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

The Leibnitz rule for differentiation of an integral is a consequence of the fundamental theorem of integral calculus. A so-called integral function is defined as $$F(x) = \int_a^x f(t)dt\;\;\;\;\;\;\;...
BakerStreet's user avatar
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5 votes
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Marginal and Average Cost in the Romer Model of Endogenous Growth

The cost minimization problem (in general) is given by: $$ \min_{L_i} \int_0^A p(i) L(i) di \text{ s.t. } \left(\int_0^A L(i)^{\phi}\right)^{1/\phi} = y. $$ where $y$ is the output level. The ...
tdm's user avatar
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4 votes

a question on the endogenous growth model

"Endogenous Growth" is actually the short version of saying "Endogenous Technology Growth" Exogenous (Technology) Growth Models The rate technological progress $g$ is Exogenously given. In both ...
T. G.'s user avatar
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4 votes

Why, theoretically, is economic growth exponential?

There are two main theories of economic growth, the Solow-Swan growth model and Romer endogenous growth model. Both of these models allow for exponential growth. The economic output (GDP) can be ...
1muflon1's user avatar
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4 votes
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Infinite Horizon Transversality Condition

Your confusion comes from the fact that you treat the Transversality condition as a constraint, while it is a condition for optimality. So the formulation at the end of your question is wrong. What ...
Alecos Papadopoulos's user avatar
4 votes
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Endogenous growth model with externalities

Writing the production function in this way was most popularized by Lucas (1988) in 'On the Mechanics of Economic Development', though he used an externality on human capital. You can read through the ...
Fića's user avatar
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4 votes
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Present Value of flow of profits with constant interest rate

The mathematical steps to arrive from 7.12 to 7.13 are the following: \begin{aligned} & V\left(k_j\right)=\int_{t_k}^{t_{k+1}} \pi(k) e^{-\frac{v-t_{k}}{v-t_{k}} \cdot \int_{t_k}^v r(\omega) d w} \...
Don's user avatar
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4 votes

CRS assumption in Solow model

From an economic point of view, the assumption of Constant Returns to Scale can have several reasons, and they are not specific of the Solow model. I can quote what Solow himself says about Constant ...
BakerStreet's user avatar
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3 votes
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Human Capital Vs TFP

Romer (1986): Increasing Returns to Long Run Growth Lucas (1988): On the Mechanics of Economic Development Romer (1990): Endogenous Technological Change Jones (1995): Time Series Tests of Endogenous ...
quickhatch's user avatar
3 votes

Technology as an endogenous economic variable

As the other answer says there is whole literature on the subject. In fact this is not even new subject, in 2018 Romer was awarded Nobel Prize in economics precisely for his work on endogenous growth. ...
1muflon1's user avatar
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3 votes
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Hamilton-Jacobi-Bellman equation

$$V(v, t)=\int_{t}^{t+\Delta t} \exp \left(-\int_{t}^{s} r\left(s^{\prime}\right) d s^{\prime}\right) \pi(v, s) d s + \exp \left(-\int_{t}^{t+\Delta t} r\left(s^{\prime}\right) d s^{\prime}\right) V(v,...
Alalalalaki's user avatar
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3 votes
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Endogenous Growth: Balanced Growth Path with CRRA Utility

You have obtained $$ \frac{c_{t+1}}{c_t}=[\beta(\alpha+1-\delta)]^{\frac{1}{\gamma}} \equiv 1+g$$ and $$\frac{k_{t+1}}{k_t}=1+(1-\delta)-\frac{c_t}{k_t}$$ By equating you can show that there is a ...
Alecos Papadopoulos's user avatar
3 votes
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Growth rate of variables on a balanced growth path (BGP)

The concept of "balanced growth path" in economics incorporates three characteristics at the same time (related to the main macroeconomic aggregates): 1) Growth rates are constant (reflecting a ...
Alecos Papadopoulos's user avatar
3 votes

The Solow growth model

The answer: it is an assumption Solow-models usually assume that $f$ fulfills the Inada conditions, points 3. and 4. of which state $$ \begin{equation*} \lim_{k \to 0} f'(k) = \infty \\ \lim_{k \to \...
Giskard's user avatar
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2 votes
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Why do developing countries adopt 21st century technology, but stay behind in output per capita?

Probably if you go to almost any country in the world, however poor, you will find considerable use of relatively cheap cutting-edge consumer technology such as smartphones and some more expensive ...
Adam Bailey's user avatar
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2 votes

Books on Technological Progress and Growth

Daron Acemoglu's comprehensive book "Introduction to Modern Economic Growth" is a very good source of models and analysis related to technological change and growth. There is a copy of an earlier ...
luchonacho's user avatar
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2 votes

Books on Technological Progress and Growth

I'd recommend ADVANCED MACROECONOMICS Fourth Edition by David Romer. Its a textbook for advanced macroeconomics, however it covers the topics in a very precise way. Id recommend reading chapters 1 ...
EconJohn's user avatar
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2 votes

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

The way you would go about solving this problem is as the ChinG said is by setting up the Hamiltonian. In this case this is: $$\mathcal{H}:e^{-\rho t} \frac{C(t)^{1-\theta}-1}{1-\theta}+\mu(t)\left[Y(...
EconJohn's user avatar
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2 votes

Introduction of an asset tax in the AK model

I think your math is mostly correct but I have to admit that I am not used to AK models. A short answer for your main question: is it ok to introduce taxation in the model without including the ...
High GPA's user avatar
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2 votes
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Models with Learning by Doing and Knowledge Spillovers - Barro, Sala-i-Martin (2003)

We can show this by adding some public good to the model that will be financed by lump-sum taxes (which is also discussed in Barro & Sala-i-Martin (2004). Economic Growth 2nd ed. ch 4.4.1). So ...
1muflon1's user avatar
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2 votes
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Induced technical change vs. directed technical change

Directed technical change is the relatively recent name for what it was was previously called Induced technical change. Informal discussion about the endogenous direction of technical change was ...
luchonacho's user avatar
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2 votes
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Isoelastic demands and constant markup

Let's go for steps: Profit function : $\Pi(Q) = P(Q)Q -C(Q)$ Where $\Pi(Q)$ are profits and $P(Q)$ is the inverse demand function, i.e., the price at which $Q$ can be sold given the existing demand, ...
Maximilian's user avatar
2 votes
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Broad capital in the AK model - derivation

The production function $f$ is typically taken to be concave with $f(0)=0$. Taking the derivative of the function you have $$F(h) = f(h) - f'(h)(1+h)$$ where $h \equiv \frac{H}{K}$ yields: $$F'(h) = f'...
Fića's user avatar
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2 votes

Are the Solow residual and scale effects related?

Thus, my main question is whether the Solow residual and the absence of scale effects are actually two names/approaches for the same basic problem. No I do not think that is accurate. Solow residual ...
1muflon1's user avatar
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2 votes
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Find the salary and interest rate in the $AK$ model

It is difficult to provide definitive answer, if there is possibility that something is missing. it could be a trick question and $w$ could be zero given the assumptions, indeed if that is the ...
1muflon1's user avatar
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2 votes

The Solow growth model

Because $\delta k$ is linear function, so the slope of the function is always constant, whereas $sf(k)$ is typically nonlinear function exponential function like $f(k)=k^\alpha$ with $0<\alpha<1$...
1muflon1's user avatar
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2 votes
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Present Value of Profits Earned From the Discovery of New Ideas in the Romer Model

The growth rate of $w$ is $\frac{1 - \phi}{\phi}BL_A$. So: $$ w(s) = w(t) e^{\left(\frac{1 - \phi}{\phi}BL_A\right)(s-t)} $$ Similar: $$ A(s) = A(t) e^{BL_A (s - t)}, $$ and the discount rate from $t$ ...
tdm's user avatar
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2 votes

Defining endogenous vs exogenous, in layman's terms?

The terms 'exogenous' and 'endogenous' have to be understood relative to the scope of a model or a theory. Endogenous variables are those explained within the theory, while exogenous variables are not ...
E. Sommer's user avatar
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2 votes
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Social Planner vs Representative Household

If we assume that there is a single household (there are some subtleties in how one defines a representative household), then the Pareto optimality is the same as solving the planner's problem. The ...
Michael Greinecker's user avatar
1 vote

Technology as an endogenous economic variable

The whole endogenous technological change literature, a.k.a endogenous growth models, is about how various market factors affect entrepreneurs or the R&D sector conducting technological ...
Alalalalaki's user avatar
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