Questions tagged [mathematical-economics]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
34 views

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 ...
3
votes
1answer
42 views

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 ...
1
vote
0answers
19 views

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 ...
1
vote
1answer
55 views

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 ...
2
votes
1answer
59 views

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 {...
2
votes
0answers
7 views

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 ...
4
votes
0answers
41 views

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 ...
1
vote
0answers
27 views

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?
0
votes
1answer
30 views

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 ...
3
votes
1answer
46 views

How to set up the Hamiltonian for this utility maximization problem?

Consider a representative household who accumulates capitals, earns labour and capital incomes, consumes part of its incomes, buys bonds and pays taxes. The household maximizes its lifetime utility $$ ...
0
votes
1answer
22 views

Interpretation of an Interactive Dummy variable

I have the following regression, where I regress the consumption of gasoline on logarithmic variables. Meaning of the variables is: pnc=price index for cars pg=price index for gasoline, puc=price ...
2
votes
0answers
40 views

Mathematical proof of dynamic stability of equilibrium in international trade, with quantity adjustment

I am studying dynamic stability of neoclassical international equilibrium given in Giancarlo Gandolfo Economic Dynamics, but I am failing to understand an intermediate step, namely linearization of ...
2
votes
1answer
83 views

Comparative Statics: Income Effect

Much of this is setting up the problem. So if you're familiar it's likely best to start from the very bottom and work up if needed. The question is asking about the income and substitution effect. ...
1
vote
0answers
25 views

Definition of the space of a repeated game

I want to define the space of a stochastic game and it confuses me a lot, so I want someone to check please the space $\Theta$ that I define at the end and how could I define the sigma algebra of this ...
0
votes
2answers
47 views

Help with a (simple) log-linearisation

As a solution to an economic model, I end up with the following equation: $$L=\frac{\alpha f^{\epsilon}s\left [ 1-Ak(1-\alpha+\alpha f^{\epsilon}s)^{\frac{1}{\epsilon}} f^{-1} s^\frac {-1}{\epsilon}\...
1
vote
0answers
19 views

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 ...
2
votes
1answer
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 ...
0
votes
0answers
15 views

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 ...
3
votes
1answer
76 views

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 ...
2
votes
1answer
161 views

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 ...
2
votes
2answers
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 ...
2
votes
1answer
40 views

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 ...
2
votes
0answers
40 views

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 ...
1
vote
1answer
25 views

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 ...
4
votes
0answers
59 views

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 ...
1
vote
0answers
31 views

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 $(5\alpha_1-\alpha_2)-(\beta_1-\beta_2)>0$ ...
2
votes
1answer
70 views

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 ...
5
votes
2answers
71 views

What is the economic interpretation of $ \partial q / \partial p = - (1/p^2) w^T (D_w x) w $ in profit maximization?

Consider a profit maximizing firm that is perfectly competitive in both input and output markets. It takes $n$ inputs $ x \in \mathbb{R}^n_+ $ and produces $f(x)$ units of output, where $ f: \mathbb{R}...
2
votes
0answers
64 views

Mechanism design making the Government reveil its indiferrence price towards goods

In order to Tax non-monetary property and wealth the government sets an arbitrary price (they are not even personalized assesments) and often people transact below that price. I have bought and sold ...
2
votes
0answers
78 views

Show that the long-run supply curve of an increasing cost industry in perfect competition is upward sloping

Many intermediate microeconomics textbooks teach us that in perfect competition, the long-run supply curve of an increasing cost industry is upward-sloping. However, They usually give some hand-waving ...
1
vote
1answer
41 views

Help to understand a Log-linearization and subsequent Differentiation with respect to time

I was reading the following paper: https://www.jstor.org/stable/2999442?seq=1#metadata_info_tab_contents At one point there are a couple of simple passages that however I did not fully understand. In ...
1
vote
0answers
11 views

What is the difference between a communication mechanism and a protocol of communication?

What is the difference between a communication mechanism and a protocol of communication in mechanism and information design. Although most papers in the literature make this distinction, it is not ...
3
votes
0answers
38 views

Model the uncertain impact of a proposed policy by expected utility or other probabilistic approach

The impact of a proposed policy is often uncertain and subjected to randomness. As such, it seems natural to use probabilistic models. How to model the policy impact using the expected utility ...
3
votes
1answer
95 views

Expected payoff calculation difficulty in the Bayesian environment of Bergemman and Morris

Suppose that we have two states of the world equally likely to occur, and say $\psi$ is the common prior of the state $\theta\in\Theta=\{G,B\}$. The types of the players are given by the following ...
2
votes
1answer
103 views

Negative Definite vs Semi-definite Hessian - Sufficient vs Necessary conditions?

When a Hessian matrix is negative definite at a critical point then that critical point is a local maximum (Sufficient Condition). As per the calculus wiki: Link, when the Hessian is negative semi-...
0
votes
0answers
14 views

Dinamic economics, differential equiations [duplicate]

I'm investing for models of system of differential equations, that can be applied in economics. I have to make an analysis of the model, for an exposition. Now I'm trying to choose a model to present, ...
0
votes
0answers
12 views

Model economics with diffential equations [duplicate]

I'm looking for suggestions of models of system of differential equations applied in economics or maybe in another area of interes. I have to make an analysis of a model, now I'm in the process of ...
2
votes
0answers
42 views

Bayesian update in the beliefs about the signals

Suppose that we have tow states of the world $\omega_1$ and $\omega_2$, where $p(\omega_1)=p(\omega_1)=1/2$ and there are three different signals, $s_H,s_M,s_L$ that are equally likely to occur in ...
0
votes
0answers
10 views

Information acquisition problem and desing of information

I am searching some details about the information acquisition problem. I want to understand what this is about and where can I find the beginning of this literature. I think this problem is some kind ...
0
votes
0answers
23 views

Questions about the definition of a protocol

The following definition is from this paper about protocols of communications (definition $2.4$ in the paper). You can check the paper for more details and previous of my questions. $\textit{...
0
votes
1answer
163 views

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 ...
4
votes
1answer
84 views

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 ...
5
votes
1answer
67 views

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 ...
0
votes
1answer
42 views

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 ...
5
votes
0answers
40 views

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 ...
3
votes
1answer
74 views

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 ...
4
votes
1answer
44 views

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 ...
5
votes
1answer
136 views

Difficulty in understanding the notation related from probability theory with game theory

The question that I have is a little technical and it has to do with the notation and the combination between some mathamatical properties in the probability theory of information economics. Say $\...
3
votes
1answer
50 views

Existence of maximal element in a compact choice set

I have a compact subset of $\mathbb{R}$, $X$. An agent has a continuous, transitive and complete preference relation $\succsim$ over $X$. I am wondering whether there exists a $y\in X$ such that $y\...
0
votes
0answers
34 views

Von Neuman-Morgenstern utility theorem apply only to linear utility functions?

Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility ...

1
2 3 4 5
16