Questions tagged [solow]

Referring to the Solow-Swan model of economic growth.

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How do we know Solow has DRS and Harrod-Domar has CRS from the definitions of the models?

This may be a stupid questions as I am just studying undergrad economics honours but how do we know that the solow model has diminishing returns to its input and harrod-domar has constant returns to ...
3 votes
2 answers
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Are there common alternative models of economic growth, compared to Solow's model

I have been looking at the Solow growth model for many years, but after reading some of the Complexity Economics stuff, the Solow's model does seem way too simple for modelling important real world ...
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Question on the Uzawa-Lucas model

I am studying Solow growth model, I saw such a question. “ In the Uzawa-Lucas model set-up, how the growth rate of consumption changes following a natural disaster, which only destroys physical ...
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stone geary production and Multiple equilibria in a simple solow model: Do complex roots mean anything?

I have been looking at a simple solow model with stone geary production technology and law of motion of capital specified as follows: $$f(k_t)=(k_t-\bar{k})^{0.5}$$ $$k_{t+1}=(1-\delta)k_t+sf(k_t)$$ $$...
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Solow Model With Land as Factor

Given the production function: $$Y = K^\alpha (AL)^\beta R^{1-\alpha -\beta}$$. Where $L, A$ grow at exogenously given rates $n, g$ respectively. $R$ is land and is constant in supply and given that $\...
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Steady state equilibrium in Solow model with a convex production function

Suppose an economy is producing $e^k$ amount of output per capita if it uses $k$ amount of capital per capita. As the production function is strictly convex I am thinking the only steady state is at $...
5 votes
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Solow Model with DRS and Human Capital

This is a self study question. I am novice at this and have only basic knowledge of solving such problems. \begin{align} Y &= AK^\alpha H^\beta \\ \dot{K} &= s_KY - \delta K \\ \dot{H} &= ...
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How do you get to the formula L(t) = ln[L(0)] + nt on the Solow Model?

I understand the idea that the growth rate of a variable equals the derivative of the natural log of that variable, even so, i can't figure out how to get the following equation: L(t) = ln[L(0)] + nt. ...
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Steady-state VS equilibrium path

In solow model, you can find steady-state of transformed variable $\hat{y}^{*} =\left(\frac{s}{n+g+\delta+n g}\right)^{\frac{a}{1-a}}$. If $s$ goes up, $\hat{y^*}$ goes up, and we can say a higher $s$ ...
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Minimum wage in the Solow-Swan model [closed]

We introduce a minimum wage level such that the real wage may not be lower than this minimum. So, what is the effect of this policy for capital accumulation, saving rate and so on in the Solow-Swan ...
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Recent Research Topics in Macroeconomics (Hopefully Growth Theory)

Im in my last year as undergraduate and i have the opportunity to make a tesis, i have strong foundations in econometrics and macroeconomics but I don't know what the latest research on macroeconomics ...
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What does "mass" mean in a Macroeconomic model?

A Solow model problem I am trying to solve asks me to assume that the economy consists of identical agents of mass 1. I have never heard of this term before, what does this mean?
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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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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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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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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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1 answer
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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
2 votes
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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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1 vote
1 answer
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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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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?
1 vote
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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 ...
1 vote
1 answer
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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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0 votes
1 answer
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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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