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"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 Solow and RCK, we can find $A_t = (1 + g)^t A_0 \ \ $(or $A(t) = A(0) e^{gt}$ if in continuous time). $Y$ increases over time because $A$ increases over time. This ...


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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 modeled through standard Cobb-Douglas production function. For example, a classical production function is given by: $$ F(K,L) = AK^{\alpha}L ^{(1-\alpha)},$$ where,...


3

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 you do is you solve your model as usual, and then check if the solution (here the balanced growth path) satisfies the Transversality condition. The ...


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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 unique rule that maintains a balanced growth path $$\frac{k_{t+1}}{k_t}=\frac{c_{t+1}}{c_t} \implies c_t =( 1-\delta-g)k_t$$ (too much consumption, by the ...


3

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 notion of equilibrium/stability) 2) Growth rates are strictly positive (otherwise the economy would eventually vanish) 3) Growth rates are equal to each ...


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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 cutting-edge technologies used in manufacturing or service industries. However, there is a big gap between 'adopting' cutting-edge technology at that level and ...


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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 manuscript that he distributed online here.


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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 in order to review the basic Solow model and then chapter 3 to see how the model changes when accounting for human capital and endogenous technological growth. ...


2

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 government? Answer: Yes, of course. There are overwhelming literature on dynamic or static theoretical modeling of the effect of tax policy without introducing ...


2

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 suppose Cobb-Douglas is given like in Barro 1990 as: $$Y_i=AL_i^{1-\alpha} K_i^{\alpha}G^{1-\alpha} \tag{1}$$ Now for any given $G$ profit maximizing firms will ...


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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 first discussed (but not "microfounded") by Hicks (1932) and Fellner (1961). Yet, it was Kennedy (1964) who first proposed a formal model about endogenous ...


2

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 Growth Models These are all classic papers in this vein of endogenous growth and questions of cross-country convergence/divergence.


1

Is that derivation for $k(t+1)$ correct? Technically, you never reach the steady state, but only asimptotically as $t\rightarrow\infty$, but at infinity the $A(t)$ will also be infinite because it grows exponentially with time. I suspect that $k(t+1)$ should depend on $(1+g)$ instead of $A(t)$. Usually these models are expressed in units of effective labor, ...


1

The household side of this model is pretty standard. Denote $K(t)$ be household's assets at time $t$. Then the transversality condition (which is an optimizing condition, not a constraint), is $$\lim_{t \to \infty} [e^{-\rho t}\lambda(t) K(t)] = 0$$ where $\lambda(t)$ is the current value multiplier on assets in the Hamiltonian. Given the assumed form of ...


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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: $$\mathcal{H}:e^{-\rho t} \frac{C(t)^{1-\theta}-1}{1-\theta}+\mu(t)\left[Y(t)-C(t)-X(t)-Z(t)\right]$$ Taking the first order condition for this problem we get: $$\frac{\partial \mathcal{H}}{\partial C(t)}:e^{-\rho t}C(t)^{-\theta}-\mu(...


1

income is total profit plus wage income, and the two are fixed in proportions I.e. $y_t = w_t + \pi_t$ and $w_t = \alpha y_t$ and $\pi_t = (1-\alpha)y_t$, where $\alpha$ and $(1-\alpha)$ are the fixed proportions. For $y_{t+1}$ we have $y_{t+1}=(1+g_y)y_t$ and $w_{t+1} = \alpha y_{t+1} = \alpha (1+g_y)y_t = (1+g_y)\alpha y_t = (1+g_y) w_t$ and $\pi_{t+1} ...


1

You don’t explain what $w$ even is but I will assume it’s wage. The wage increases with the capital accumulation for several reasons. First, as the capital becomes more abundant the labor inputs become relatively more scarce and hence more valuable. Thus, also the price of labor relatively to capital should increase through higher wages. Second, in most ...


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When people talk about growth models, they usually mean some adaptation of the Solow model. It is a pretty ambitious task to take on this project as an undergraduate if you plan to estimate a growth model (it is ambitious for some PhDs). I would recommend looking at the one child policy using a non-econometric approach, and perhaps make reference to ...


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An obvious way to approach this would be to compare projections based on a China without the one child policy (pre 1979 pop growth rates) and on a China with the one child policy (post 1979 pop growth rates). Pop growth rates are constant but different in the two cases.


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The approach is not correct, because $\mu^{BGP}$ is a result of underlying structural parameters. So to say "when $\mu^{BGP}$ increases..." immediately begs the question why it increases, which underlying parameter(s) has changed to cause such an increase... assume it was $\epsilon$ that decreased. But in this case $g_k$ is not affected at all, so you see ...


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The price $χ_L(j)$ is 1! You only need to integrate a constant. That's why you have that equation. (See p. 789, second paragraph, when he normalizes it to 1)


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