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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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1answer
23 views

Dot over a variable, Neoclassical growth model?

Looking at the Neoclassical growth model, I have hard time understanding what dot over a variable mean? I know it is short for taking the derivative with respect to time, I don't understand the ...
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0answers
20 views

Indifference curves and equivalence classes

Last week in class, my professor described indifference curves in the context of modelling consumer choice with multiple goods. He defined a partial-ordering operator $\prec$ and an equivalence ...
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0answers
20 views

Existence of the general equilibrium

In the proof of the existence of the Walrasian equilibrium, there is a map defined using the Max map. Why this map is defined in this way?I am reading " Microeconomics; Gravelle, Rees". On page 257 ...
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0answers
18 views

Linearisation of the IS curve?

How to the IS curve linearised around the structural equilibrium?, what is the math behind it?
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0answers
14 views

Who was the inventor of Utility function?

To my knowledge, the idea of representing weak-order with a function dates back to Cantor. So my questions are: 1) Was Cantor the first person who rigorize these kinds of representation? 2) Were ...
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1answer
22 views

Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve

I am reading Modern Microeconomics by Koutsoyiannis. In a Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve. Firm A produces half the total market demand to ...
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1answer
60 views

Reference Request - Dynamic Optimization with More Than One State Variable

I would like to understand how to solve dynamic optimization problems involving more than one state variable and state equation (to apply to long-term economic models with more than one capital good). ...
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1answer
21 views

What is the “bequest condition” in a finite-horizon discrete optimization problem?

For a finite-horizon discrete time optimization problem, my textbook provides a condition called the "bequest condition", which I'm not familiar with. Specifically, where the state at time $t$ is ...
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1answer
46 views

Advance Microeconomics [closed]

Show that u=a+bM-yM^2 represents a risk averter's utility function who is interested only in the mean and the variance of the state distribution of Income M. Can anybody send me the full solution. ...
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1answer
22 views

What data/factors/attributes do the professionals monitor in a top-down analysis on the macroeconomics?

I am learning to do top-down analysis on a number of sectors in the US equity markets. I have never done it before and I would appreciate it if some professionals can share their experiences with me. ...
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1answer
21 views

equality between 2 operations using mean [closed]

why when we do the following operation mean (10 ,20,30)= 20 is different from (mean(10,20)+30)/2=22,5 there are no equality between the 2 operations using mean ? why? thanks a lot in advance for ...
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1answer
37 views

Second order partial derivative and cross second-order partial derivative

I'm following a paper (Full text available here!) where at some point (pag.17 and 20) the author get the following derivative: $$\frac{\partial V}{\partial L}=Y-X\frac{dY}{dX}=\alpha X^{-\frac{c}{b}}...
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2answers
29 views

If the consumer is not a price taker, does she still set marginal rate of substitution equal to the price ratio?

Consider some consumer who consumes good $x$ and $y$. The price of $x$ is fixed to be $k$. The price of $y$ is $c(y)$. The consumer's marginal rate of substitution is given by $\frac{-x}{y}$. If the ...
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1answer
64 views

Calculating the elasticity of substitution between factors of production

Following the work of Lu (1967) (Full text available here!) I got stuck trying to derive the elasticity of substitution between factors. He use the formula developed by Allen, that when the production ...
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1answer
35 views

Whats the rationale for using taylor series in economics?

I've been reading about the translog production function and know its really just a log-log production function approximated using a first order maclauren series. Why not just leave the function as ...
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0answers
33 views

What is Application of Vector Algebra in Economics?

I through one tutors heard that vector is used in economics . But on searching about it on internet could not find anything Recently I studied about Vectors in Mathematics So I was wondering how ...
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2answers
58 views

Linking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated?

I have a question about the contents of this paper*, which links a building energy model and a utility-maximization component. In it, the author tests several electricity prices using a Cobb-Douglas ...
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0answers
16 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 $\...
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1answer
42 views

Evaluate value added of a company

i have the value added of a company for 2 years 2016 and 2017 so to compare these values and to see its evolutioon i divided the value of 2017 by the one of 2016 but some friends told ...
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1answer
48 views

Maximizing a Cobb-Douglas Function

Suppose that a competitive firm receives a price of $P$ for its output, and pays prices of w, r and v for its labor $(L)$, capital $(K)$ and natural resources $(R)$ inputs, respectively. The firm ...
2
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1answer
155 views

Showing marginal product of capital is independent of the scale of production

The image is pretty much self-explanatory. To add some context, I'm learning Solow-Swan Growth Theory and my professor said that the marginal product will not change if both capital and labor increase ...
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1answer
67 views

Can there be a sample such that SRF and PRF do not intersect?

I am confused if it is possible for to randomly select a sample such that SRF and PRF do not intersect. I have thought of the concept of parallel lines, which allows for such a case but I am unsure if ...
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1answer
84 views

Income effect $-\frac{\partial x_i}{\partial m} x_i$ or $\frac{\partial x_i}{\partial m}x_i$?

Recall that the slutsky equation is: $$\frac{\partial x_i}{\partial p_i}=\frac{\partial h_i}{\partial p_i}-\frac{\partial x_i}{\partial m}x_i$$ I know $\frac{\partial h_i}{\partial p_i}$ defined as ...
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1answer
63 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 ...
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0answers
30 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 ...
2
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1answer
52 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 ...
4
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1answer
123 views

Deriving average productivity from a CES production function

Following the work of Raurich et al. (2012) I got stuck trying to derive the average productivity starting from the following CES production function: $$Y=A\left [ \alpha K^{\frac{\sigma -1}{\sigma }}...
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0answers
46 views

Applications of Pure Mathematics in Economics

Are there any applications of number theory and abstract algebra in economics? An economist had told me that number theory had an application to a theorem in economics, however he did not remember ...
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0answers
34 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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1answer
158 views

Is this Cost function concave or convex?

Given the following cost function, where t is the quantity of some product. $$C(t) = 1/3t^3 - 7t^2 +11t + 50$$ here is a graph between $t= 0$ and $t = 25$ We are asked if this function is convex or ...
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1answer
67 views

How likely are the Sonnenschein-Mantel-Debreu results?

I have been reading about the SMD results and it's "damning" nature for GET. My understanding of the result is as follows: price changes not only cause a substitution effect but also change the wealth ...
2
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1answer
84 views

Help needed to understand proof in Myerson and Satterthwaite (1983)

The following image is an excerpt taken from Myerson and Satterthwaite's 1983 paper Efficient Mechanisms for Bilateral Trading: I know what the theorem is all about, all I need is some help with the ...
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0answers
15 views

Value of companies with circular ownership [duplicate]

Given two companies, total assets of $100 million each. Company 'A' owns \$50M of company 'B'. Company 'B' owns \$50M of company 'A'. If you look at the value of both companies do you ...
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0answers
21 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 ...
1
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1answer
33 views

Purpose of Semidefinite Integral

I want to know the meaning of Semidefinite Integral. I am used to read definite and indefinite integral but I want to know the meaning of such equation : $\pi(e)\left(1-F\left[-\frac{a}{\pi(e)}\...
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2answers
62 views

Simplest model of an economy exhibiting (hyper)inflation

I would like to find a minimal mathematical model for describing financial crises of the type that produces hyperinflation. Here's a naive attempt, just to give the idea of what I'm thinking of. ...
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0answers
46 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 ...
2
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1answer
240 views

Euler's Theorem

Can anyone give me connection and intuition behind each of the following euler's equation- Euler's equation in production function represents that total factor payment equals degree of homogeneity ...
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0answers
30 views

Including definite integrals inside definite integrals - Crossposted from MathSE

This question is cross-posted from MathSE: link I have the following differential equation from a journal article: $\dot{g}(t) - \delta(t)g(t) = -H(t) --- (1) $, which is integrated between t and T. ...
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0answers
213 views

Is Gaussian distribution the proper choice for step in financial time series? E.g. DJIA ROI suggests Laplace instead

Data compression uses Laplace distribution ($\rho=\exp(-|x-\mu|/b)/2b$) for probability distribution of differences, while I see it seems economy uses Gaussian distribution everywhere (?), e.g. in ...
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2answers
48 views

How do I calculate the amount of money I get from an investor and the percentage I give him in return?

Let's say I owe a company. At the final state I want to be left with 1M cash for myself and 50 percent of the company. The investor is not willing to buy shares and give me the money but only invest ...
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0answers
31 views

Is this way of modeling undisclosed debt correct?

I am woking with a model like the one in Alfaro and Kanczuk (2006), that is in turn based in Arellano (2008), where sovereign´s preferences are given by: that in case of not defaulting is subject to: ...
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1answer
19 views

Devising a model for inflation for a closed points system

I am working on a project that involves points. The idea is that users will earn points and redeem them for certain rewards. The means via which the users earn are fairly limited (They can attend a ...
2
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1answer
40 views

How does this demand function satisfy the Weak axiom if it doesnt satisfy the necessary and sufficient conditions?

Let $x_k = \frac{w}{\sum{p_l}}$ for $k = 1...L$ be the demand function. This demand function does satisfy the weak axiom and this can be shown simply. The slutsky matrix is an $L \times L$ matrix ...
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1answer
122 views

Did I calculate the expected value and the variance correctly?

I have the following assignment to solve but I'm not sure if I solved it correctly. Questions Let the stochastic process $(Y_t)_t$ be defined by $Y_t = \mu + Y_{t-1} + \varepsilon _t$ with $(\...
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22answers
10k views

Criticism of Math in Economics

I've been reading and speaking to a number of educated economists and economics PhDs who are against the use of intense mathematics and mathematical proof in economic theory. Specifically I've been ...
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0answers
212 views

How can I determine if a token economic is viable?

Given a system where you incentivize people to do actions in a system, we might have good and bad actors. I would like to know if there is a software or framework where I could put the different <...
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0answers
27 views

Deriving Single Good Demand Curve

came across a problem set that I had no clue how to tackle, but looks painfully simple. It's a market for electricity where households utility is represented by: U(E) = aE - 2mL2 (Household Utility) ...
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1answer
381 views

Prove all cost functions are concave in input prices and demand for inputs is downward

I've seen proofs that cost functions are concave of the form $C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$ although this neither feels convincing nor does it seem like a ...
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1answer
36 views

Simple Regression With Dummy Variable

Consider a simple linear model: $Y = \beta_1 + \beta_2 MALE + u$ where $MALE$ is a dummy variable. $MALE = 0$ if female, $MALE = 1$ if male. A model is fitted: $\hat{Y} = \hat{\beta_1} + \hat{\...