Questions tagged [solow]

Referring to the Solow-Swan model of economic growth.

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Derivation of Solow Growth Model (Solow, 1956)

In Solow's "A Contribution to the Theory of Economic Growth" paper, how do we go from this equation to such that Could you please give me a hint about that derivation?
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Solow model response function

Consider a Solow model without technological progress so that the steady state $k^*$ occurs at $sf(k^*) = (n+\delta)k^*$ where $n$ is population growth rate, $\delta$ is capital depreciation rate and $...
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How to draw a diagram like Solow model to prove growth rate in Harrod-Domar model won't converge?

Solow model defines income per capita function f(k)=F(K/L,1) with f'(k)>0 and f''(k)<0 and proves that there must be an intersection with (gL+gA+δ)k where growth rate converges. But it confuses ...
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What is a rest-function in a Solow model?

I am trying to better understand the Solow-Swan growth model and the golden saving rate. When searching around I came across a blog explaining the intuition differently. Instead of in the standard ...
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33 views

Economic growth in a DSGE model, despite mean-zero shocks

The DSGEs I've seen have steady-states, and mean-zero shocks. Can these predict growth in GDP / capital etc? Is this possible despite them being equilibrium models, or do you have to completely change ...
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Constant returns to scale and diminishing marginal returns in the Solow model

My introduction to economics course had a section on the Solow model which I'm revising for next year. I'm a little confused by two of the assumptions which our lectuer taught us are made by the Solow ...
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Human Capital Vs TFP

I'm interested in familiarizing myself with some of the intra-debates that have occurred over the years, having to do with Mankiw, Romer, Weil (1992) and Klenow, Rodriguez-Clare (1997). Some argue ...
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Solow model: Partial derivative of k* with respect to g

Given the solow model $sf(k)=(n+g+\delta)k$, written as $$F=sf(k^\star)-(n+g+\delta)k^\star=0$$ I am trying to find the partial derivative of k* with respect to n Here is what I've tried: I use the ...
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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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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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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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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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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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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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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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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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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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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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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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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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"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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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) ...