...