Questions tagged [solow]
Referring to the Solow-Swan model of economic growth.
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Solow model - max steady state output per worker vs max steady state consumption per worker
$$Y=K^{1/3}G^{2/9}(AL)^{4/9}\\\frac{\dot{A}}{A}=\frac{\dot{L}}{L}=0.01\\\dot{G}=tY-0.03G\\\dot{K}=0.2(1-t)Y-0.03K$$
So far, we have a system that shows a basic Solow model with public and private ...
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1answer
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Transitional Dynamics of consumption per capita in solow model
I can write the transitional dynamics of output per capita as follows
$$y=f(k)$$
Take its derivative with respect to time t
$$ \dot{y} =f’(k) \dot{k}$$
Divide it by $k/k$
$$ \dot{y} =f’(k) \frac{\dot{...
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How do I work with the growth accounting framework in a regression?
I am currently writing my master's thesis with the topic "The impact of digitalization on economic growth in China and Germany".
My idea is to take a technology such as Industry 4.0, IoT or ...
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Regression based on the Solow Model
If we have the following regression based on the Solow model:
log(yi) = β0 + β1 * log(si) + β2 * log(ni + gi + δi ) + ei
And we know that based on:
y* = 〖(s/(n + δ + g))〗^(α/(1-α))
log(y*) = α/(1-α) * ...
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1answer
36 views
Is this a total derivative - if yes, why minus
This is the beginning of the derivation of equation of motion from the Solow model (Romer, 2019):
My question is: is this the total derivative (w.r.t. ultimate source of change "t")? If yes,...
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1answer
31 views
Would some help me fill in missing steps from a textbook exercise left for the reader
Question: Suppose $C_t=(1-s)Y_t-\lambda G_t$ where $s>\sigma$ as in the basic Solow model.
Out of the government expenditure , proportion $\phi$ is invested in public capital formation. Hence we ...
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1answer
31 views
Would someone be able to help me solve capital per capita in the steady state (check my work)
Question: Suppose $C_t=(1-s)Y_t$ where $s>\sigma$ as in the basic Solow model. Solve for capital per capita in the steady state.
$Y_t=K^{\alpha}_tL^{1-\alpha}_t$
$Y_t=C_t+I_t+G_t$
$K_{t+1}=I_t+(1-\...
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1answer
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Matlab: Solow Model Convergence of capital
I am currently trying to create a while-loop which iterates the evolution of the capital stock until it converges on the n-th digit. As I am still quite new to Matlab I face a lot of problems. I would ...
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1answer
28 views
Solow model and a change in the savings rate
In the solow model why does an increase in the savings rate shift the investment curve instead of move along it? Intuitively not mathematically
Thanks
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2answers
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Why does a rise in the savings rate result in an increase in the capital stock intuitively?
I understand mathematically how it works. But what is the actual process intuitively.
Thanks
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1answer
71 views
How to take the derivative and show that MPL in the Solow model is equal to real wage w
I am taking macro course this Fall and my calculus is quite rusty. So in the lecture notes they derive the following:
$$MPL = dY/dL = d(ALf(k))/dL = Af(k) + ALf'(k) (-K)/(L^2 A) = A(f(k) - kf'(k)) = ...
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Could you guys recommend lecture notes or papers that show the step by step of the uzawa-lucas growth model?
I have to study the differences between the model of uzawa-lucas, solow and harrod-domar, so if you guys could reccomend me something to study the uzawa-lucas model, with an easy lecture notes to ...
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1answer
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Are business cycle fluctuations usually studied in a (New Keynesian) DSGE model, or can they also be studied in a growth model?
I wonder if business cycle fluctuations are usually studied in a (New Keynesian) DSGE model, or can they also be studied in a growth model?
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1answer
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Solow model and economic interpretation of $\dot{K}=sY(t)$
I am reading Robert Solow's 1956 paper, entitled 'A Contribution to the Theory of Economic Growth'. I am trying to understand the economic interpretation of the differential equation $$\dot{K}=sY(t),$$...
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1answer
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The Solow model and his 1956 paper
Reading through Robert Solow's 1956 paper, entitled "The Theory of Economic Growth", I was hoping to find his fundamental difference equation. I was wondering if the following equation is indeed that ...
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2answers
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“If markets are competitive, the rate of return on capital equals its marginal product, $f'(k)$ minus depreciation $\delta$”?
Consider Solow model with $Y=(AL)^{1-a}K^a$. Then output per effective labor is $y=k^a$ where $k=\frac{K}{AL}$.
"If markets are competitive, the rate of return on capital equals its marginal product,...
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In Solow growth model, increasing consumption drops production which should measure GDP?
Consider Solow growth model $Y=F(K,AL)$ where $A$ measures knowledge progress, $K$ is capital and $L$ is label. I have suppressed temporal dependence. I am going to assume $L$, $A$ grow exponentially ...
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28 views
Solow model: effect on a sudden fall in population? [closed]
my question is, what happens in the Solow model when a sudden fall in population happens? let's say a bomb killed many people.
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1answer
34 views
Is the steady state of $k$ enough to show $Y$ grows at the rate $n+g$?
To provide some context for the question: I was approached by a student needing help for a an empirical thesis based on Solow-Swan model. She had trouble solving the theoretical model she wanted to ...
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How to derive and draw phase diagrams: Ramsey-Cass Koopmans model
I am confused by how to construct phase diagrams. For instance, I have been given the following two equations from the Ramsey model:
\begin{align*}
\frac{\dot C}{C}=&\frac{1}{\gamma} (F_K(K) - \...
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How does identical capital-output ratios imply identical rental prices of capital?
In the context of the Solow model, I need to show that if two countries have the same capital output ratio then they have the same rental prices of capital (they have same production functions). I ...
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Which model gives a more accurate representation of growth?
Does the Solow model or the combined Romer - Solow model give a more accurate representation of growth?
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Steady state growth of output
In the long run Solow steady state, the growth rate of output in a country is g + n. If there is some other country with exactly the same properties of the first country and the same initial ...
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Solow growth model on firms level
Probably a silly question, but I just have to make sure. I am wondering whether it is acceptable to use the solow / solow-swan growth model to model the growth of firm instead of growth of an economy?
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1answer
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Attributing Labor Productivity Gains to Capital Deepening vs. Total Factor Productivity Growth
In a traditional Solow-Swan growth model, you can decompose growth in labor productivity (output/hour) into a component stemming from total factor productivity growth and another stemming from capital ...
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1answer
38 views
Looking for help with Solow Model Question [closed]
The question is this:
Suppose there is a production function of $Q=F(K, L)=\sqrt{K}\sqrt{L}$. Suppose that MPC=0.8 and the labor force is growing at a rate of 0.05 per year. Also labor force ...
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1answer
226 views
Data Set for Mankiw, Romer, and Weil 1992
I am trying to replicate the results of Mankiw, Romer and Weil 1992, and cannot seem to find the original data.
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2answers
102 views
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?
This question is in context of this problem I was trying to solve:
The answer given is (a). But I think the answer is (C). My arguments are as follows:
First, the golden rule level of capital ...
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1answer
195 views
Wages in Solow growth model with savings = 0
I am trying to understand the change of wage rate and rental rate in the Solow growth model with s = 0. It is clear that capital per capita will approach 0 (due to depreciation of capital). Also is ...
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Here's a question about the solow model [closed]
At first, I was confused by how y keeps increasing after depreciation exceeds savings, then I finally found what was truly bothering me. The fact that when depreciation exceeds savings, capital per ...
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1answer
71 views
Growth Rate of Solow Model
Conside the following Cobb-Douglas Production Function:
$$Y_t=\bar AK_t^{1/3}\bar L^{2/3}$$
The growth rate of per capita GDP for this equation in continuous time is $\frac{y'_t}{y_t}= \frac{1}{3K_t}$...
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1answer
272 views
The growth rate in the Solow model
Consider a very simple version of the Solow model with discrete time, a fixed population size and no technological progress (a fuller description of the assumptions is outlined here). Capital is at '...
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1answer
154 views
How to Calculate the productivity multiplier?
Given a Cobb Douglas
$Y_t = A (K_t^\alpha L_t^{1-\alpha}) $
$ K_{t+1} = sY_t + (1-\delta) K_t$
How do we get the multiplier on productivity to be equal to $ \frac{1}{1-\alpha}$?
I understand ...
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Solow Model - criticism of Harrod model
I have started out reading seminal paper of Solow - Solow Growth model. It starts out with discussing weaknesses in Harrod Domar Model, a simple model of economic growth which featured prior to solow'...
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1answer
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Solow model golden rule with my exact answer
In a perfectly competitive Solow economy with physical capital accumulation, population growth and a Cobb-Douglas production function, show that the “golden rule” steady-state would be reached if at ...
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Improve my solution: Question on solow model
There is a question about Solow growth and Ramsey model,
compared to solow model, the Ramsey model is better to explain growth patterns across countries because it predicts a slower convergence ...
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Solow growth model deriving solutions
I was reading a note on Solow model in continuous time, and it said we can derive K, C, and Y from the key equation. But the steps were omitted, and I have no clue with it. How can I derive these ...
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1answer
140 views
Sustainable growth in the long run [closed]
Suppose that, in addition to physical capital and labour, an economy requires a fixed factor and a non-renewable resource to produce the final good. Prove that an economy with these input requirements ...
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Trying to apply Solow model to the US econmy
In a textbook application I try to apply Solow model to the US economy. What will be a ballpark estimate of the saving rate and the depreciation rate?
Edit: To follow up, assume Cobb-Douglas with ...
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1answer
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How is the Solow residual measured?
In the Solow model, we have the Solow residual often referred to as the level of technology A.
More particularly : \begin{equation} Y(t) = [K(t)]^{\alpha} [A(t)L(t)]^{1-\alpha} \end{equation}
Here ...
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1answer
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Macroeconomic Measures of Human Capital
How exactly do you measure human capital for a given country and what numbers are included in that measure.
The reason why I ask is because im interested in simulating the Mankiw–Romer–Weil version ...
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1answer
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Was there a Role of Technology in Macroeconomic Models before Solow?
Was the role of technological progress formalised by Solow (1956) for the first time? or at least he provided the initial formal insight into the role of technological progress in economic growth?
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1answer
832 views
Solow growth model - analytic proof that Inada conditions imply steady state capital is increasing in the savings rate
Let's take the example of a generic Harrod-neutral (labor-augmenting) production function $f(k)$; all letters denote the growth rates they usually would. In the regular Solow growth model with the ...
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Effect of population growth on Solow steady state
My textbook says that:
Ratio of capital per capita to income per capita in the steady state is a positive function of s and an inverse function of η and δ. Thus, k*/y* is a constant. This means ...
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1answer
131 views
What happens to aggregate C, K, and Y when TFP increases permanently?
I was wondering what would happen to aggregate capital, consumption and output (i.e. K, C, Y) in the Solow model with constant population growth (i.e. n > 0) and no technological growth (i.e. a = 0) ...
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Basic Solow Growth Model: Stability Proof
I am reading through McCandless "The ABCs of RBCs" this summer to get a preview of what I need to know for the coming Fall semester. It did not take long to find a statement that I can easily accept ...
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1answer
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How to estimate a constant elasticity of substitution for a country in a solow model including human capital and scarce resources
For my thesis I was looking for some help due to the facts of my little knowledge of econometrics. I appreciate any help whether its directly dealing with my question or literature advice.
Basically ...
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1answer
472 views
Taylor Series Approximation around steady state in Solow
In my Advanced Macro script, the professor says take TSA1 of the following equation:
$(1+g)(1+n)k_{t+1} = sk^\alpha_{t+1} + (1-\delta)k_t$
where $g$ is technological progress, $n$ population growth, ...
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1answer
936 views
Taking the derivative of capital per effective unit of labor in the Solow model [closed]
I'm taking an intro macro course, and my calculus is pretty rusty. I'm going through some lectures notes right now where they derive the growth rate of capital in the Solow model like so:
I'm ...
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Growth regressions over 3-year periods; regressors in average or year values?
Say that I want to estimate a growth regression basically similar to the Augmented Solow Model one, except my dependent variable is not Y/L, but it's the average GDP growth over a 3-year period. As my ...
