Questions tagged [mathematical-economics]

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

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About infinite strategy sets and $\epsilon$-equilibrium from Game Theory: Analysis of Confilct by Roger Myerson

I am studying infinite strategy sets using Myerson's Game Theory: Analysis of Conflict. On Page 143, he defines an $\epsilon$-equilibrium as follows: Definition For any nonnegative number $\epsilon$, ...
Beerus's user avatar
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Auction with independent private values - An example from Game Theory: Analysis of Conflict by Roger Myerson

I have difficulties understanding the equilibrium analysis of the following auction game: Suppose that there are $n$ bidders in an auction for a single indivisible object. Each player knows privately ...
Beerus's user avatar
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Complex Analysis VS Differential Geometry as signals/preparation for grad school?

I am an undergrad (in math and econ) interested in pursuing a PhD in the latter. I can afford a pure math elective this semester and I am torn between diff geom and complex analysis. Which one is more ...
keynesian geometer's user avatar
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27 views

Does the payoff in a future option contract include the price of the future contract?

This website has this diagram which shows the payoff as $0$ for $S_T\leq X$ or $S_T\geq X$ (depending on the position-option combination). But isn't the buyer/seller of the position down/up the ...
mjc's user avatar
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Understanding Duality between Individual and Collective Maximization in Macroeconomic Models

I'm currently studying macroeconomic models, specifically from the book "Recursive Macroeconomic Theory." In Chapter Seven, it is mentioned that some economic models involving firms and ...
jrudd's user avatar
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MCQ on income and substitution effects

Person A spends their income only on bread and cheese. Given a rise in the price of bread leaving income constant and the price of cheese constant, the consumer consumes less bread and less cheese. ...
secretrevaler's user avatar
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53 views

How do I show this function is a bijection?

Let $\geq$ be a partial order on a set $X$. For each $x\in X$, let $F(x)\equiv \{a\in X:a\geq x\}$ and $\mathcal{F}\equiv\{F(x):x\in X\}$. I want to show that $F:X\to\mathcal{F}$ is a bijection. First ...
Accept Cookies's user avatar
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Equilibrium of Perturbed Dollar Auction Game - An Example from Game Theory: Analysis of Conflict by Roger Myerson

I am studying game theory using Myerson's textbook (Chapter 3 - Equilibria of Strategic-Form Games, Section 3.6 - The Decision-Analytic Approach to Games). I have difficulties understanding and ...
Beerus's user avatar
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Design of a money skew economy (target: museums/libraries loan rotation sharing)

I was thinking about libraries and museums, and began wondering how such institutions might institute what I would describe as a "money skew economy." Skew in the math sense, of two lines ...
G. Putnam's user avatar
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Ramsey no ponzi condition

Please help me understand how to create these functions, sometime they use "t" denote, sometime use "r" denote that make me feel confuse. Function (17) and from (19) to (23)
Huy Lê Thanh's user avatar
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Ramsey model problem

Explain the no-Ponzi game condition throughout the function. Does the constrain function: also reflect include the No-Ponzi condition?
Huy Lê Thanh's user avatar
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Question About Stochastic Choice - MWG Exercise 1.D.5

I am studying microeconomic theory using MWG. I got stuck on Exercise 1.D.5, specifically part (c), but I would also like to have my part (a) and (b) checked by someone. Here is the exercise and my ...
Beerus's user avatar
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Cost Minimization

Guys in the following optimisation problem why are we not considering the partial derivate of K and L in the Lagrangian in the first two equations
user205152's user avatar
1 vote
1 answer
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direction of causality between Increasing returns to scale and economies of scale

Does increasing returns to scale cause economies of scale OR is it the other way around?
user205152's user avatar
3 votes
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Capital-Output Ratio using Nominal GDP and Nominal GFCF

I have this assignment which asks the following: "Compute the average capital-to-output ratio in Australia from 1960 to 2022. Explain how to compute the average ratio. (Hint: use the nominal GDP ...
Liam Gannaway's user avatar
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21 views

Cutoff rule-mechanism question

I was checking on this paper where they define some rule-mechanism that is called cutoff rule-mechanism. I do not really understand why is this useful and how is this defined. Any help would be ...
Oliver Queen's user avatar
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60 views

What is the most general category-theoretic description of a market?

In the history of economic theories, various formalisms of "a market" or "the marketplace" have been used to explain various facets of economic behavior, starting roughly with Nash ...
Corbin's user avatar
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About Proof of Theorem 21.3 in Mathematics for Economists by Simon and Blume

Background Information I am studying concave and convex functions using Mathematics for Economists by Simon and Blume. I have difficulties understanding their proof of the following theorem: Theorem ...
Beerus's user avatar
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The sufficient condition for unique interior solution in utility maximization problem

Suppose the utility function is continuous, differentiable, strictly increasing and strictly quasiconcave. Whether the utility maximization problem has unique interior solution? If not, is there any ...
23134's user avatar
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Determine Whether A Preference Relation Satisfies The Continuity Axiom - from Exercise 1.1 in Game Theory: Analysis of Conflict by Roger Myerson

I am self-studying game theory using Game Theory: Analysis of Conflict by Roger Myerson. Here is an exercise from the textbook. I tried it myself, but I am not sure if it is correct. I would really ...
Beerus's user avatar
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Quasiconvexity of the indirect utility function for Cobb-Douglas utility

I've recently started Mas-Colell's, Green's and Whinston's Microeconomic Theory. In section 3.D, the authors define the indirect utility for a price vector $p$ and wealth $w$ as the utility derived ...
chsk's user avatar
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Ramsey model condition

Why are transversality conditions and no-ponzi game conditions needed in the Ramsey model? And why do we assume that is a CIES utility function?
Huy Lê Thanh's user avatar
1 vote
0 answers
31 views

What is the relation between Blackwell's order and Stochastic Dominance order?

In Kamenica and Gentzkow (2017) as well as in Bergemann and Morris (2016) the notion of Blackwell comparioson of experiments is used to compare different information structures. I am trying to find ...
Oliver Queen's user avatar
3 votes
1 answer
45 views

Consumer theory with subproblem

Say the agent's problem is $$\max_{c,\{h\}, N}\{U(c, v(\boldsymbol{h} ; \boldsymbol{\theta}))+\lambda(w N-c)\}$$, subject to $\sum_{i=1}^{I} h_{i}+N \leq 1, \quad N \in \mathcal{N}$. Assume $U(c, v(\...
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How often (if ever) do currency exchange cross rates differ from actual rates?

Do major currencies' cross rates ever differ from their actual ('bilateral') exchange rates, and if so, how often does it happen in practice? I guess it would never happen (beyond, say, the fourth ...
stevec's user avatar
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About Characterization of Homothetic Function - Mathematics for Economists by Simon and Blume Chapter 20 Exercise 18(3)

I am studying homothetic function and got the following problem: Problem Determine whether the function $x^3y^6 + 3x^2y^4 + 6xy^2 + 9$ is homothetic or not. Here is my attempt. My Attempt I did it ...
Beerus's user avatar
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1 answer
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what to learn to write a comprehensive strong paper?

to write an excellent comprehensive paper, what topics and techniques must an economist learn? One of my former professors wrote a paper I read, there are theories, calculations, and empirical tests. ...
Volkan Veli's user avatar
3 votes
1 answer
80 views

Economic models that are useful to understand macroeconomics

I started to study economics. Since I majored in Mathematics, I'd like to learn the principles of macroeconomics through the analysis of a simple economic models (using equations). That's why I ...
rfloc's user avatar
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1 answer
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About Proof of Theorem 20.8 in Mathematics for Economists by Simon and Blume

I am studying homothetic functions using Mathematics for Economists by Simon and Blume. I am reading their proof of the following theorem: Theorem$\quad$ Let $u: \mathbb{R}_+^\mathbf{n} \to \mathbb{R}...
Beerus's user avatar
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1 answer
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About The Bayesian Conditional-Probability Systems in Myerson's Game Theory: Analysis of Conflict

I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his Bayesian conditional-probability system. The Bayesian conditional-probability ...
Beerus's user avatar
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1 answer
32 views

Showing that reward function is bounded (dynamic programing)

I have the following dynamic programming problem: $$\max_{\{x_t,y_{t+1}\}_{t=0}^\infty}\sum_{t=0}^\infty \beta^tu(F(x_t)-y_{t+1})\;\;\;\;\;\text{s.t}\;\;\;\;y_{t+1}\in\Gamma(x_t)$$ where $\Gamma(x)=\{...
manifold's user avatar
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2 votes
2 answers
223 views

The Solow growth model

I wonder why at the beginning sf(k(t)) is steeper than δk(𝑡), but at some point, it starts flatter than δk(t)?
Huy Lê Thanh's user avatar
1 vote
1 answer
51 views

Solow Model in disrectly and continuously

what is the differences between solow model in disrectly time and continuously time? Why in disrectly time function use the equation: k(t+1)=(1-δ)k(t) + sf(k(t)) and in continuously time function use: ...
Huy Lê Thanh's user avatar
2 votes
2 answers
137 views

CRS assumption in solow model

Can you explain why does Solow growth model assume "constant returns to scale"?
Huy Lê Thanh's user avatar
1 vote
1 answer
100 views

About Theorem 1.1 in Game Theory: Analysis of Conflict by Roger Myerson

I am self-studying game theory using Myerson's Game Theory: Analysis of Conflict. I got some trouble understanding his proof of Theorem 1.1, the Expected-Utility Maximization Theorem. The Theorem goes ...
Beerus's user avatar
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1 answer
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Prove Any Strictly Increasing Function is Equivalent to A Homogeneous Function of Degree 1 - Mathematics for Economists (Simon & Blume) Exercise 20.14

Question Proof that any function $f: \mathbb{R}^1 \to \mathbb{R}^1$ with $f' > 0$ everywhere is equivalent to a homogeneous function of degree one. My Attempt Note that all strictly monotonic ...
Beerus's user avatar
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1 answer
245 views

Quasiconvex and quasiconcave utility function

I saw that the model of the quasi-convex utility function is similar to the concave utility function and also the quasi-concave utility function is similar to the convex utility function. How can ...
Huy Lê Thanh's user avatar
0 votes
0 answers
29 views

Convexity preferences

What is the difference between convexity and strict convexity preferences? What is the difference between quasi-concavity and quasi-convexity? And is MRS still true in concave preferences?
Huy Lê Thanh's user avatar
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0 answers
19 views

Samuelson Consumption loan paper and Overlapping Generations

The famous Samuelson paper on consumption loan and interest rates is a bit odd in my opinion. I wanted to understand it a bit better. The paper outline 3 generations. Youth that produce 1 unit. The ...
Ramesh Kadambi's user avatar
3 votes
1 answer
55 views

When could value functions in Bellman equations be calculated explicitly?

Given the simplest form of a Lucas model, i.e., a Bellman equation given by \begin{align} J(x_t) & = \max_{c_t, x_{t+1}} \{ u(c_t) + \beta E_{\pi} [ J(x_{t+1})] \} \\ & \textrm{ s.t. } ...
Eddie's user avatar
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3 votes
1 answer
93 views

Continuity of preference

"A preference is continuous if for any $a,b\in X$ with $a\succsim b$ there are some neighborhoods $N_{\varepsilon}(a)$, $N_{\delta}(b)$ around $a$ and $b$ such that for every $x \in N_{\...
Huy Lê Thanh's user avatar
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0 answers
17 views

Moral Hazard in Teams. Deriving Nash Equilibrium with bonus paying sheme

I have a few mathematical problems with the paper Moral hazard in teams, by Bengt Hölmstrom 1982. Theorem 4 Denote the conditional distribution of $x$, given the action vector $a$, by $F(x, a)$ and ...
contracttheory's user avatar
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30 views

Value of information in the Moral hazard in teams context

I have a few mathematical problems with the paper Moral hazard in teams 1982 by Bengt Holmstrom, especially in chapter 3. (sufficient statistic) page 330 following The welfare problem can be stated as:...
contracttheory's user avatar
3 votes
0 answers
99 views

Generalization of Debreu's additive utility function $\sum_nu_n(x_n)$ with infinite number of commodities

I want to generalize: $\sum_nu_n(x_n)$. Here $x_1,x_2,..,x_n,...$ are commodities. There are infinite number of commodities: $n\in\mathbb N$ or $n\in \mathbb R_+$ The following not a candidate: $\...
High GPA's user avatar
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Estimation of learning model with finite horizon forward-looking individuals

I am stuck with the estimation of learning model where individuals are forward-looking in a finite horizon. Specially, a user is watching a TV program containing many episodes, and he doesn't know the ...
S.X's user avatar
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6 votes
2 answers
157 views

Integrate a sufficient statistic

I have a few mathematical problems with the paper Moral hazard in teams 1982. How do I get from (2) to (1) by integrating and why is the qualification necessary "for almost all" $$g(y,a)=h_i(...
contracttheory's user avatar
2 votes
0 answers
51 views

Habit formation ala Constantinides (1990)

Consider the following problem, from Constantinides (1990). \begin{align} V(W_0, x_0) \equiv \max_{c, \alpha} \mathrm{E}_0 \int_0^\infty e^{-\rho s}\gamma^{-1}[c(s) - x(s)]^\gamma \mathrm{d}s, \end{...
Wittgenstein's Poker's user avatar
1 vote
0 answers
179 views

Question About Non-Degenerated Constraint Qualification (NDCQ)

I am studying constrained optimization using Mathematics for Economists by Simon and Blume, and I have some difficulties understanding the Non-Degenerated Constraint Qualification (NDCQ). I would like ...
Beerus's user avatar
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2 votes
1 answer
119 views

Frameworks and models in economics

A framework is not a model of a specific system, but a way of formulating and studying a variety of systems. Classical mechanics, quantum mechanics and statistical mechanics are all really frameworks. ...
quanity's user avatar
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3 votes
1 answer
255 views

Does this utility function work?

I'm reading over some models and I found a paper in progress that uses this model $$U_i(c_i, n, \theta_i) = \log(c_i) + \log(n) + \theta_i$$ where $c_i \text{ and } n \geq 0$ , but when you consider ...
Hans Brecker's user avatar

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