# Questions tagged [proof]

The tag has no usage guidance.

32 questions
Filter by
Sorted by
Tagged with
3k views

• 41
96 views

• 155
116 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 ...
• 977
484 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 ...
• 285
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 ...
71 views

### Proof of the Lucas' Cost of Business Cycles

I am trying to derive the parameter used by Lucas to measure the cost of business cycles, namely: derived in the paper "Macroeconomic Priorities". I already searched in several papers but I ...
1 vote
669 views

### Weak preferences and negative transitivity

Let $\succ$ be a binary relationship on the set $X$ such that, given any $x, y, z\in X$, if $x\succ y$: (Asymmetry): $\neg(y\succ x)$, (Negative transitivity): $(x\succ z) \vee (z\succ y)$. ...
• 113
1 vote
252 views

1 vote
109 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]...
• 11
1 vote
37 views

### Existence of best and worst lotteries with finite outcome set and IIA

In the context of expected utility theory, I want to prove that if the set of outcomes is finite and an agent has a rational preference relation over the set of lotteries, and if that preference ...
• 63
1 vote
27 views

### How to prove Kelly criterion maximizes wealth compared to other betting strategies, and how to generalize such a proof

The Kelly criterion approach to a betting situation basically involves maximizing the expected logarithm of one's wealth. The assumption is that maximizing the logarithm appears to inadvertently ...
• 111
254 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 ...
• 76
583 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 ...
• 151
77 views

### About Theorem 3.5 (The Finite-Approximation Theorem) in Game Theory: Analysis of Conflict by Roger Myerson

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 ...
• 325