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
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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
172 views

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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1 answer
171 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 ...
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
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1 answer
80 views

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
30 views

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
466 views

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
  • 33
6 votes
0 answers
5k views

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
791 views

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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1 answer
262 views

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
0 answers
27 views

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
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1 vote
1 answer
256 views

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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