Questions tagged [mathematical-economics]

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

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3
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1answer
17 views

Expected payoff calculation difficulty in the Bayesian environment of Bergemman and Morris

Suppose that we have two states of the world equally likely to occur, and say $\psi$ is the common prior of the state $\theta\in\Theta=\{G,B\}$. The types of the players are given by the following ...
2
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1answer
59 views

Negative Definite vs Semi-definite Hessian - Sufficient vs Necessary conditions?

When a Hessian matrix is negative definite at a critical point then that critical point is a local maximum (Sufficient Condition). As per the calculus wiki: Link, when the Hessian is negative semi-...
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0answers
14 views

Dinamic economics, differential equiations [duplicate]

I'm investing for models of system of differential equations, that can be applied in economics. I have to make an analysis of the model, for an exposition. Now I'm trying to choose a model to present, ...
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12 views

Model economics with diffential equations [duplicate]

I'm looking for suggestions of models of system of differential equations applied in economics or maybe in another area of interes. I have to make an analysis of a model, now I'm in the process of ...
2
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0answers
37 views

Bayesian update in the beliefs about the signals

Suppose that we have tow states of the world $\omega_1$ and $\omega_2$, where $p(\omega_1)=p(\omega_1)=1/2$ and there are three different signals, $s_H,s_M,s_L$ that are equally likely to occur in ...
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0answers
10 views

Information acquisition problem and desing of information

I am searching some details about the information acquisition problem. I want to understand what this is about and where can I find the beginning of this literature. I think this problem is some kind ...
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0answers
23 views

Questions about the definition of a protocol

The following definition is from this paper about protocols of communications (definition $2.4$ in the paper). You can check the paper for more details and previous of my questions. $\textit{...
-1
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0answers
32 views

Choice under uncertainty with multivariate log normal distribution [closed]

I am currently studying for my entrance exams and saw this question in a past questions folder: Consider a decision maker with wealth 𝑤 > 0 and a strictly concave utility function 𝑢(𝑥) = −𝑒 −𝜆�...
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1answer
155 views

System of differential equations in economics and areas of interest

More than a question, I'm looking for suggestions of models of system of differential equations applied in economics or maybe in another area of interes. I have a research homework and I have to make ...
4
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1answer
84 views

What can be considered as a "message"

As a sequel of some other questions that I have done for communication and information mechanisms with respect to the paper of Gossner I have a question for the signal function. Fix a finite set of ...
5
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1answer
64 views

Bayes correlated equilibrium of Bergemann and Morris

The paper of Bergemann and Morris proves a theorem based on some foundations about the information sets and their expansions. I am trying to understand theorem one intuition, more precisely I cite the ...
0
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1answer
42 views

Convex sets definition

I want to understand why do we have to define a function on convex set before we define concavity or convexity. https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/CVN/t#d:CvxSet I am ...
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0answers
37 views

Providing an example in cooperative - games and coalitions

Here is the paper from chich I previously posted another definition here Definition of a $k-$strong Nash Equilibrium I am trying to construct an example to understand the idea of the following ...
3
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1answer
67 views

Mechanisms of communication in game theory

In the spirit of the previous question that I have done, here considering the paper here I am trying to make the matching definition $2.2$ here. I will give two definitions and I would like to clarify ...
4
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1answer
43 views

Definition of a $k-$strong Nash Equilibrium

Consider a game $G=(N, (A^i)_{i\in N}, (g^i)_{i\in N})$, $N=\{1,2,\dots,n\}$, $A=\Pi_{i\in N}A_i$ is the set of actions and $g^i:A\to \mathbb{R}$ is the payoff function. The latter can be extended ...
5
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1answer
133 views

Difficulty in understanding the notation related from probability theory with game theory

The question that I have is a little technical and it has to do with the notation and the combination between some mathamatical properties in the probability theory of information economics. Say $\...
3
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1answer
43 views

Existence of maximal element in a compact choice set

I have a compact subset of $\mathbb{R}$, $X$. An agent has a continuous, transitive and complete preference relation $\succsim$ over $X$. I am wondering whether there exists a $y\in X$ such that $y\...
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0answers
3 views

how to calculate whether a series is convergent or divergent? [migrated]

If a series is given for example 1 - 1/2 + 1/4-1/8+1/16-1/32+.... up-to infinity how to check whether the series converges or diverges? is there any particular formula?
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32 views

Von Neuman-Morgenstern utility theorem apply only to linear utility functions?

Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility ...
1
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1answer
45 views

Question on a passage from N.OKISHIO's Constant and Variable Capital

Sorry if this a dumb question, I am an undergrad economics student and am currently reading this paper from Okishio on the Marxist concept of Constant and Variable capital, my issue is on this ...
4
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1answer
124 views

Defining the set of strategies, mixed strategies and the simplex set

Suppose that we have a two players game, where $(S^i)_{i=1}^2$ denotes the set of pure strategies for each one. The set of mixed strategies of player $i$ is denoted by $\Sigma^i=\Delta(S^i)$ while $\...
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0answers
30 views

Strategy definition in an extensive form game

How a (pure ) strategy is defined in an extension form game with information sets? I would like to have both an intuitive and a formal definition. Thank you in advance!
6
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1answer
54 views

Proove that for every Nash equilibrium $\sigma^*$, the probability distribution $p_{\sigma^*}$ is a correlated equilibrium

This is a classic theorem in game theory, that is left as an excersice in my textbook. Can anybody proove it? I can not thing of anything excpet from the definition of the correlated equilibrium in ...
1
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1answer
25 views

What is the meaning of the support set in game theory?

What is the meaning of the support set in game theory? I have seen it, in many papers, however none there explains how did they find it or why did the define it in a specific way. I understand that ...
1
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2answers
66 views

Kronecker Product in Econometrics

I wondered if someone could explain the motivation for using a Kronecker product in econometrics. I understand that if we had two matrices, A + B, then the Kronecker would take each element from A and ...
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0answers
12 views

Does using different Analysis Methods give the same better alternative to choose between economic projects?

Will all analysis methods (PW-FW-AW-ROR-B/C) that we can use for determining project acceptability on an economic basis gives you the correct same-alternative for the same cash-flow always?
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2answers
108 views

Mathematically show that MC cross AC can only occur on upward sloping part of MC curve

Question as in title, does anyone know how to show it? with mean value theorem? I can prove that AC is minimised at MC=AC but I'm not sure how to show MC can only cross AC at upward-sloping point of ...
3
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1answer
61 views

Proof of Quasiconcavity of Utility Function

How can I show that the function $u(x_1,x_2)=(x_1x_2)^\alpha$ is quasiconcave, given $\alpha>1,x_i\geq0$? I managed to find the bordered Hessian, whereby $(-1)^1B_1=\alpha^2(x_1x_2)^{2(\alpha-1)}x^...
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1answer
658 views

How can I prove this?

I was reading a book on econometrics and I found this algebraic transformation and I don't know how I can get there.I would appreciate some help. $\sum_{i=1}^n (X_i-\bar{X})\cdot (Y_i-\bar{Y})=\sum_{i=...
4
votes
1answer
150 views

Pigouvian tax equivalent to Coasian payments

Consider an economy with two goods, $x$ and $y$. Suppose person a's consumption of good $y$ imposes a negative externality on person b. Person a's utility maximisation problem is $$\max_{x_a,y_a} \ ...
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1answer
41 views

Algebra for two period forecasting in AR (3) Model

I wondered if some folks could help fill in a knowledge gap for me with some time-series algebra please regarding the following AR (3): $$x_t = \phi x_{t-1} + \phi_2 x_{t-2} + \phi x_{t-3} + \...
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0answers
18 views

Event study on market revenue

I am interested in performing an event study. Can it be modified to assess the impact of an event/s on a market's revenue as opposed to the value of a firm? Thanks
5
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2answers
104 views

Olivier Gossner - Secure Protocols or How Communication Generates Correlation

The paper of Olivier Gossner in Security Protocols in 1998 has some definitions that confuse me too much. I will cite here these definitions and my questions and I hope someone is familiar with these ...
2
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1answer
83 views

Alternative way to calculate the symmetric BNE of the game

My problem. Consider the following auction for a single object. There are $n \geq 2$ bidders. They submit their bids simultaneously. The object is allocated to the player who submits the largest bid. ...
1
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1answer
59 views

Show that slope of MR (marginal revenue) is negative for monopolists

I want to show that the marginal revenue is negative for monopolists. We assume $P(Q)$ is homogenous of degree 1, so it is linear (affine, strictly speaking): $P(Q)=a-bQ$. As we know, $\frac{dP(Q)}{dQ}...
1
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1answer
33 views

Differentiation in a inflation tax calculation

everyone. I am studying Advanced Macroeconomics, by Derek Leslie, and I am having some troubles in understanding the result of a differentiation in the Chapter 1, section 5. This section approaches ...
1
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1answer
43 views

Why do we call certain linear (affine) demand curves "elastic" or "inelastic" even though PED varies along the slope of an affine function?

I get that PED varies along linear (strictly speaking, affine) demand curves in a way that for a demand function $Q(P)=\alpha - \beta P$: $$|\epsilon_D|=1 \iff \frac{\alpha}{2\beta}=P \land |\...
2
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1answer
74 views

Demand derivation in vertical differentiation with a bad characteristic

Today's question is about a variant of Tirole vertical differentiation framework. I am stuck thinking about the demand and profit function derivation where consumers can pick the level of $x$ at their ...
6
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1answer
135 views

GE with an intermediate good

intro I'm looking at a simple model with 1 consumer, 2 goods and 2 firms. I'm trying to get a price vector [p0, p1] that makes it work. By makes it work, I mean, ...
0
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1answer
68 views

How to get the condition of OLS mathematically?

From this discussion, I asked @tdm about the condition of OLS but I still cannot get it, and it is not easy to answer the mathematic equation in comment part so I want to ask here. One way to see this ...
1
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1answer
113 views

Why standard errors in country-level variables are higher than that in firm-level variables?

From this dicussion, the commentor said Lastly, firm fixed effects may absorb more variation and likely reduced the size of their standard errors. In practice, I also mainly see that the standard ...
0
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1answer
51 views

Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$

I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
1
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1answer
87 views

Why excluding intercept is dangerous if there is no literature back up in DID setting?

Recently, I run the regression for the generalised DID following this paper: $Y_{it}$ = $\alpha$ + $\beta$ $(Leniency Law)_{kt}$ + $\delta$$X_{ikt}$ + $\theta$$_t$ + $\gamma$$_i$ +$\epsilon$$_{it}$ (1)...
1
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1answer
23 views

What does "dependent and independent variables only vary at the ($g,t$) level mean?

From de Chaisemartin and D'Haultfoeuille 2020, p.2969 I saw an equation $D_{g,t}$ $=$ $\alpha$ + $\gamma_g$ + $\delta_t$ + $\epsilon_{g,t}$ $D_{g,t}$ is the treatment in group $g$ at period $t$ They ...
1
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1answer
47 views

What does expectation of $\varepsilon_{c,t}$ conditional on $_c$ mean?

From a discussion, I recieve a mathematic answer, I understand until one point This decomposition can always be made by setting $\delta_c$ to be the expectation of $\varepsilon_{c,t}$ conditional on $...
2
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2answers
111 views

Learning Economics in Three Dimensions

I am trying to teach myself microeconomics via video series. I have a fairly good mathematics foundation, currently studying Partial Differential Equations and having gone through all the prereqs you ...
3
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1answer
56 views

Current valued VS Present Valued Hamiltonian Differing Euler equations

I have been having some difficulties with recovering the same euler equation from the following optimal control problem when comparing the present valued hamiltonian to the current valued hamiltonian. ...
2
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0answers
40 views

Demand function for substitutes

I have a problem where my answer does not seem to be right anywhere. For the following set up: Budget constraint: $400=40x+20y$ Utility function: $u(x,y)=3x+y$ the problems asks to derive the demand ...
3
votes
1answer
56 views

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. ...
2
votes
1answer
53 views

Multivariate implicit differentiation (Samuelson, 1948)

I am studying "The Simple Mathematics of Income Determination", by Paul Samuelson (from book is called "Macroeconomia (artigos selecionados)", by APEC-CAEN. It is the 1st chapter ...

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