# Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

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### Elasticity of substitution

So, this is an economics question but the problem I have is a pure math problem I guess. So I have the following equation:f(x,y) this function have the elasticity of substitution(EOS): 1/(1-beta). a,...
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### What guarantees that endowed agents have non-zero prices in an Arrow-Debreu Economy

In my research I am trying to find minimal conditions to guarantee a quasi-equilibrium must always be a typical Arrow-Debreu equilibria in a rather specific production setting. This may be rather ...
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### Prove that the set $X = \{x \in R^L_+| u(x) \geq \bar u\}$ is closed

Prove that the set $X = \{x \in R^L_+| u(x) \geq \bar u\}$ is closed. Saw this statement in the textbook but I'm not sure how this is the case when we don't have any restrictions on $u(x)$ such as ...
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The classic literature refers to the problem where information asymmetry exists between an informed and an uninformed counterpart as the adverse selection problem, but how can we verify what kind of ...
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### Quasilinear utility: if $x \succeq y - ae_1$, does it mean $x + ae_1 \succeq y$?

Quasilinear preference is defined to be: $x \sim y \Rightarrow x+ae_1 \sim y+ae_1$ and $x + ae_1 \succ x$ with $e_1 = (1,0,0,...)$, Given a quasilinear preference, if f $x \succeq y - ae_1$, does ...
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### Supporting Hyperplane Theorem and quasiconcave utility function

My notes says that if $u(.)$ is strictly quasiconcave and differentiable, by the supporting hyperplane theorem, there exists $p >>0$ and $w \geq 0$ such that $x = x(p,w)$ $\forall x$. I am ...
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### Neoclassical Economic Growth Model Shadow Price for Discrete vs Continuous Time

I recently learned about the neoclassical growth model in both discrete and continuous time. The intuitive meaning of the shadow price for both cases is that it represents the value of one additional ...
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### What is the the return to scale of per capita production function?

If $Y=f(AL,K)$ is CRS, $a_k+a_L=1$ by the Euler Theorem. However, I wanted to know the return to scale of $y=f(1,k)$ (i.e. $Y$ divided by $AL$). I tried $z=p/AL$ , then $py=f(p,pk)$, differentiate w....
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### Questions regarding 'Efficient Trade with Interdependent Values' by Marek Pycia and Peng Wang,2015

This question is with reference to the paper 'Efficient Trade with Interdependent Values' by Marek Pycia and Peng Wang,2015(See here). At page no. 4 of the paper, the authors describe $v_i$ as the ...
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### Index of an Excess Demand Vector

Mas-Colell, Whinston and Green, in Microeconomic Theory (third edition), postulate the concept of an index for an excess demand vector, which is later used in the Index Theorem: A regular equilibrium ...
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### How do I calculate quarterly Sharpe Ratio USING geometric averages?

I am looking to calculate the Sharpe ratio using Geometric average. The issue is I don't understand how to find the standard deviation term. Any help would be greatly appreciated.
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### What is the difference between a growth shock and a productivity shock

In a RBC context, what I mean by growth shock is a total factor productivity shock that follows a stochastic trend $ln(a_t) = ln(a_{t−1}) + \gamma + \epsilon^a_t$. I.e. the technology $a_t$, has a ...
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### Derivation of demand function

Hello. I'm graduate student in Japan. This time, what I want to ask is how to solve the profit maximization problem using the image production function and derive the demand function. This ...
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### Envelope Theorem in Hopkins and Kornienko (2010)

This is from Hopkins and Kornienko (2010). In this model, $x$ is investments, $s$ is status, and $y=z-x$ is leisure, where $z$ is endowments. $x(r)$ is the optimal investment, and the relative ...
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### What experiment could I run in order to test the 'Independence of Irrelevant Alternatives' axiom?

I need some help in designing an economics experiment to test the IIA axiom. My understanding of it is if you rank A above B then if you introduce C or D, you must still always rank A above B in any ...
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### How to calculate payback period of the project?

In order to finish a technological product, it was spent 50000 dollars (for materials, salary). 500 dollars per month is needed for support of the project (will be spend for servers). This product ...
Define the CES function $q : \mathbb R_+^n \to [0,1]$ by \begin{align} q(x) = \left[\frac{1}{n}\sum_{j=1}^n{x_j^\frac{\sigma-1}{\sigma}}\right]^\frac{\sigma}{\sigma-1} \end{align} where \$x \in \mathbb ...