# 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 $\epsilon$, ...
65 views

### 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 ...
1 vote
46 views

### 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 ...
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 ...
67 views

### 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 ...
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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. ...
1 vote
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 ...
1 vote
43 views

### 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 ...
9 views

### 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 ...
23 views

### 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)
35 views

### Ramsey model problem

Explain the no-Ponzi game condition throughout the function. Does the constrain function: also reflect include the No-Ponzi condition?
41 views

### 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 ...
48 views

### 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
1 vote
68 views

### 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?
75 views

### 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 ...
1 vote
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 ...
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 ...
75 views

### 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 ...
1 vote
121 views

### 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 ...
104 views

### 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 ...
1 vote
58 views

### 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 ...
1 vote
82 views

### 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?
1 vote
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 ...
45 views

1 vote
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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 ...
1 vote
32 views

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### 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 ...