Questions tagged [endogenous-growth]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3 votes
1 answer
52 views

Marginal and Average Cost in the Romer Model of Endogenous Growth

On page 124 of David Romer's Advanced Macroeconomics (5th Ed), he mentioned that for the Romer model, Because firms producing final output face constant costs for each input and the production ...
Tan2525's user avatar
  • 33
0 votes
0 answers
23 views

Final demand for CES nested in Cobb-Douglas production function

I am deriving the final demand for intermediate good $x_j$ for the following final producer's problem: \begin{equation} \max_{{ k_{t}, x_{j,t}}} K^{1-\alpha}X^\alpha - R_tK_t - \int_{0}^{N_t}p_{j,...
Ciz1997's user avatar
0 votes
0 answers
33 views

non-ponzi condition

What Is The Differences Between R(T) And R(S) In No-Ponzi Condition In Ramsey Growth Model?
Huy Lê Thanh's user avatar
2 votes
2 answers
238 views

The Solow growth model

I wonder why at the beginning sf(k(t)) is steeper than δk(𝑡), but at some point, it starts flatter than δk(t)?
Huy Lê Thanh's user avatar
2 votes
2 answers
227 views

CRS assumption in Solow model

Can you explain why does Solow growth model assume "constant returns to scale"?
Huy Lê Thanh's user avatar
1 vote
2 answers
71 views

Find the salary and interest rate in the $AK$ model

I'm trying to solve this exercise for Macroeconomics III (the course covers long-run growth models). Find the wage $w_t$ and the interest rate $r_t$ in the $AK$ model, i.e., the production function is ...
Nicolas Torres's user avatar
2 votes
1 answer
101 views

Present Value of flow of profits with constant interest rate

I'm studying Schumpeterian Models of Quality Ladders from the Barro's book (Ch.7). I have problems in getting the derivation of equation $(7.13)$ as follows The basic idea of those models is: when an ...
Maximilian's user avatar
0 votes
1 answer
49 views

How do I derive optimal tax on pollution causing intermediate products?

I am reading "The Environment and Directed Technical Change" by Acemoglu et al. (2012). I cannot understand how the optimal tax in \eqref{eqA10} is derived. $$\tau_t = \frac{\omega_{t+1} \xi}...
SirLaptop's user avatar
1 vote
0 answers
39 views

Algebra and interpretation of recombinant growth theory Weitzman 1998

I do not understand how Weitzman 1998 (https://scholar.harvard.edu/files/weitzman/files/recombinant_growth.pdf) arrives at the following expression (equation 5 in the above article). $$ \alpha[N(1)-1/...
yomath's user avatar
  • 43
4 votes
1 answer
237 views

How to use Leibniz Rule of integration to find interest rate in Expanding Variety model

I'm studying growth theory from Barro/Sala-i-Martin and I stumbled upon a problem where some more advanced level of calculus is required in chapter 6 (Models with Expanding Variety: p. 294 eq. 6.18). ...
Dario's user avatar
  • 75
2 votes
0 answers
42 views

Deriving a welfare function

I saw this in a paper (however, I cannot derive it): We define the growth rate of consumption as $g_{C, s} \equiv \frac{C_s}{C_{s-1}}$ and use $C_t=\left(\prod_{s=1}^t g_{C, s}\right) C_0$ to rewrite ...
Emmanuel Ameyaw's user avatar
0 votes
1 answer
220 views

Isoelastic demands and constant markup

Why if the monopolists face isoelastic demands, profit maximization(for monopolists) implies that each of them sets a constant markup over the marginal cost? ADD DETAILS: This is a common situation ...
John M.'s user avatar
  • 245
1 vote
0 answers
37 views

Brand Proliferation with Knowledge spillovers

I'm studying from the Gene Grossman and Helpman textbook (1993), the brand proliferation model with knowledge spillovers (Ch.3) I'm trying to understand the equilibrium dynamics of the model. In this ...
Maximilian's user avatar
1 vote
0 answers
60 views

Schumpeterian Growth paradigm

I'm working on a Schumpeterian R&D growth model, and I assume that the quality gap between a new machine and the replaced one, i.e. $\lambda$ is sufficiently large such that I have drastic ...
Maximilian's user avatar
1 vote
1 answer
94 views

Hamilton-Jacobi-Bellman equation

Let us consider the lab-equipment model developed by Romer with input varieties. The value of owning the blueprint of a machine of a variety $\nu$ is given by: And: denotes the profits of the ...
Maximilian's user avatar
0 votes
1 answer
120 views

Endogenous growth model with externalities

I have a following model of endogenous growth where each firm has the following technology; $$y_t=AK_t^{1-\alpha} k_t^{\alpha} n_t^{1-\alpha}$$ The production function above defines an externality. I ...
studentp's user avatar
  • 120
2 votes
0 answers
444 views

Question on Ramsey model with shock on technological level

I have a question on Ramsey Model. Consider the following one-sector, closed, representative household economy. I have the following Cobb Douglas production function in intensive form $$f(k)=Ak(t)^{\...
studentp's user avatar
  • 120
0 votes
2 answers
46 views

Technology as an endogenous economic variable

Most of the economic literature on technical progress either treats it as an exogenous variable, often as a stochastic shocks or without specifying the origin of technological progress. On the other ...
Davius's user avatar
  • 288
2 votes
1 answer
55 views

Broad capital in the AK model - derivation

I have difficulty with understanding how the AK model is derived from a one-sector model with physical and human capital. The interpretation of the AK model is that capital should be viewed broadly to ...
freakonomist's user avatar
1 vote
1 answer
33 views

Are the Solow residual and scale effects related?

On the one hand, "the cross country variation in output by inputs [is] termed the Solow residual" (Acs et al. 2014). (This also applies across time to single countries.) In my own words, ...
syre's user avatar
  • 121
5 votes
1 answer
260 views

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} &= ...
Dayne's user avatar
  • 1,725
1 vote
1 answer
70 views

Showing Growth rates are equal in BGP?

One feature of Balanced Growth Path is that growth rates are equal along it: Consider the following conditions: $y_t= Xk_t$ $y_t = c_t + i_t$ $k_{t+1} = (1-\delta)k_t$ From first equation it is easy ...
Kinno's user avatar
  • 155
2 votes
1 answer
77 views

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 ...
Friendlyperson2020's user avatar
0 votes
1 answer
96 views

Question on overlapping generations

My question is from over lapping generations Question is as follows I found that $$k(t+1)= \frac{\beta(1-\alpha)}{(1+\beta)(1+n)}A(t)k(t)^{\alpha}$$ How can I deal with A(t) to find the steady state $...
studentp's user avatar
  • 120
2 votes
0 answers
209 views

Capital accumulation equation in steady-state (OLG model)

So I was given a question to derive the equation for aggregate capital accumulation. $K_{t+1}$, and explain if the economy has a stationary steady-state with zero growth. The model is as follows, ...
tonissimoe's user avatar
1 vote
1 answer
140 views

Introduction of an asset tax in the AK model

Let's start by analyzing the family's problem with the imposition of a tax. Assuming a CRRA utility function: \begin{equation} U = \int_0^\infty e^{-(\rho-n)t} \cdot \left[ \frac{c^{1-\theta}-1}{1-...
Pedro Cunha's user avatar
1 vote
1 answer
114 views

Models with Learning by Doing and Knowledge Spillovers - Barro, Sala-i-Martin (2003)

Consider the model of endogenous growth with learning by doing and knowledge spillovers presented in Barro & Sala-i-Martin (2003), chapter 4, section 4.3, starting in page 212. In equilibrium, the ...
Pedro Cunha's user avatar
0 votes
1 answer
212 views

Why, theoretically, is economic growth exponential? [closed]

Despite the experimentally well-observed exponential nature of GDP growth, I've never actually seen a theoretical reason or "prediction" why it should be so. (Even if the answer is "...
Abhimanyu Pallavi Sudhir's user avatar
0 votes
1 answer
97 views

How to derive the standard euler equation from the Expanding Variety Model

In the standard expanding variety model where the representative household faces the following CRRA utility function $$ \int_{0}^{\infty} \exp(-\rho t) \frac{C(t)^{1-\theta}-1}{1-\theta}dt $$ and ...
Finalblue's user avatar
0 votes
1 answer
34 views

Wage Growth Rate in the R&D Model

I am trying to understand the R&D model and how to calculate the growth rate of wage in this model. There is no equation given, but it’s stated that : household income must equal total ...
randomname's user avatar
0 votes
1 answer
34 views

Endogenous Growth in the case of externalities (Learning by doing)

so for the Learning by doing model productivity is defined as $$A_t=BK_t$$. Inserting this into the optimum conditions leads us to the following:$$r_t=\alpha BL^{1-\alpha}$$ and $$w_t=(1-\alpha)B^{1-\...
randomname's user avatar
0 votes
2 answers
357 views

a question on the endogenous growth model

I have such a question on the endogenous growth mode”: In the macroeconomics literature there are various ways in which the growth process in the Ransey-Cass- Koopmans model has been endogenized. ...
mnm123's user avatar
  • 63
1 vote
0 answers
174 views

Estimating Endogenous vs Exogenous growth models

Exogenous economic growth models (mostly those that take technological progress, or change in TFP as exogenous and random) are rather easy to estimate econometrically. But how about endogenous ...
Rokis1990's user avatar
  • 151
3 votes
1 answer
158 views

Induced technical change vs. directed technical change

I am trying to get a better grip on the literature on directed technical change and induced technical change. In other words, I am trying to understand if these concepts are the same and used ...
london's user avatar
  • 1,990
2 votes
1 answer
53 views

How to prove that GDP grows at the same rate as consumption on Lab Equipment Model?

I'm studying the Lab Equipment Model (Barro-Sala-i-Martin, Chapter 6). I'm having trouble when trying to prove that every variables grows at the same rate as consumption. I was able to prove that $\...
Raul Guarini Riva's user avatar
0 votes
2 answers
89 views

Books on Technological Progress and Growth

I've done some google search for good, reader friendly albeit technical, books on technological progress/change and economic growth. However, I've not found what I want. If you are using or have heard ...
london's user avatar
  • 1,990
0 votes
2 answers
75 views

Decreasing labor force and GDP

I'm a bachelor student writing a paper on the effects of China's one child policy on future GDP. My professor told me to use growth models. However, I'm unsure which growth model I need to use for ...
DuEllier's user avatar
2 votes
1 answer
76 views

Comparative Statics on Balanced Growth Path

It would be a silly question. In a model, I have found the BGP (balanced growth path) for all key variables. As expected, these variables are constant variables ; $$\mu^{BGP}=\frac{\alpha+\rho+\pi}{...
optimal control's user avatar
0 votes
1 answer
67 views

Directed technical change, Acemoglu (2002) framework - trying to understand how an equation is derived

You may have read Acemoglu (2002) on the topic of directed technical change. I am reading a similar research paper, and I could not understand how the author derived the final equation using ...
london's user avatar
  • 1,990
1 vote
1 answer
2k views

Growth rate of variables on a balanced growth path (BGP)

Normally, in the very basic endogeneous model of growth. It is said that all variables grow at a constant rate. Let's take the basic capital accumulation ; $$\dot{K}=Y-C$$ If I write this in ...
optimal control's user avatar
3 votes
1 answer
160 views

Why do developing countries adopt 21st century technology, but stay behind in output per capita?

The economic growth rate of Latin America has been about 3% per year for decades; but if you have ever visited, many of the natives have: internet, smartphones, tomography, hybrid cars, etc. Why don'...
Fix.B.'s user avatar
  • 2,648
6 votes
1 answer
3k views

Infinite Horizon Transversality Condition

This question is an extension of Endogenous Growth: Balanced Growth Path with CRRA Utility however, this question asks about a specific concept used in that question, and I think it would be helpful ...
DornerA's user avatar
  • 1,568
4 votes
1 answer
712 views

Endogenous Growth: Balanced Growth Path with CRRA Utility

I've got a model of endogenous growth due to spillovers. $\textbf{Model:}$ $$K_t=\frac{1}{n}\sum_{t=1}^nk_t$$ In this model, $k_t$ is chosen by agents, and $K_t=\bar{k}_t$ (the average of all $k_t$). ...
DornerA's user avatar
  • 1,568