6 votes
Accepted

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
  • 3,697
4 votes
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Dealing with integrals in econ models

The Lagrangian is the following: $$ L = \left(\int_0^1 C_t(i)^{1 - \frac{1}{\varepsilon}}di \right)^{\frac{\varepsilon}{\varepsilon-1}} - \lambda\left(\int_0^1 P_t(i) C_t(i) di - Z_t\right) $$ Let $\...
tdm's user avatar
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4 votes

How to handle multiple lagrange multipliers in a maximization problem?

When we allow for debt, somebody else does the lending. So our debt is an asset for somebody else. From the lender's point of view, a transversality condition arises, related to the holding of assets ...
Alecos Papadopoulos's user avatar
4 votes
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How to handle multiple lagrange multipliers in a maximization problem?

This is less than a full answer but hopefully will be of some help. A general observation is that complex optimization problems do not always have an analytical solution. So although you show a ...
Adam Bailey's user avatar
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4 votes
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Why do we omit the integral when deriving the f.o.c.’s in long-run growth models such as Romer (1990)?

The justification for this rule of thumb is the calculus of variations, specifically with the functional derivative. First, note that the problem is static, so for ease of notation I'll drop the ...
Wittgenstein's Poker's user avatar
2 votes

Revisiting development of Solow Model with no population growth and no technical progress

You can use the following results provided below to try and answer the problem yourself. Consider a Constant Returns to Scale(CRS) production function $F:\mathbb{R}_+^2\to \mathbb{R}$ Let $Y=F(K,L)$ ...
mynameparv's user avatar
2 votes

Lagrangian for the utility-mazimization of a household in a Menu Cost model, first order condition to Ci?

This can be solved using Feynman’s differentiation under the integral sign. By the chain rule, $\frac{d}{dC_i} [\int_{i=0}^{1} C_i^\frac{\eta -1}{\eta} di ]^\frac{\eta}{\eta-1}$ $ = \frac{\eta}{\eta -...
Nicolas Torres's user avatar
2 votes

Frameworks and models in economics

What you call framework would be probably more appropriately called paradigm in philosophy of science, following the terminology set up by Kuhn in his seminal work. There are paradigms or frameworks ...
1muflon1's user avatar
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1 vote
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Decoding Endogenous vs Exogenous - Parameter vs Decision Variable - and Independent vs Dependent

Am i correct? Most of the things mentioned are correct. Some things that are incorrect include: Making a difference between exogenous and independent and endogenous and dependent variable. Those are ...
1muflon1's user avatar
  • 56.4k
1 vote

Decoding Endogenous vs Exogenous - Parameter vs Decision Variable - and Independent vs Dependent

I will put things much more easy. What you presented is a a very simple utility constrained maximization problem. What is endogenous is what is determined within the model. The solutions for this ...
Tony's user avatar
  • 1,262
1 vote

Revisiting development of Solow Model with no population growth and no technical progress

To find the per-worker production function we need to divide the given production function with L i.e. $\frac{F}{L}$ = $$\frac{K^{0.3}L^{0.7}}{L}$$ $$y=\frac{K^{0.3}}{L^{0.3}} = k^{0.3}; k =\frac{K}{...
Aditya Agarwal's user avatar
1 vote
Accepted

Habit forming Model & State Variables

It seems that your transition equation is not standard. I took the liberty to change it like this: $$ \begin{align} &\max \sum^T_{t=0} \beta^t ( u(c_t) + \gamma u(c_{t-1}) ), \\ &\text{s.t. } ...
teddi's user avatar
  • 106
1 vote

2 intercepts in a probit model about WTO/GATT concessions?

The dependent variable is level of concessions, which takes on one of three values: $y_i \in \{\text{None, Partial, Full}\}$ If you know the ordered probit model, then you should see that a dependent ...
user18214's user avatar
  • 805
1 vote
Accepted

How do we know Solow has DRS and Harrod-Domar has CRS from the definitions of the models?

This is just assumption on the model. There are some functions for which you can mathematically say they always have constant returns to scale. For example, if $F(K,L)=AK^{0.5}L^{0.5}$ then we know it ...
1muflon1's user avatar
  • 56.4k
1 vote
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Model for how the shifting of industries affect job creation

You can find an economics model of endogenous job creation across different industries in "Acemoglu, D., & Restrepo, P. (2018). The race between man and machine: Implications of technology ...
Alalalalaki's user avatar
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