Questions tagged [real-analysis]

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Max and Min with $\leq$ and $=$ constraints. General questions

I wrote this question on Maths.stackexchange but perhaps this community suits better (?) I need to ask you for this question, which is a rather general one, in order to understand how to behave when ...
Numb3rs's user avatar
  • 101
2 votes
1 answer

Differentiability of value of convex optimization problem

Setup: Consider the problem $$ V(y) \quad = \quad \min_{x \in \mathbb R^N} f(x) \quad \text{s.t.} \quad g(x+y) \leq 0 $$ where $f$ and $g$ are convex functions and $y \in \mathbb R^N$ is a parameter ...
John Sturm's user avatar
6 votes
1 answer

Prove 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 ...
Hunger Learn's user avatar
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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 ...
Nav89's user avatar
  • 468
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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?
Carlos Werbock's user avatar
0 votes
1 answer

Indifference Curve Analysis [closed]

I would like to analyse how COVID-19 has impacted the aviation industry by looking at how the demand for airlines + holidays has fallen via an indifference curve analysis. However, I'm not sure where ...
Lucy Swift's user avatar
3 votes
0 answers

Proof of Criteria for Local Identification in Rothenberg (1971)

My question is regarding Theorem 1 (page 579) of Rothenberg (1971). It is associated with four assumptions given on the same page. But, I only have a question about a single step of the proof, so I ...
Derby's user avatar
  • 31
1 vote
1 answer

Budget Set- closed and boundedness

I am fairly new to economics, and we were introduced to budget sets, The professor mentioned that the budget set $B(p,w) = \{x \in R^{l}_{+}: px \leq w\}$ is non empty and closed - I could prove the ...
Doubts's user avatar
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6 votes
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Topological intuition to continuous preference relation

For a Microeconomics Course, we are going through MWG, and in the lecture we discussed the notion of a continuous preference relation. A preference relation $\succsim$ on a set $X$ is called ...
J. Dekker's user avatar
4 votes
1 answer

Concavity of Cobb-Douglass Utility Function on Non-Open set

My textbook argues that the Cobb-Douglass utility function $u=(x1)^a(x2)^b$ with $a,b>0$ and $a+b<1$ is concave on $R2+$ by computing the Hessian and showing it to be negative semidefinite for ...
Jacob Bak's user avatar
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Relationship between strictly convex preference and convex preference

Let X be a convex subset of linear topological space and let binary relation >= be a complete preordering. prove: If preference relation is strictly convex and continuous, then it is convex. Since ...
deepanshu's user avatar
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Calculating elasticity between terms in a regression equation

Given the following regression: $ln(w_i)=\beta_1+\beta_2age+\beta_3age_i^2+\beta_4Y_i+\beta_5T_i+\beta_6Mar_i+\epsilon_i$ I am asked to calculate the elasticity of wages with respect to age. Is the ...
Bob Charles's user avatar
1 vote
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What problems arise when the minimum wage is directly linked to the inflation rate?

For example if the minimum wage is 10, and the inflation for the year is 3%, then next year the minimum wage is 10*1.03 =10.30. the next year, inflation is 5%, so the minimum wage becomes 10.82. The ...
tuskiomi's user avatar
  • 111
1 vote
1 answer

Supporting Hyperplane Theorem and quasiconcave utility function

My notes says that if $u(.)$ is strictly quasiconcave and differentiable, by the supporting hyperplane theorem, there exists $p >>0$ and $w \geq 0$ such that $ x = x(p,w)$ $\forall x$. I am ...
Rainroad's user avatar
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