Hot answers tagged

6 votes

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 ...
user avatar
5 votes
Accepted

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 ...
user avatar
  • 8,642
5 votes
Accepted

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, ...
user avatar
  • 840
5 votes

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 ...
user avatar
  • 923
4 votes

Basic Solow Growth Model: Stability Proof

For completeness, let me illustrate this in the continuous time framework. The Solow equation, in the simplest of cases, is $\dot{k} = s f(k) - \delta k = \phi(k)$ Then we have $\frac{\partial \...
user avatar
  • 141
4 votes

Data Set for Mankiw, Romer, and Weil 1992

Have you seen the GitHub Project Replicating Mankiw, Romer and Weil 1992? It seems to have both the data and a replication of the original results. For the curious, the paper is A Contribution to ...
user avatar
  • 15.9k
4 votes

"If markets are competitive, the rate of return on capital equals its marginal product, $f'(k)$ minus depreciation $\delta$"?

An answer along macro textbook lines is given by @1muflon1. A shorter answer is as follows. Consider an investor who borrows capital from household (who owns the capital, in growth models) to invest ...
user avatar
  • 2,569
4 votes
Accepted

"If markets are competitive, the rate of return on capital equals its marginal product, $f'(k)$ minus depreciation $\delta$"?

This is not proven in Romer but it is a well known result. To derive it mathematically you need to take the following steps: First, the capital as in Romer depreciates so the evolution of capital ...
user avatar
  • 43.4k
4 votes
Accepted

The Solow model and his 1956 paper

I will assume that you are talking about the Solow, R. M. (1956). A contribution to the theory of economic growth. The quarterly journal of economics, 70(1), 65-94. as to my best knowledge Solow did ...
user avatar
  • 43.4k
4 votes
Accepted

Matlab: Solow Model Convergence of capital

Since, I was urged to present an answer for didactic reasons to which I totally agree, I will provide the full set of corrections to avoid any ambiguity. ...
user avatar
4 votes
Accepted

Constant returns to scale and diminishing marginal returns in the Solow model

These two assumptions are not necessarily contradictory. Just check whether the assumptions are satisfied by any candidate function. For example, take $F(K,N) = K^{\alpha}N^{1-\alpha}$, with $\alpha \...
user avatar
  • 1,036
4 votes
Accepted

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 ...
user avatar
  • 1,036
3 votes
Accepted

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 ...
user avatar
3 votes
Accepted

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 ...
user avatar
  • 1,960
3 votes

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 ...
user avatar
  • 224
3 votes
Accepted

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 ...
user avatar
3 votes

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 ...
user avatar
3 votes

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 ...
user avatar
  • 1,405
3 votes
Accepted

Solow growth model - analytic proof that Inada conditions imply steady state capital is increasing in the savings rate

We want to prove that $$\frac{n+g+\delta}{s} > f'(k^*)$$ Replace the left hand side with the equivalent from the expression $sf(k^*)=(n+\delta+g)k^*$, and you get: $$ \frac{f(k^*)}{k^*} > f'(...
user avatar
  • 8,477
3 votes
Accepted

Basic Solow Growth Model: Stability Proof

For stability, we want $$\frac{\partial k_{t+1}}{\partial k_t}\Big|_{\bar k} <1 \implies \frac{(1-\delta) + \sigma A_0 f'(\bar k)}{1+n} <1$$ $$ \implies f'(\bar k) < \frac {\delta+n}{\...
user avatar
3 votes

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 ...
user avatar
  • 43.4k
3 votes
Accepted

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 ...
user avatar
3 votes
Accepted

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 ...
user avatar
  • 753
3 votes
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 ...
user avatar
  • 26.6k
2 votes
Accepted

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 (...
user avatar
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 ...
user avatar
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^*) ...
user avatar
  • 170
2 votes

Effect of population growth on Solow steady state

if the population growth rate grows, why could the capital and income per capita decreases This is basically asking "why does higher population growth lower the steady state capital per worker"? ...
user avatar
  • 8,477

Only top scored, non community-wiki answers of a minimum length are eligible