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Questions tagged [mathematical-economics]

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

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6
votes
2answers
414 views

Which areas of mathematical knowledge are required for understanding different genres of theoretical economics literature (and at which level)?

I would like to know which mathematical skills are most important to understanding different types of theoretical economics literature. An ideal answer would list disciplines used for different '...
7
votes
3answers
131 views

Interchangeability between knowing an event obtains with probability 1 and knowing an event obtains with absolute certainty?

In the literature of interactive epistemology, for a player, knowing an event obtains with probability one and knowing an event obtains with absolute certainty are different. Is there a nontrivial (...
5
votes
2answers
3k views

Relationship between the Lagrangian and consumption euler equation?

I think that the best way for me to ask my question would be to start with an example. Suppose that consumers have a two-period horizon and their instantaneous utility is: $\:$ $U(C_{t})=ln \: C_{t}...
3
votes
1answer
123 views

How can I solve for total money spent if I use a non-constant MPC?

Background Today in my macroeconomics class my teacher taught us three concepts. The first is very simple: consumption $c$ is a linear function of national income $y$. Mathematically, $$c = My + b$$...
6
votes
1answer
279 views

Present value of a payment

Suppose I've just won 1'000'000 dollars in a game show. At the end of the program they tell me that they will pay me the prize as following: they will deposit in my bank 50'000 dollars every year for ...
1
vote
0answers
169 views

Finding the result when Demand is not given within an Economic Order Quantity question?

I recently came across the following problem on a set of past examination papers for a university module I'm currently taking: 'A video manufacturer produces 8500 video recorders on a continuous ...
2
votes
0answers
55 views

Test Series for Stationary Process

I want to apply grangers' Test between GSDP and Electricity production in the state. The state is a newly formed in the year 2000 and hence I have only 13 data points, as mentioned below Year | ...
3
votes
1answer
167 views

Random Utility interpretation

Can someone explain intuitively, the Block-Marschack Polynomials that completely characterize random utility.
7
votes
1answer
155 views

How to see that upper-semicontinuity and supermodularity are equivalent in a supermodular game context?

One requirement for a supermodular game $(I, \mathbf S, \mathbf u)$ is usually presented in two ways (e.g. in this note): For $i \in I$, $u_i$ is supermodular in $S_i$, when $s_{-i}$ is fixed, i.e. ...
8
votes
2answers
328 views

Does economic theory support the notion that the wealth of the wealthy is based on the poverty of the poor?

Almost any discussion about poverty and wealth and income inequality at some point includes arguments based on the premise that the wealth of the wealthy is causally related to the poverty of the poor;...
1
vote
1answer
85 views

For linear quadratic approximation of RBC model, why does matrix $P$ of value function $V = F^TPF$ has to be negative semi-definite matrix?

In http://www.compmacro.com/makoto/note/note_rbc_lq.pdf page 5, it is said that for value function $V = F^TPF$ (Bellman equation) $P$ has to be negative semi-definite matrix. Why does it have to be ...
6
votes
2answers
113 views

Comparative dynamics in forward-looking equation

I have set up and solved an optimization problem with time $t$ endogenous state variables, $\alpha_t$ and $\beta_t$ and choice variable $s_t$. After some manipulation, the first-order condition for $...
3
votes
1answer
202 views

Does rioting impair the economy?

In this article, the author looks at some of the indirect effects caused by the rioting in Ferguson, Missouri after the jury's decision not to indict the police officer. He explains that the rioting ...
8
votes
7answers
2k views

Macroeconomics Textbook on New-Keynesian models

I'm looking for textbooks that explain the New-Keynesian models, without taking shortcuts on the mathematics, that would go in depth on the derivations of the formulas. I appreciate rigour, and ...
3
votes
3answers
385 views

How to solve a linear forward-looking equation $x_t = \beta E_t[x_{t+1}] + k$ where $\lim_{t \to \infty} x_t = 0$ and $0<\beta < 1$?

How does one solve a linear forward-looking equation $x_t = \beta E_t[x_{t+1}] + k$ where $\lim_{t \to \infty} x_t = 0$ and constant $k,\beta \in \mathbb{R}$, $0<\beta <1$?
8
votes
1answer
177 views

Rationality and Common Belief in Rationality in Brandenburger & Dekel (1987)

One of the fundamental results in epistemic game theory is that the solution concept of correlated rationalizability gives exactly those action profiles that are compatible with rationality and common ...
15
votes
2answers
741 views

Complete Markets in Continuous Time

In the standard discrete time economies with a finite number of states, $n$, a complete markets economy is simply an economy with $n$ independent assets (Think Ljunqvist and Sargent Chapter 8). This ...
10
votes
3answers
893 views

What is the calculable effect of counterfeiting on an economy?

I'm curious whether one can numerically calculate the effect that counterfeiting has on an economy. As I understand it, counterfeiting essentially amounts to theft of the wealth of everybody holding ...
2
votes
1answer
84 views

Is there always at most one full-support extreme symmetric equilibrium?

Given a ($n$-player) symmetric game and two equilibriums $s_1,s_2$, is it true that if the support (the set of strategies with positive probabilities) of $s_1$ is identical to the support of $s_2$ ...
14
votes
4answers
2k views

Use of mathematics and imprecise definition of terms

As a postgraduate student of economics I've been trying to expand my mathematical "toolset". While doing so I've talked to engineers, physicists and mathematicians, many of which have disdained the ...
5
votes
1answer
158 views

Risk Premia in Continuous Time

Take some state variable $X(t)$, which follows the law of motion $$ \dot X(t) = f(t)X(t) $$ where $f(t)$ is a policy function, and determines the growth rate of $X(t)$. As a second shock, we have $\...
4
votes
1answer
366 views

Aren't all cost functions step functions?

Long Question: Overview: While I understand that over certain intervals (i.e. less than the width of the step), they may appear not to be because the step is outside of consideration, and over other ...
7
votes
2answers
416 views

Why not talk about utility functions on the surreal line when preferences are lexicographic, etc?

I've been reading about the surreal numbers out of curiosity. Though I don't totally understand them, I wonder why I don't see them used more often. Surreal numbers extend the real line to also ...
8
votes
2answers
921 views

When can one safely talk about decreasing marginal utility?

One thing I hear a lot is talk of decreasing marginal utility—the idea being that additional units of a good become progressively less attractive the more units of that good one has already. However, ...
21
votes
2answers
26k views

How can I obtain Leontief and Cobb-Douglas production function from CES function?

In most Microeconomics textbooks it is mentioned that the Constant Elasticity of Substitution (CES) production function, $$Q=\gamma[a K^{-\rho} +(1-a) L^{-\rho} ]^{-\frac{1}{\rho}}$$ (where the ...
6
votes
2answers
154 views

How Do Economists Quantify Contagion?

In the context of international financial crises, what mathematical methods have Economists employed in order to quantify financial contagion? Note: For a working definition of contagion I'll use the ...
2
votes
2answers
93 views

Utility and the tyranny of a minority

Follow on to this question. Using similar constraints: The constraints regarding the system I'm modeling are (and looking for a general solution to): Marginal Utility for every unit of a ...
16
votes
5answers
3k views

Topological concepts in economic theory

QUESTION: What are the major or systematic applications of post-1960s mathematics to microeconomics? For example, in the late 19th century, Fisher first used the mathematical ideas of Gibbs to ...
4
votes
2answers
695 views

What are the most recent devopments with applying fractals to economics?

I was researching fractals for my senior mathematics presentation and discovered that one of the most recent pioneers in that section of the field was able to apply fractal mathematics to the field of ...
12
votes
3answers
814 views

Consumer optimum in an economy with a continuum of commodities

Consider an economy with a continuum of commodities, with one commodity for each point in $[0,1]$. Suppose a consumer wants to maximise $$U = \int_0^1 c_i^\theta\,di\qquad 0<\theta<1$$ subject ...
7
votes
4answers
721 views

Simulating a Hamilton-Jacobi-Bellman

Say I have solved an HJB of the form: $\rho V(k) = \max_c g(c) + V'(k)(z - c)$ I have calibrated $\rho$ to monthly parameters. I would like to simulate the development of $k$. I start with $k(0)$. ...
5
votes
0answers
78 views

Simulations Using Binomial Coefficients

In closed loop toy models with a fixed money supply, what are the downsides of calculating probable outcomes with a binomial coefficient? For example, given a toy economy where trades yield a profit ...
12
votes
4answers
8k views

Is complex analysis used in economics?

It's frequently useful in physics and engineering applications; are there any applications in theoretical economics? (If not, were there any attempts at incorporating CA that just never caught on?) ...
66
votes
13answers
17k views

Fundamental equations in economics

For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important ...
5
votes
1answer
177 views

The relation between the Black-Scholes model and quantum mechanics [closed]

As an active participant on the Physics Stack Exchange I have, on several separate occasions, run into some vague remarks about the 'intimate relation' between the famous Black-Scholes model in ...