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# Questions tagged [mathematical-economics]

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

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94 views

### Maximization problem FOC and Euler equation

Can someone please help me with the Lagragian and the derivation of the following objective function ? Beneath I provide the objective function, the constraint and the Euler equation that results from ...
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### Economic Metrics (ROI, PP, NPW)

So I am doing this project, which includes in calculating the Economic Metrics for a profitability analysis. I have calculated Return on Investment (ROI), Net Present Worth (NPW) and Payback Period (...
135 views

### WARP implies completeness, transitivity and thus rationalizability. What is wrong with the statement?

Let $A$ be a menu and $R$ be a complete and transitive binary relation. Define choice correspondence generated by $R$: $$c_R(A)=\{x\in A|| xRy \ \forall y\in A\}.$$ Theorem (from Kreps 1988): for ...
33 views

### Afriat theorem for negative goods

GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...
71 views

### Symmetric Cournot equilibrium: suffciency without second order conditon

Let $q_i \in Q = \mathbb R_+$ denote the quantity produced by firm $i \in \{1,2\}$. Further let $\pi_i(q_1,q_2) = (1-q_1-q_2)q_i$ denote the profits of $i$. A Nash equilibrium $(q_1^*,q_2^*) \in Q^2$ ...
66 views

### What mathematical structure or formalism can be used for modelling strategic investment decisions of agents in the context of competition?

I'm trying to analyze the decisions of agents in investing scarce resource like time and money into developing their product/service/offering in the presence of competition. I need to know what kind ...
43 views

### Probability of the event knowing that I received no informations

First I want to thank you if you pay attention to my post. I apologize if it seems elementary to you, note that I searched a lot an answer before posting. I have a particular informational framework ...
228 views

### Is it possible to give, in economics, an example of a relation ( set of ordered pairs) that is not a function?

In mathematics, some relations ( sets of ordered pairs) are not functions. I know economists make use of functions. But do they also consider relations that are not functions. In which branch of ...
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186 views

### Equivalence of definitions of upper contour sets

Mas-Collel, Winston and Green's Microeconomic Theory (3rd editions) offers two definitions of the upper contour set: How can the equivalence between the two definitions be proved?
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### What model to use when defining a 20-year growth path in a developing country?

What economic growth model is commonly used for formulating a 20-year national development plan in a small open developing country?
48 views

### Constrained Optimization using Lagrangian method

The stationary points that we derive by solving the first order conditions of the Lagrangian are those points global optimum points or local optimum points?
28 views

### What is the reason behind the demand function of a perfect complement good?

so I know that usually the income curve is equal to: $$x_1p_1 + x_2p_2 = m$$ if we rearrange this equation we get that the demand for good one ($x_1$) is equal to: $$x_1 = \frac{m-x_2p_2}{p_1}$$ None ...
128 views

### What are eigenvalues and eigenvectors used for in economics?

In economic and econometric literature, i see references to eigenvectors and eigenvalues. Having taken my fair share of linear algebra and econometrics courses I have not really seen how exactly they ...
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### Dot over a variable, Neoclassical growth model?

Looking at the Neoclassical growth model, I have hard time understanding what dot over a variable mean? I know it is short for taking the derivative with respect to time, I don't understand the ...
67 views

### Indifference curves and equivalence classes

Last week in class, my professor described indifference curves in the context of modelling consumer choice with multiple goods. He defined a partial-ordering operator $\prec$ and an equivalence ...
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### Existence of the general equilibrium

In the proof of the existence of the Walrasian equilibrium, there is a map defined using the Max map. Why this map is defined in this way?I am reading " Microeconomics; Gravelle, Rees". On page 257 ...
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### Linearisation of the IS curve?

How to the IS curve linearised around the structural equilibrium?, what is the math behind it?
76 views

### Who was the inventor of Utility function?

To my knowledge, the idea of representing weak-order with a function dates back to Cantor. So my questions are: 1) Was Cantor the first person to rigorize these kinds of representation? 2) Were ...
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### Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve

I am reading Modern Microeconomics by Koutsoyiannis. In a Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve. Firm A produces half the total market demand to ...
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### Reference Request - Dynamic Optimization with More Than One State Variable

I would like to understand how to solve dynamic optimization problems involving more than one state variable and state equation (to apply to long-term economic models with more than one capital good). ...
26 views

### What is the “bequest condition” in a finite-horizon discrete optimization problem?

For a finite-horizon discrete time optimization problem, my textbook provides a condition called the "bequest condition", which I'm not familiar with. Specifically, where the state at time $t$ is ...
62 views

Show that u=a+bM-yM^2 represents a risk averter's utility function who is interested only in the mean and the variance of the state distribution of Income M. Can anybody send me the full solution. ...
28 views

### What data/factors/attributes do the professionals monitor in a top-down analysis on the macroeconomics?

I am learning to do top-down analysis on a number of sectors in the US equity markets. I have never done it before and I would appreciate it if some professionals can share their experiences with me. ...
23 views

### equality between 2 operations using mean [closed]

why when we do the following operation mean (10 ,20,30)= 20 is different from (mean(10,20)+30)/2=22,5 there are no equality between the 2 operations using mean ? why? thanks a lot in advance for ...
88 views

### Second order partial derivative and cross second-order partial derivative

I'm following a paper (Full text available here!) where at some point (pag.17 and 20) the author get the following derivative: \frac{\partial V}{\partial L}=Y-X\frac{dY}{dX}=\alpha X^{-\frac{c}{b}}...
Consider some consumer who consumes good $x$ and $y$. The price of $x$ is fixed to be $k$. The price of $y$ is $c(y)$. The consumer's marginal rate of substitution is given by $\frac{-x}{y}$. If the ...