Questions tagged [solow]

Referring to the Solow-Swan model of economic growth.

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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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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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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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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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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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Steady state Solow model with exogenous technological change

Consider the following question: So, assume the standard function for production: $$Y_t = A_t K^\alpha_tL^{1-\alpha}$$ where $L$ is fixed. Then, the growth rate of output is: $$g_Y \approx g_A + ...
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Alpha interpretation in Solow growth model

Consider the Solow model (without technology): $Y = F(K, L) = K^\alpha L^{(1-\alpha)}$ What's the economic interpretation of $\alpha$? Prove and argue the result. I see it as a share that goes into ...
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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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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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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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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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Capital stock depreciation rate, how to calculate?

I am trying to work out the depreciation rate using the following information, it is an extract from a longer data set on capital stock: Just wanted to find out what the rate of depreciation is for ...
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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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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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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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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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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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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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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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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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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 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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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 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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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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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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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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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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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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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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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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Solow model, time and steady state

Suppose we have a Solow model: $$ Y(t)=C(t)+I(t) $$ $$ I(t)=sY(t) $$ $$ \dot K=I(t)-δK(t) $$ With a given Cobb-Douglas: $$ Y(t)=Z(t)K^aL^{1-a} $$ $$ y(t)=Y(t)/L(t) $$ $$ k(t)=K(t)/L(t) $$ $$ y=...
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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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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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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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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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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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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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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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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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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 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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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 ...
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Growth accounting: technological progress grows at near zero rate

In a growth accounting exercise I backed out the time path of technical progress augmenting a factor. Annual growth rate of this factor saving innovation is very close to zero in the last few years. ...
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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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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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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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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 $...
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