Questions tagged [proof]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2
votes
1answer
109 views

Can I assume utility functions strictly increasing?

I am required to show that if: $f:R^L \rightarrow R$ is a strictly monotonic function and $u:R^L \rightarrow R$ is a utility function representing a preference relation $\succsim$, then the function $...
1
vote
1answer
43 views

How do you establish uniqueness of a rational preference relation?

Going through a proof in Mas Colell and I am not understanding how (iii) shows uniqueness of the rationalizing preference relation. I understand that well $\beta$ is the power set so it contains all ...
0
votes
0answers
18 views

Beginner's Guide to Econometrics [duplicate]

I was wondering if you could guide me to a book that I can use as a starting point for preparing myself for graduate level econometrics. I will be applying for MA programs this fall and wanted a head ...
3
votes
2answers
340 views

Under what condition is a cost function strictly concave in prices?

Define the unit cost function as $$ c(w) = \min_{z\geq 0} w\cdot z $$ subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
3
votes
2answers
166 views

Prove that the profits of the firm weakly decreases with input prices

Prove that the profits of the firm weakly decreases with input prices. More formally, suppose that the firm has a production function f, so that its profit function is π(p, w) = max(x≥0) $pf(x) − w · ...
0
votes
0answers
30 views

Where can I find an endogeneity proof for bias by LLN?

It is intuitive that E[xe] is non-zero but the result E[xe]=sigma(x)*sigma(e)*corr(xe) seems odd. Please help point me in the right direction.
1
vote
2answers
143 views

Expected Utility with expected value and variance

I'm having trouble with a question from Ariel Rubinstein's book, Lecture Notes in Microeconomic Theory. It's the problem 2 from Problem Set 7. Here's the question: Show that the utility function $u(...
0
votes
1answer
137 views

Solution to maximization not Pareto efficient

In my economics class, we saw a proof that if an allocation $ ((\hat x_h), (\hat y_f)), h\in H$ (the set of households), $f\in F$ (the set of firms) is Pareto optimal/efficient, it must necessarily be ...
2
votes
1answer
321 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 ...
0
votes
1answer
288 views

Prove that $u$ is a utility function for $\succsim$

If X is finite, define this function $u : X \rightarrow \mathbb{R}$ by $u(x) = |\{z\in X:z \prec x \}|$. Prove that $u$ is a utility function for $\succsim$. Is it sufficient to prove that the ...
3
votes
0answers
96 views

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 ...
3
votes
1answer
3k views

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 ...
1
vote
1answer
103 views

Help with Monopolistic Competition Proof, Prove Love for Variety

I need some help with a proof. Assume η = 2 and there are just two goods. Verify that the following utility function exhibits Love for Variety tastes, show that: u(λa + [1 − λ]b, λb + [1 − λ]...
1
vote
1answer
114 views

Can one prove Pareto efficiency in an n-party system by showing all Pareto improvements between any two given parties are made?

I've made a proof of Pareto efficiency of a funding system that I've developed. There are effectively four types of actors. I've shown all Pareto improvements are made between any two given parties ...
3
votes
2answers
944 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 ...
2
votes
1answer
2k views

How to prove convexity + quasilinear preferences imply concave utility?

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 ...
3
votes
1answer
1k 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, $\...
8
votes
3answers
2k views

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(...