Questions tagged [mathematical-economics]

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

126 questions with no upvoted or accepted answers
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13
votes
0answers
281 views

How accurate is duality?

In economic theory we know that with the use of some calculus, Hotellings Lemma and Sheppards lemma we can derive a given firms supply function and in term its Profit function. With data of a given ...
10
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710 views

Modern theory of integrability of demand?

I am aware of Hurwickz Uzawa work in integability, neatly summarized by Border http://people.hss.caltech.edu/~kcb/Notes/Demand4-Integrability.pdf I am wondering if there is any modern treatment of the ...
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497 views

Calculus and Indifference Curves in an Urban Economics Example

I am reading the paper 'The Structure of Urban Equilibria' by Jan Brueckner. It uses a monocentric city model, where all consumers earn income $y$ at the centre of the city. They buy $q$ housing for ...
8
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308 views

Local and Central Wage Bargaining: What Is the Difference?

Consider the following setting: Profit maximizing firms with production functions $\Pi(w,L)$, where $w$ is the wage and $L$ is employment. Unions who want to maximize the expected utility of their ...
8
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261 views

Show that $W_t - \int_0^t \xi_s ds$ is forward-measure-Brownian

Definitions and stuff: Consider a filtered probability space $(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P)$ where $$T > 0$$ $$\mathbb P = \tilde{\mathbb P}$$ This is risk-...
7
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1answer
94 views

Uniform bounds on rate of merging for Bayesian learners

Update. Cross posted at Cross Validated. In a well-known paper, Blackwell & Dubins (1962) show that the posterior probabilities of two Bayesian agents, whose priors agree on events of measure $0$,...
5
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0answers
266 views

On the uniqueness of utility functions for both risk and time

I have a question regarding the uniqueness of preference functionals under risky and dynamic settings. Two well known models to represent preferences for both settings are the Expected Utility Model ...
5
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0answers
79 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 ...
4
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41 views

Afriat theorem for negative goods

GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...
4
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0answers
60 views

How to econometrically identify perfect complements in production?

The production $$f(x_i,...,x_n)=\min\{x_i,...,x_n\}$$ is pretty straight forward and usually with smaller size data sets and can usually be picked up on rather quickly in an intuitive sense. ...
4
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127 views

Does a determinant ever have its own interpretation in economics?

I know there are applications of determinants in economics to compute equilibrium, aide in identifying profit maximisation/cost minimisation and in calculating elasticity of substitution. However, is ...
4
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48 views

Common knowledge in model formulation and solution

Economics models usually assume that the structure of the economy is common knowledge among agents. Mathematically, an event is common knowledge if it lies in the meet of all agents' information ...
4
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67 views

References on mathematically rigorous general equilibrium theories

I'm looking for a relatively recent survey on the state of the art for mathematical general equilibrium. I'm especially interested in questions of uniqueness, stability and dynamics. (I'm planing on ...
4
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1answer
383 views

Criticism of “Modern Political Economics” by Varoufakis, Halevi, Theocarakis

The book "Modern Political Economics" is quite critical about "neoclassical economics", the basic claim being, if I understand correctly, that the models which "neoclassical economics" (armed with ...
3
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73 views

Bliss point hamiltonian function

I have the following utility function $$u(c_t)=g(c_t-b)^2$$ for constants $g,b>0$ Edited: in order to be bliss utility function, It must be g is negative. But in the question g is given to be ...
3
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53 views

Existence of symmetric trembling hand perfect equilibria

Consider symmetric and finite game. By Nash (1950), the game must have at least one symmetric equilibrium (proof). Also, it must have at least one trembling hand perfect equilibrium (proof). ...
3
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78 views

Linear Homothetic Utility

A Homothetic Utility is where $$ \forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y) $$ (or its monotonic transformation). A linear Homothetic utility is defined as $$ \forall x,y, \forall ...
3
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1answer
39 views

Existing metric for personal productivity hours needed per life hour?

With about 50 hours of productivity a week, including work, cooking, etc. I can complete the tasks and pay the expenses necessary to live about a week. Subtract maybe 5 hours of labor that goes into ...
3
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48 views

How should I calculate bulk selling price for a small business?

Some friends of mine run a small business, in a small garage-like space, with a few employees, making and selling "plumbuses". The typical customer orders about 5 plumbuses at a time. When I heard ...
3
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78 views

Open Foundational Problems in Mathematical Economics

What are some open problems in mathematical economics which are treated as if they have been solved in economics papers? As an example, one of my teachers has previously pointed out to me that there ...
3
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66 views

Mathematically optimal age to begin drawing Social Security retirement benefits as a function of expected life span?

So, for most of us Americans, our official retirement age is 66 and we get 100% of our retirement benefits. If we delay retirement, that benefit increases by 8% each year (up to age 70) and if we ...
3
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0answers
318 views

A theoretical/mathematical approach to cost-benefit analysis and cost-utility analysis in health economics

I am looking to get some resources looking at health economics from a pure mathematical point of view, ie developing models using partial differential equations or complex analysis. In particular, I ...
3
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95 views

Solving this system of ODE

I have the following system of equations $$ \rho V(u, \epsilon^i) = F(u, \epsilon^i) + V_u(u, \epsilon^i)g(u, V(u, \epsilon^i) + \lambda^i \left(V(u, \epsilon^{-i}) - V(u, \epsilon^i)\right)$$ with $...
3
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0answers
128 views

Ultrafilters in Social Choice Theory Literature Request

I am an undergraduate math major who is intrigued about social choice theory. I am in the early stages of planning my senior project and was wondering if anybody had some recommendations of literature ...
2
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0answers
54 views

Linearization of the dynamic system (I did it, but I have a mistake that I cannot catch. Help me please)

I have the following dynamic system in discrete time For p is price, d is demand and s is supply. $$p_{t+1}-p_t= a(d_t-s_t)$$ $$s_{t+1}-s_t=bp_ts_t-ws_t$$ $$d_t= k-gp_t$$ I have to linearize this ...
2
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29 views

Behavioral Dictator Game

I am doing a self study on behavioral economics and I am trying to solve behavioral version of the dictator game with following utilities for person 1 and 2. $$ u_1( \sigma_1, \sigma_2 ) = \...
2
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0answers
49 views

Finding optimal path in continuous time

I have the following optimal control problem $$\max_{c_t,l_t} \int_0^{\infty} [ln(c_t)+\theta ln(1-l_t)]e^{-pt}dt$$ st. $$\dot{k_t}=k_t^{1/2}l_t^{1/2}-c_t-\beta l_t$$ $$k_0>0$$ I do big part of ...
2
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1answer
50 views

How to test if the effect of one regressor entirely comes from other regressors?

I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know ...
2
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28 views

Software used for solving demands of different functions

I'm currently doing some research on demand systems and have been experimenting with different underlying utility functions which will generate different systems of demands. However I've been doing ...
2
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0answers
50 views

Neoclassical Economic Growth Model Shadow Price for Discrete vs Continuous Time

I recently learned about the neoclassical growth model in both discrete and continuous time. The intuitive meaning of the shadow price for both cases is that it represents the value of one additional ...
2
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0answers
105 views

Derivation of demand function

Hello. I'm graduate student in Japan. This time, what I want to ask is how to solve the profit maximization problem using the image production function and derive the demand function. This ...
2
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0answers
29 views

Showing that a market model has arbitrage and describing martingales

This is an exercise which I came upon while studying an introduction to financial mathematics. Exercise : Consider the finite sample space $\Omega = \{\omega_1,\omega_2,\omega_3\}$ and let $\...
2
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0answers
40 views

Mean Field/Differential Game and Measurability

Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ...
2
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103 views

Use of the Lagrangian in empirical work

In my own studies I have noticed that many of the constrained optimization type questions that are often covered in intermediate/advanced microeconomics courses are seldom seen in more empirical types ...
2
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0answers
392 views

Second order condition for symmetric game

Denote by $i \in \{1, \ldots, n\}$ an economic agent. Let $\mathbf x \in \mathbb R^n$ denote a vector of actions and $x_i \in \mathbf x$ a typical element. Let further $f_i : \mathbb R^n \to \mathbb ...
2
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0answers
83 views

Visualising eigenvectors/values

This might seem like an odd question but seeing as I haven't had any formal education in solving ratex models yet, it is something I have been thinking about a lot recently. Consider the following ...
2
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0answers
39 views

Question on a sufficient condition of contractiveness of best reply functions in Vives (1999)

I have trouble in understanding why a sufficient condition that a best reply function is a contraction. The following is a screenshot of Xavier Vives's Oligopoly Pricing: Old Ideas and New Tools from ...
2
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0answers
202 views

Bayes Nash Equilibrium in a game with continuous actions

I am attempting to think through a particular type of game with continuous strategies, with Bayes Nash equilibrium as the solution concept. I first describe the game below, followed by questions. ...
2
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0answers
50 views

What model did the MONIAC use?

Phillips designed a hydraulic computer to model the UK economy in 1949; 12-14 copies were built. What model did it compute with? How have modern models of the UK built on that work?
2
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613 views

Euler's Homogenous Function Theorem with elasticity

I'm currently reviewing my prof's slides in preparation for an exam. In one of them, he talks about Euler's Homogenous Function Theorem: Let $f(x_1, x_2, ..., x_n)$ be a function homogenous in ...
2
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0answers
248 views

Fisher Separation with negative interest rate

In class we discussed Fisher Separation which states that the investment decision is independent of the financing decision. The optimality conditions are that MRS = MRT = (1+i) (i = interest rate). ...
2
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0answers
47 views

Are there any models which allow to calculate a discount?

I want to progressively calculate a discount based on the amount of product sold. Are there any models which allow to take into account different type of products and can calculate the discounts based ...
2
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0answers
1k views

First and Second Order Lagrangian-Multiplier Conditions for Optimization

The Statement of the Problem: Let $f,g$ be two functions on $\mathbb R^n$ and assume $\nabla f $and$ \nabla g$ are nonzero everywhere. Write the first and second order Langrangian-multiplier ...
2
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0answers
61 views

How this ex ante game induce a uniform distribution for interim stage?

In an article (see here) from the blog leisure of theory class, it is shown, in an interim stage for a Baysian game, we could run into a technical problem that the induced belief space for a player ...
2
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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 | ...
1
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0answers
23 views

Shortcuts for elasticity of substitution

How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
1
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1answer
49 views

How do we define an efficient tax in microeconomics?

I am currently working through problems to study for an upcoming exam. I am not seeking a solution per se. I am looking at the intertemporal choice model. I am looking at two periods where consumption ...
1
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0answers
58 views

Writing constraint

A firm accumulates useful knowledge $k$ by investing in R&D activities. Specifically, if the firm invests $r > 0$ dollars into R&D, the stock of useful knowledge grows by about $2\sqrt{r}$ ...
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0answers
80 views

What is Economic Interpretation of three nonlinear equations?

I have the following nonlinear system $w$ is wealth $c$ is consumption $r(w)$ is gross return on wealth $a,b, d$ are parameters which are strictly positive and fixed. $$\dot{w} =r(w)w-c$$ $$\...
1
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1answer
44 views

Regarding the Expenditure Function Underlying a Bliss Point

I've been looking at expenditure systems and have been really interested in the behaviour of the demand system that underlies bliss points: Consider the bliss point utility function of the following ...