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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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42 views

Maximization when parameters are unknown

I would like to know if my understanding about how to find a maximum of the function when some parameters are unknown is correct. Consider the following maximization problem. $\max_{x}V=\int_0^{a(x)}...
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11 views

How do I calculate quarterly Sharpe Ratio USING geometric averages?

I am looking to calculate the Sharpe ratio using Geometric average. The issue is I don't understand how to find the standard deviation term. Any help would be greatly appreciated.
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22 views

What is the difference between a growth shock and a productivity shock

In a RBC context, what I mean by growth shock is a total factor productivity shock that follows a stochastic trend $ln(a_t) = ln(a_{t−1}) + \gamma + \epsilon^a_t$. I.e. the technology $a_t$, has a ...
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98 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 ...
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1answer
56 views

Envelope Theorem in Hopkins and Kornienko (2010)

This is from Hopkins and Kornienko (2010). In this model, $x$ is investments, $s$ is status, and $y=z-x$ is leisure, where $z$ is endowments. $x(r)$ is the optimal investment, and the relative ...
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18 views

What experiment could I run in order to test the 'Independence of Irrelevant Alternatives' axiom?

I need some help in designing an economics experiment to test the IIA axiom. My understanding of it is if you rank A above B then if you introduce C or D, you must still always rank A above B in any ...
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2answers
37 views

How to calculate payback period of the project?

In order to finish a technological product, it was spent 50000 dollars (for materials, salary). 500 dollars per month is needed for support of the project (will be spend for servers). This product ...
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0answers
74 views

On complements and substitutes with a CES function

Define the CES function $q : \mathbb R_+^n \to [0,1]$ by \begin{align} q(x) = \left[\frac{1}{n}\sum_{j=1}^n{x_j^\frac{\sigma-1}{\sigma}}\right]^\frac{\sigma}{\sigma-1} \end{align} where $x \in \mathbb ...
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1answer
94 views

Maximization problem FOC and Euler equation

Can someone please help me with the Lagragian and the derivation of the following objective function ? Beneath I provide the objective function, the constraint and the Euler equation that results from ...
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1answer
22 views

Economic Metrics (ROI, PP, NPW)

So I am doing this project, which includes in calculating the Economic Metrics for a profitability analysis. I have calculated Return on Investment (ROI), Net Present Worth (NPW) and Payback Period (...
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1answer
135 views

WARP implies completeness, transitivity and thus rationalizability. What is wrong with the statement?

Let $A$ be a menu and $R$ be a complete and transitive binary relation. Define choice correspondence generated by $R$: $$c_R(A)=\{x\in A|| xRy \ \forall y\in A\}.$$ Theorem (from Kreps 1988): for ...
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33 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 ...
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1answer
71 views

Symmetric Cournot equilibrium: suffciency without second order conditon

Let $q_i \in Q = \mathbb R_+$ denote the quantity produced by firm $i \in \{1,2\}$. Further let $\pi_i(q_1,q_2) = (1-q_1-q_2)q_i$ denote the profits of $i$. A Nash equilibrium $(q_1^*,q_2^*) \in Q^2$ ...
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1answer
66 views

What mathematical structure or formalism can be used for modelling strategic investment decisions of agents in the context of competition?

I'm trying to analyze the decisions of agents in investing scarce resource like time and money into developing their product/service/offering in the presence of competition. I need to know what kind ...
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1answer
43 views

Probability of the event knowing that I received no informations

First I want to thank you if you pay attention to my post. I apologize if it seems elementary to you, note that I searched a lot an answer before posting. I have a particular informational framework ...
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2answers
228 views

Is it possible to give, in economics, an example of a relation ( set of ordered pairs) that is not a function?

In mathematics, some relations ( sets of ordered pairs) are not functions. I know economists make use of functions. But do they also consider relations that are not functions. In which branch of ...
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1answer
34 views

Financial economics: Bond Price

I know that if the coupon rate on a bond is larger than the yield-to-maturity, then the price must be higher than the par value. Yet I have the bond price equation $P=\frac{c}{y}\left(1-\frac{1}{(1+y)^...
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1answer
133 views

Is First Order Stochastic Dominance (FOSD) relation convex?

A convex relation is that $x\succeq y$ implies $\alpha x+(1-\alpha)y\succeq y$. Let $>_{FOSD}$ be $\succ$, is the FOSD convex? Intuitively it seems convex.
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15 views

Is there such a thing as resonance in economic underliers?

In physics the occurence of resonance is explained and widely understood in its linear form and subject to research in nonlinear resonance. Example for instance are resonant frequencies of objects. ...
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1answer
131 views

Average employment length

From Macroeconomics 7th edition by Gregory Mankiw, p166. Here’s a numerical example. Suppose that 1 percent of the employed lose their jobs each month ($s$ = 0.01). This means that on average jobs ...
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1answer
143 views

Need a math help for the Cagan's model in macroeconomics

From the appendix after the chapter 4 in Macroeconomics 7th edition by Gregory Mankiw. To keep the math as simple as possible, we posit a money demand function that is linear in the natural ...
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1answer
48 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. ...
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1answer
34 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
181 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 ...
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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 ...
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2answers
88 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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186 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
48 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
28 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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128 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 ...
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1answer
19 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
186 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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0answers
43 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
60 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
64 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
67 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
39 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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24 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
76 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
92 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
70 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
26 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. ...
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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 ...
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1answer
88 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
43 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
210 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 ...