All Questions
Tagged with macroeconomics solow
72 questions
0
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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 ...
- 223
0
votes
1
answer
79
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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 ...
1
vote
1
answer
65
views
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 ...
1
vote
1
answer
61
views
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 ...
5
votes
1
answer
310
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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(...
2
votes
1
answer
151
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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) ...
- 21
2
votes
1
answer
130
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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_{...
- 25
2
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0
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150
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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 ...
- 430
2
votes
2
answers
253
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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}
...
- 430
2
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0
answers
44
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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 ...
- 21
0
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1
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49
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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 ...
1
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0
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123
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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 ...
1
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0
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61
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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: $\...
- 11
2
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2
answers
288
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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 $\delta k(t)$?
- 131
1
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1
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54
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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: ...
- 131
1
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1
answer
114
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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 ...
- 35
4
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1
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1k
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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
- 277
2
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0
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275
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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 ...
- 277
6
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1
answer
649
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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
3
votes
1
answer
613
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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
3
votes
1
answer
218
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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. ...
- 277
3
votes
1
answer
68
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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 - \...
2
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0
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80
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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 ...
- 121
2
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1
answer
583
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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 ...
user43302
0
votes
1
answer
29
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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
1
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2
answers
320
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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 ...
- 21
3
votes
2
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769
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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 ...
3
votes
2
answers
402
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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 ...
- 385
0
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0
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180
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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 $\...
- 1,817
5
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1
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314
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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} &= ...
- 1,817
0
votes
2
answers
271
views
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.
...
- 25
1
vote
0
answers
86
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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
0
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0
answers
71
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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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3
votes
1
answer
269
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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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0
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1
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130
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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?
- 11
2
votes
1
answer
76
views
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 $...
- 57
1
vote
0
answers
34
views
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 ...
- 11
2
votes
1
answer
247
views
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 ...
- 157
1
vote
1
answer
47
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 ...
- 87
1
vote
1
answer
124
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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-\...
- 87
2
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1
answer
608
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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 ...
- 107
1
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1
answer
323
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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
- 31
2
votes
2
answers
640
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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
- 31
1
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1
answer
520
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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:
$$MPL = dY/dL = d(ALf(k))/dL = Af(k) + ALf'(k) (-K)/(L^2 A) = A(f(k) - kf'(k)) = ...
- 95
2
votes
1
answer
858
views
Solow model and economic interpretation of $\dot{K}=sY(t)$
I am reading Robert Solow's 1956 paper, entitled 'A Contribution to the Theory of Economic Growth'. I am trying to understand the economic interpretation of the differential equation $$\dot{K}=sY(t),$$...
- 145
2
votes
1
answer
187
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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 ...
- 145
3
votes
2
answers
486
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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,...
- 145
1
vote
1
answer
50
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 ...
- 58.5k
-2
votes
1
answer
57
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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 ...
- 81
-3
votes
1
answer
40
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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 ...
