# Questions tagged [mathematical-economics]

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

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### What is the economic intuition behind cross derivatives?

Suppose I have a utility function $u(c,l)$, where c is consumption and l is leisure. What does $u_{cl}$ mean in economic terms for example, or in general what is the economic meaning of cross ...
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### Bergemann and Morris information designer and decision rule concept

Taking a look in the paper of Bergemman and Morris in 2016, they refer to the desicion rule as mapping $$\sigma:\Theta\times T\to\Delta(A)$$ The explanation to understand the notion of it is given as ...
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### How do thresholded incentives influence behavior?

I'm trying to understand how incentives can change crowds in terms of their work performance. I have metrics describing said performance and I'm trying to see how introducing incentives might change ...
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### Comparative statics of the Ramsey model, the effect of a change in population growth on the steady state capital-labor ratio

In Acemoglu's book "Introduction to Modern Economic Growth" there is Proposition 8.3 which states that the impact of a change in the population growth rate on the steady state capital-labour ...
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### What's the origin of the naming of Euler equation in economics?

In Economics, Euler equation is: $u'(c_{t})=\beta Ru'(c_{t+1})$ What is the origin of the name of 'Euler' in this equation? I know that, in fluid dynamics, Euler equation is \begin{aligned}{D\mathbf {...
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### What are good sources for the economics of patents?

I am curious about how the stimuli patents exercise, upon innovation, may be counteracted by their slow down of the dissemination of technology. Reading suggestions will be very much appreciated. My ...
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### Repeated Games of Incomplete information set up and questions

The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration). The preliminaries of the model Formally, a repeated game with incomplete information is given by the ...
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### Perfect recall vs perfect monitoring

Following my previous previous post here, I would like to add another question. Is perfect recall the same with perfect monitoring? If not, what are their differences?
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### Perfect recall assumption

When we assume that the players can recall perfectly everything about the previous stages of a game, in essence we assume that they know the history path that they followed until they reached to some ...
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### How to define a dynamic programming problem in an incomplete information game?

How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
74 views

### Why are production functions linear in technology?

Economists often assume a production function of the form $Y = A f(K, L)$, where $Y$ is output, $K$ is capital, $L$ is labour and $A$ is technology. This form of production function can describe ...
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### How does this definition change when we introduce some kind of information?

In Heller et al, they use the Osborne and Rubinstein formal definition for the extensive form games with public information. However, the model can work with the same definitions in case all players ...
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### Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?

I am given $U(x,y,z) = x^\frac{2}{3}y^\frac{1}{3} + z$. I am asked to solve the following: (i) Prove the convexity of these preferences (convex, strictly convex or neither?) (ii) Solve for the ...
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### Understanding the properties of extensive form games

In Heller et al, they use the Osborne and Rubinstein formal definition for the extensive form games with public information. To some point they refer to the following two properties $P$ is a mapping ...
201 views

### Violation of Monotonicity of preferences

Hi I am reading Jehle and Reny in my master's course and I have come across a problem in one of the exercises. My instructor herself was a bit confused when a student gave her a counter-example and ...
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### Drawing a Probability simplex

There are 3 possible payoffs - \$4, \$9 and \$36. The utility function for these payoffs is$\sqrt x $. I have to find all the lotteries preferable over getting$9 with probability 1 in a probability ...
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### Constrained optimization problem written as minimax Lagrange

I am reading a note on moral hazard and it shows that a problem like $\max _{s(x)} \mathbb{E}[V(x-s(x))]$ s.t. $\mathbb{E}[U(s(x))] \geq \bar{H}+c\left(a^{*}\right)$ can be solved by setting up a ...
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### Gini coefficient of output per capita across regions

The Gini coefficient is widely used to measure the concentration of income in a population. Similarly, the Gini coefficient can be used to measure the concentration of economic output or population ...
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### Algorithmic game theory and decentralized exchange of information

An intresting topic that I want to understad has to do with the decentralized exchange of information among a network of agents, however there is not a specific theory to make such a mathematical ...
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### Tullock Contests and Multiple Equilibria

I am reading this paper on the existence of multiple equilibria in Tullock contests. The authors state on page 3 that "The additional restriction $(5\alpha_1-\alpha_2)-(\beta_1-\beta_2)>0$ ...
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### Application of vector calculus in economics

What are some relevant examples of the application of vector calculus in economics, apart from using gradients and Hessian matrices for optimization? I'm mostly referring to the topics and concepts ...
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### System of differential equations in economics and areas of interest

More than a question, I'm looking for suggestions of models of system of differential equations applied in economics or maybe in another area of interes. I have a research homework and I have to make ...
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### What can be considered as a "message"

As a sequel of some other questions that I have done for communication and information mechanisms with respect to the paper of Gossner I have a question for the signal function. Fix a finite set of ...
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### Bayes correlated equilibrium of Bergemann and Morris

The paper of Bergemann and Morris proves a theorem based on some foundations about the information sets and their expansions. I am trying to understand theorem one intuition, more precisely I cite the ...
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### Convex sets definition

I want to understand why do we have to define a function on convex set before we define concavity or convexity. https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/CVN/t#d:CvxSet I am ...
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### Providing an example in cooperative - games and coalitions

Here is the paper from chich I previously posted another definition here Definition of a $k-$strong Nash Equilibrium I am trying to construct an example to understand the idea of the following ...
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### Mechanisms of communication in game theory

In the spirit of the previous question that I have done, here considering the paper here I am trying to make the matching definition $2.2$ here. I will give two definitions and I would like to clarify ...
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### Definition of a $k-$strong Nash Equilibrium

Consider a game $G=(N, (A^i)_{i\in N}, (g^i)_{i\in N})$, $N=\{1,2,\dots,n\}$, $A=\Pi_{i\in N}A_i$ is the set of actions and $g^i:A\to \mathbb{R}$ is the payoff function. The latter can be extended ...