Questions tagged [comparative-statics]
The comparative-statics tag has no usage guidance.
24
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Ratio of two Jensen inequality
I have these pair of numbers
$ (a, b) = (\frac{4}{9}, \frac{1}{9}) $ and $(c, d) = (\frac{1}{2}, \frac{1}{6}) $. (Number mean nothing, just for illustration and simplification)
Note that - (a, b) are ...
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1
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How do I use total derivatives of an implicit function to solve this problem?
Suppose a consumer has a utility function $u(x_1,x_2)$, where $u_1>0, u_2>0, u_{11}<0,u_{22}<0,u_{12}=u_{21}>0$. The prices are fixed. The consumer's income comes from working and the ...
2
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2
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Question About Implicit Function Theorem and Comparative Statics - Mathematics for Economists by Simon and Blume Chapter 15 Exercise 32
I am studying Implicit Function Theorem and its application on comparative statics using Mathematics for Economists by Simon and Blume. Here is the question:
Consider a pure exchange economy with two ...
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Meaning of "everything else remaining the same"
Suppose in an economy, there is a representative firm, the government and a representative household who all have their individual budget constraints. The household maximizes its utility function and ...
2
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How to derive (mathematically and intuitively) the relationship between expected price level and natural rate of employment?
We know that
$ W = \mathbb{E}(P)f(u, z) $
, so that nominal wage $ W / P = (\mathbb{E}(P) / P)f(u, z) $
From Blanchard.
Furthermore,
$ W / P = 1/(1+m) $ (where m is defined as the markup on wages to ...
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Income and Substition Effect: Assumptions: Normality vs. Inferiority of Goods
A question concerning the income and substitution effect when the wage changes
Let us assume that the substitution effect leads to more less leisure as the relative price of leasure increases, and ...
- 11
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1
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99
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Total derivative evaluates to zero: problem while doing comparative statics
I am playing with a toy model version for my research and I have an implicit equation defining the equilibrium:
$$\phi = \frac {S}{NF(\phi(u-\eta)+\eta - c)}$$
where $S,N,u,\eta,c$ are parameters and $...
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1
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74
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Proof of a comparative statics result in a maximization problem
I am thinking about the following question.
Let $f(x,\theta)$ be a strictly concave real-valued function in $x$ and $c(x)$ be a strictly convex real-valued function in $x$, both $x$ and $\theta$ ...
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2
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1
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Comparative Statics: Income Effect
Much of this is setting up the problem. So if you're familiar it's likely best to start from the very bottom and work up if needed. The question is asking about the income and substitution effect.
...
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Comparison of two variables
I have a model where I have to compare the values of y(x) and z(x).
But expressions are complex and what I am getting is
$x= f(y(x))= \frac{\sin({y(x)}) + \sqrt{(y(x))^3}}{(\frac{y(x)}{1-y(x)}) ^{1/4}}...
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Super and sub modular games
I was trying to read up on super and sub modular games. I have started with basic survey papers like the one by Rabah Amir (2005). Research papers assume a lot of common knowledge (the papers that I ...
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330
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Optimal residential location and multivariate Frechet distribution
I was reading the paper "Housing Constraints and Spatial Misallocation"
by Chang-Tai Hsieh and Enrico Moretti.
First they define the utility function
$$ \ \ V_{ji}=\varepsilon_{ji}\frac{W_{i}...
- 165
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Comparative statics of a monopoly
Consider a profit maximising monopolist with linear demand Q(P*) and total production cost C(Q(P*)) who faces a per unit tax t. Suppose the slope of marginal cost is decreasing in some parameter, μ. ...
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1
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Muth-Mills Model
I am exploring the Muth-Mills monocentric city model covered in Brueckner's article.
It is given that consumers earn the same income $y$ and buy $q$ housing for a price $p$ at distance $x$ from the ...
- 327
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Comparative statics with multiple equations using calculus
I am currently learning a three market model of the economy, with the goods market, money market and factor market being in equilibrium respectively when-
$$Y=C(Y-tY)+ I(r) + (\bar G) + \bar{NX}$$
$$\...
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Why should $dp_2=dm =0$ in this problem?
I am studying Essential Mathematics for Economic Analysis and in chapter 12 problem 10 there is a problem that I can solve but I do not understand why the solution works.
The problem asks us to ...
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1
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Brueckner's basic urban model, comparative statics
I was reading through Jan Brueckner's "Lectures on Urban Economics" (2011), which is a "rigorous, but non-technical" explanation of various topics in urban economics. It was ...
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1
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156
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Comparative statics question with an application
In the state of Mexas, two politicians (Mr. BO, or "Politician 1" and Mr. TC, or "Politician 2") are competing intensely for a senate seat. The two politicians spend on advertising to increase the ...
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Topkis' Theorem
Suppose my optimization problem is stated as follows
$\max\limits_x f(x,t)$
$s.t.$ $g(x,t) \leq 0$
I am interested in finding the direction $x^*$ changes with the parameter $t$. Can someone ...
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What are some helpful online tools (databases, etc..) for economic analysts?
More specifically, I'm looking for a online database of US economic statistics that is regularly updated. Most of my searches result in older data, that is not particularly useful for what I need it ...
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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 ;
$$\mu^{BGP}=\frac{\alpha+\rho+\pi}{...
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285
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Converse in supermodularity and single-crossing
Suppose I denote $$f(x,t)=g(x,t)+h(x)$$ where $X\in \mathbb{R}$, $t\in [0,1]$ and $h(x)$ is any function.
I want to prove that if the single-crossing property holds in $f(x,t)$, then $g(x,t)$ must be ...
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Analyse the data of two responses while having two different scales
I am working on data analysis these days and stuck on analysis when I have to compare the two kinds of responses.
First, I have data on the self assessment, I have asked students to rate them on a ...
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331
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Do there exist 'comparative statics' for fixed points?
I have a basic question about comparative statics. In Wikipedia, it is mentioned that:
As a study of statics it compares two different equilibrium states...
What exactly is an equilibrium? ...
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