# Questions tagged [proof]

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### Quasilinear Utility: Pareto Optimality Implies Total Utility Maximization?

I read that if we have quasilinear utility for all consumers, then any pareto optimal allocation maximizes the sum of utility levels of all consumers. That is: $\textbf{What we know:}$ 1)\quad u^i(...
746 views

### Basic Solow Growth Model: Stability Proof

I am reading through McCandless "The ABCs of RBCs" this summer to get a preview of what I need to know for the coming Fall semester. It did not take long to find a statement that I can easily accept ...
181 views

### Proof of Expected utility theorem with three outcomes

I am trying to prove the expected utility theorem with three outcomes. The expected utility with $n$ outcomes is rather cumbersome and long in the economics textbook Mas-Colell. But I was hoping that ...
760 views

### Equivalence of Definitions of Continuity of Preferences

We have two definitions of the continuity of preferences: Def 1: $\succcurlyeq$ is continuous if for any sequences $\{x^n\} \subset X$ and $\{y^n\} \subset X$, then $n \in \mathbb{N}$ such that, ...
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### Open Foundational Problems in Mathematical Economics

What are some open problems in mathematical economics which are treated as if they have been solved in economics papers? As an example, one of my teachers has previously pointed out to me that there ...
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### Prove all cost functions are concave in input prices and demand for inputs is downward

I've seen proofs that cost functions are concave of the form $C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$ although this neither feels convincing nor does it seem like a ...
Let $\succsim$ be a strictly convex and quasilinear preference relation. It's defined over, say, $\mathbb{R}^2_{+}$ and is quasilinear on good 1. So, $U(x_{1},x_{2}) = x_{1} + f(x_{2})$. How to prove ...