Questions tagged [mathematical-economics]

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

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4
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1answer
49 views

Convex games: equivalence of definitions

Let $N \subset \mathbb N$ denote the set of players and $v : 2^N \to \mathbb R$ , $v(\emptyset) = 0$, the characteristic function. We call $(N,v)$ a cooperative transferable utility (TU) game. ...
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 ...
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1answer
212 views

Utility maximimization for unusual Leontief utility function

The problem is basic utility maximization subject to a budget constraint with $$u(x,y) = min\{x+y,4\sqrt{x},4\sqrt{y}\}$$ $$p_x = 1, p_y = 1, M = 4$$ I will have to first plot the Indifference ...
0
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1answer
30 views

Here's a question about the solow model [closed]

At first, I was confused by how y keeps increasing after depreciation exceeds savings, then I finally found what was truly bothering me. The fact that when depreciation exceeds savings, capital per ...
3
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2answers
89 views

Mechanism Design: Proving that the expected utility is differentiable

Given a direct mechanism, we define a buyer's expected utility $u(\theta)$ conditional on her type being $\theta$ by $u(\theta)=\theta q(\theta)-t(\theta)$, where $q:[\underline{\theta},\bar{\theta}]\...
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0answers
222 views

Equivalence of definitions of upper contour sets

Mas-Collel, Winston and Green's Microeconomic Theory (3rd editions) offers two definitions of the upper contour set: How can the equivalence between the two definitions be proved?
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17 views

What model to use when defining a 20-year growth path in a developing country?

What economic growth model is commonly used for formulating a 20-year national development plan in a small open developing country?
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1answer
49 views

Constrained Optimization using Lagrangian method

The stationary points that we derive by solving the first order conditions of the Lagrangian are those points global optimum points or local optimum points?
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1answer
30 views

What is the reason behind the demand function of a perfect complement good?

so I know that usually the income curve is equal to: $$x_1p_1 + x_2p_2 = m$$ if we rearrange this equation we get that the demand for good one ($x_1$) is equal to: $$x_1 = \frac{m-x_2p_2}{p_1}$$ None ...
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0answers
168 views

What are eigenvalues and eigenvectors used for in economics?

In economic and econometric literature, i see references to eigenvectors and eigenvalues. Having taken my fair share of linear algebra and econometrics courses I have not really seen how exactly they ...
0
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1answer
20 views

What does the sun product of price times quantity divided by average price

I have a very simple question, what is the meaning, if any, of this? I.e. Economically what does the following calculation mean? $$ \left(\frac{(Q1\cdot P1)+(Q2\cdot P2)+(Q3\cdot P3)}{Q1 + Q2 + Q3}\...
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2answers
199 views

Purpose of a monotonic transformations in utility functions

Based on my economics book, monotonic transformations for a utility function can look something like this: $f(u) = u + 17 $ or even like this: $f(u) = u^3$ That being said what it purpose in the ...
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1answer
44 views

Can I normalise the Dixit-Stiglitz price index to 1?

I've built a model that I am trying to solve in Matlab. The model has Dixit-Stiglitz preferences and $m$ goods, so admits a price index of the following form: $ P = \bigg[ \sum_m p_m^{1-\varepsilon} \...
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44 views

Estimation of a Non-linear production function with Non-linear least squares

Suppose that you have to estimate a Non-linear production function (for instance a Cobb-Douglas or a CES) by using Non-linear LS (and hence without log-linearization). You have just aggregate time ...
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0answers
74 views

Euler equation of consumption in RCK model

(...) usually called the Euler equation for consumption (in effective units of labor) or the Keynes-Ramsey Rule (after those first deriving it): $$ \frac{\dot{c}(t)}{c(t)} = \frac{r(t) - \rho -\...
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1answer
79 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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2answers
71 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
41 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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26 views

Linearisation of the IS curve?

How to the IS curve linearised around the structural equilibrium?, what is the math behind it?
4
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2answers
82 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 to rigorize these kinds of representation? 2) Were ...
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1answer
110 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
72 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). ...
1
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1answer
28 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
62 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. ...
0
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1answer
28 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
23 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 ...
0
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1answer
102 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
44 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
222 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
105 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
118 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 ...
3
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2answers
74 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 ...
2
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0answers
27 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 $\...
0
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1answer
54 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
215 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
205 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 ...
1
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1answer
114 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 ...
0
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1answer
111 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 ...
1
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1answer
225 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
43 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
70 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
255 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
140 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
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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1answer
358 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 ...
7
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1answer
84 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 ...
3
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1answer
113 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
55 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 ...
3
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0answers
45 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
40 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)}\...