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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 function …

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 …

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 i …

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 …

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 $\epsilon$, …

I am self-studying the mathematical appendix of Microeconomic Theory (MWG). They defined a stable matrix as follows: Definition$\quad$ A matrix is stable if all of its characteristic values have nega …

I am studying Implicit Function Theorem and its application on comparative statics using Mathematics for Economists by Simon and Blume. Here is the question: Consider a pure exchange economy with two …

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 …

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 …

I am study infinite strategy set using Myerson's Game Theory textbook. The author stated the following theorem (Theorem 3.5) but did not prove it. I tried the proof, and would really appreciate it if …

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 ap …

Problem I am asked to prove the following result (MWG Exercise 2.F.5): The law of demand always holds if the walrasian demand function $x(\mathbf{p},w)$ satisfies the weak axiom of revealed preferenc …

In Microeconomic Theory by Mas-Colell, Whinston, and Green, the definition of monotone preference relations is given as follows: Definition 3.B.2$\quad$ The preference relation $\succsim$ on $X$ is m …

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 sys …

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 derivi …