# Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

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238 views

### What is the concept of ordinal utility?

I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used. If that is so, how can one define a mathematical function for utility which gives a ...
44 views

### Anscombe and Auman Expected Utility

I would like to hopefully get some insights on the Anscombe and Aumann Expected utility. I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers ...
70 views

### Proving the existence of Nash Equilibrium using alternate approaches

Most of the standard books/papers/reading materials prove/state the existence of a Nash Equilibrium by appealing to Sperner's Lemma, or to Brouwer's/Kakutani's FPT. However, I've recently come to know ...
260 views

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### Kuhn Tucker optimization problem

Assume that the player I select $x_i \ge 0$ at constant cost level $c>0$ The payoff function for player i is $$v(x_i,t)-cx_i$$ where $t$ is technology parameter. The function v(.)is twice ...
290 views

### Question on subgame perfect equilibrium

Consider a world of complete information with two agents X and Y and two time periods 1 and 2. Person X only lives in second period. Person Y lives in 1st and 2nd periods both. X and Y are each ...
115 views

### Can we use hotelling's lemma as a rule of thumb when wage rate can vary?

Disclaimer: I've been doing some simulation with excel to see how Hotelling's Lemma behaves when allowing another parameter to vary. I did this by producing 150 randomly generated profit functions (...
357 views

### Modifying Hotelling's lemma: Is this valid?

Hotelling's lemma is stated as: $$\frac{\partial \pi}{\partial p}=y$$ knowing however that on the more basic level, output $y$ is determined by the input(s) $x(p,w)$,let the profit function be ...
106 views

### How is it economically responsible to destroy proprty which has value? [closed]

precursor: bitcoin.stackexchange.com/q/1851 How can it be economically responsible to destroy property which has value? If a property is destroyed (which is the right of the property holder in most ...
173 views

### Euler equation through tangency conditions

I am rather new to economics in general and to the Neoclassical Growth Model in particular and I was wondering if there was a way to get the Euler equation for consumption without using the Lagrangian ...
3k views

### Why is Roy's Identity so important?

I've been reviewing some of my microeconomics theory and have been reading up on Roy's Identity. Recall that Roy's identity is defined as: x^*_{i}(\text{p},m)=-\frac{\frac{\partial v}{\partial p_{i}...
259 views

### Correlated Equilibrium for Rock Paper Scissors

Consider the game of Rock, Paper, Scissors (RPS), with payoffs given as follows: Is there a correlated equilibrium in this game? Consider, for example the signal given to both players not to play ...
2k views

### Mixed strategy Nash equilibrium in 3x3 game

What is the MSNE for the following game? I think you can eliminate strategies $A$ for player 1 and $C$ for player $2$, as these will are weakly dominated by all other strategies. Then, the game ...
1k views

### In auction theory, why is my own valuation a random variable?

Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other ...
139 views

### Lotteries and expected utility

Suppose we have the following four lotteries: $L_{1}=[(1,\$1)]L_{2}=[(0.01,\$0),(0.89,\$1),(0.1,\$5)]$ $L_{3}=[(0.9,\$0),(0.1,\$5)]$ $L_{4}=[(0.89,\$0),(0.11,\$1)]$ If our agent says that he ...
I don't know how to compute the average income and the average utility for the second case. It is confused because I have to consider two densities $[0,0.5]$ and $[0.5,1.2]$.Can anybody tell me how to ...