Questions tagged [solow]
Referring to the Solow-Swan model of economic growth.
103 questions
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Labour saving technological change VS Capital saving technological change
I have been learning about technological change in relation with production functions(cobb Douglas) and isoquants and I'm very confused as the explanations can be somewhat vague and not clear enough.
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Endogenous vs exogenous variables
I know there were several questions asking about this topic with the definition along the lines of exogenous variables are fixed / independent variables / determined outside the model and endogenous ...
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Derivation in Robert Solow's "A Contribution to the Theory of Economic Growth"
I am attempting to go through the derivations in Robert Solow's 1956 paper 'A Contribution to the Theory of Economic Growth'. On pages 73 to 76 he goes through an example where the production function ...
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Data for Augmented solow growth model
I am writing my bachelor thesis currently on the growth determinants of Central and Eastern European nations in the 21st century. In it, want to look at how the neoclassical/Solow growth model fits ...
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Origin of terms Harrod neutral, Solow neutral and Hicks neutral
I just looked for the same question on the exchange but I didn't find anything, I even tried to look for the answer on Google but it seems it's not present. Could someone give me the origin of these ...
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balanced growth path clarification and why wage rate and consumption on BGP have same growth rate
We say the economy converges to a balanced growth path if all variables are growing at a constant rate. But what does it mean? For example in Solow model with production function $F(K_t,A_tL_t)$ where ...
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What would happen if we had decreasing returns to scale in the solow-swan growth model? Would there still be a steady state and perfect competition?
I understand with IRS we have explosive growth and a single firm would eventually dominate the market since MC < AC, and hence P < AC, so firms would leave the market. I am struggling to find ...
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Capital income growth equals labor income growth along the balanced growth path
I am trying to show that when technological and population growths are (non-negative) constants, the rate of growth of capital income and labor income in the steady state will be equal. Assume that ...
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Definition of wage in the Solow Model with Technological Progress
Consider the Solow model with technological progress. Suppose the production function is given by $F(K(t),A(t)L(t))$. The variables used are standard.
Questions:
Assuming the output price is ...
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Balanced Growth (Solow Model)
Sometime ago, I asked for the definition of steady state in the Solow Model. I came to the conclusion after reading the answer that the steady state is the sequence $\{(K(t), L(t), Y(t), C(t), w(t), r(...
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Solow Model: Steady state when there's population and technology growth
How is the steady state of a Solow Model defined when there's population growth and technological growth? The usual definition is to have $\dot{k} = 0$ (or $k_{t+1} = k_t$ in case of discrete time) ...
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Production function in Solow Model
I was studying about the Solow Model from Acemoglu. One of the properties of the production function $Y = F(A,K,L)$ is that it exhibits diminishing marginal products. That is, $F_{KK} < 0$ and $F_{...
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Derivation from Solow-type neoclassical growth equation?
In Chapter 6 of the 12th edition of "Economic Development" by Michael P. Todaro & Stephen C. Smith, an equation is introduced to illustrate the consequences of rapid population growth, ...
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Global Asymptotic Stability in the Solow Model - Rigorous proof
Consider the (simplified) Solow equation, which is a first-order non-linear difference equation:
\begin{equation}
k_{t+1} = sf(k_t) + (1-\delta)k_t
\end{equation}
where $s$ and $\delta$ are two ...
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Proving the Global stability in the Solow Swan Model
Consider a simplified version of the Solow-Swan model in discrete time, where technology is normalized to one and the population size is constant.
The Solow equation is given by
\begin{equation}
...
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Balanced growth path in the Hicks neutral technology and CES function
In an another post (Balanced growth path definition in the Hicks neutral steady state with technology), the problem of having a not stationary steady state in a Solow model with Hicks neutral ...
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Difficulties in translating my equations into R
I have calculated my own Solow model with energy as an input factor. I'm already pretty sure that the equations are correct but the problem I have are the results from the loop I build for the ...
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linear stability analysis of basic Solow model
I'm currently reading Romer's advanced macroeconomics, and encounter a question of linear stability of the model at the steady state.
We have the key equation $k'(t)=sf(k(t))-(n+g+\delta)k(t)$, where $...
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Solving an equation for k_t in a modified Solow model
I want to solve my modified solow equation for k_t to get the steady state. But since I also inclueded the marginal product for the price of Energy its pretty difficult for me to find a solution.
here ...
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Solow model with three input factors
My problem is that I want to construct a Solow model with three input factors; labour, capital and energy. But when trying to divid the equation by labour to get the per capita variables, it doesn’t ...
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how to derive that golden rule steady state = alpha in the solow model?
I have successfully derived the Golden Rule steady state for capital, but I'm struggling to derive the saving rate = equal to alpha (α) for the Golden Rule level. Have I made an error in my ...
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Durable goods in a (two sector) necolassical growth model
i want to add a firm to a neoclassical growth model that produces a durable good which it rents out in each period to the consumers.
Right now i'm using the following approach:
The firm maximizes: $\...
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In Solow model, on the balanced growth path, why aren't wages zero?
According to this primer on the Solow Growth model, wages are equal to $w = \frac{\partial Y}{\partial L} = A \left(f(k) - f^{\prime}(k)k\right)$.
In the balanced growth path we know that $\dot{k} = 0 ...
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The Solow growth model
I wonder why at the beginning $sf(k(t))$ is steeper than $\delta k(t)$, but at some point, it starts to become flatter than $\delta k(t)$?
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Solow Model in disrectly and continuously
what is the differences between solow model in disrectly time and continuously time?
Why in disrectly time function use the equation: k(t+1)=(1-δ)k(t) + sf(k(t)) and in continuously time function use: ...
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Solow-Swan Model - Diagram and Equation
In the Solow-Swan Model, why is the (n+δ)k curve drawn as a line from the origin? What is the economic intuition underlying the same? Also, what is the economic intuition underlying the fundamental ...
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Revisiting development of Solow Model with no population growth and no technical progress
Consider an economy descried by the production function: 𝑌 = 𝐹(𝐾, 𝐿) = 𝐾0.3𝐿0.7.
a) Derive the per-worker production function.
b)Assuming no population growth or technological progress, find the ...
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Three types of Neutral technological Change
Can you tell me why the isoquants changes as per pic below in the three cases of neutral technological change: i) Hicks neutral, ii) Solow neutral, iii) Harrod neutral
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Solow Model - speed of convergence
This is a question also for those with a good expertise in micro. For micro guys who wanna go streight to the question, just jump to equation $(1)$
I'm studying the Solow growth model.
Let's write the ...
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Balanced growth path definition in the Hicks neutral steady state with technology
In the Hicks neutral Solow Model with technology where $Y_t = A_t F(K_t,L_t)$, and labour and technology growths are held constant (exogenously), how is the balanced growth path defined?
I read that ...
user43302
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Solow model with multiple steady state equilibria
Consider the continuous-time Solow model without technological progress and with constant population growth rate equal to $n$. If capitalists don't save and the workers save a fraction $s \in (0,1)$ ...
user43302
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Solow model - concavity vs strict concavity
I'm studying the Solow growth model from the Acemoglu's book.
Consider the following standard assumptions:
The fact that $F()$ exhibits constant returns to scale means that F() is linear homogenous. ...
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Solow-Swan Model: Show that $\overline{Q_t} = A_t f(\overline{Z}) e^{gt}$ along the balanced growth path
Suppose a Solow-Swan model with $Y_t = F(K,AL)$ as the production function. Suppose the growth rate of $A$ and $L$ are $g > 0$ and $n > 0$ respectively. It is also given that $\dot{K} = sY - \...
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Elasticity of substitution between capital and effective labour
While going through the derivation of elasticity of substitution between capital and effective labour in economic materials for a Slow growth model, I found the following step there:
$\frac{\partial ...
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Transitional dynamics in Solow model
I am trying to understand the transitional dynamics of the Solow model. Let's take the case of forward movement (or when the capital-labour ratio $k(t)$ increases).
I have a bunch of questions ...
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Output growth in a Solowian economy
Consider a Solowian economy governed by the Cobb-Douglas production function. Further assume the owners of capital receive two-thirds of the national income and the labourers receive the remaining one-...
user43302
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Discrete time Solow model golden rule saving rate
I have a discrete time Solow model and need to derive the golden rule for the economy by setting maximization problem. How can I do that, if I can’t take derivative?
Note: required investment can’t be ...
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Solow model continuous time - definitions
Given that the per-capita capital $ k = \frac{K}{L}\ $ (total capita divided by labor force), and we want to find $ \dot{k}\ $, it seems that
$ \frac{\dot{k}}{k}\ = \frac{\dot{K}}{K}\ - \frac{\dot{...
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Solow model with population growth - proof of steady state level of capital per worker
Hello everyone, I am trying to obtain the requested solution as shown in the image (last equation of the image attached), however, after I calculate the law of motion, I only obtain only part of the ...
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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 ...
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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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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 $...
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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 ...
user40550
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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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