Questions tagged [mathematical-economics]

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

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2
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1answer
57 views

Applying real growth rate to nominal value

What happens if one applies a real GDP growth rate to a nominal GDP value? The result can't be a GDP figure in constant prices, since that would imply applying a real GDP growth rate to constant GDP ...
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1answer
259 views

Text book for mathematical economics?

I need a text book for mathematical economics with real world examples. Currently I'm using A.C Chiang (very good) and Henderson and Quandt ( not the best book for matheco). Can someone recommend any ...
0
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1answer
392 views

Government's intervention question [closed]

Given that demand for a good X is equal to $q_D=393-2p$ and market supply is $q_S=p/4-12$. Find equilibrium price and quantity, consumer and producer surplus and draw a diagram illustrating the ...
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1answer
130 views

How to find the variance co-variance matrix for 4 assets and market returns using the CAPM?

I understand the process on excel: calculate betas, calculate covariance with $Cov(R_{i,t},R_{j,t}) = \beta_{i,m} \cdot \beta_{j,m} \cdot \sigma^2_m$ where m is the market return and i and j are ...
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1answer
342 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-...
6
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1answer
427 views

Is there any economic meaning to log returns?

I recently had a discussion with a friend regarding log returns and any economic meaning that could have as a measure in the sense of "assessing the benefit received for compensating work done in a ...
1
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1answer
134 views

Expenses as a function of Income

I am wondering if any one has attempted to describe household expenses as a function of income. I have an idea that the curve should look something like a natural log over a root function. It creates ...
4
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1answer
409 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 ...
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1answer
1k views

What Math is used in Development Economics?

I would like to ask what kind of math is used in Development Economics? I have one more semester in my Master of Math programme before hopefully entering a PhD in Economics and am considering ...
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1answer
99 views

MLE using multivariate normal distribution

I am reading econometrics lecture notes of a Japanese professor. To explain MLE estimation he uses multivariate normal distribution. As you can see, the first line is the loglikelihood function and ...
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1answer
105 views

How to relate real rate of return on capital to bond interest rate: Lagrangian

Suppose that household resource constrain equation is as follows: $$P_tC_t + Q_tB_t+ P_tI_t \leq W_tL_t+R_tK_t+B_{t-1}+D_t$$ where $P_t$ is price at time $t$, $Q_t$ is the price of one bond quantity, $...
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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 ...
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0answers
55 views

Separate optimization problem versus one big Lagrangean

I am a bit confused about when to consider a separate optimization problem and when to combine different problems into a single optimization problem. Consider an individual who derives utility from ...
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1answer
106 views

Textbook covering calculus and probability theory

Is anyone able to recommend a textbook that covers the following topics at a level suitable for econ undergraduates? Differential calculus, including the various rules of differentiation and partial ...
3
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2answers
104 views

Properties of orders and preference relations

Suppose I have alternatives $A$, $B$, and $C$. If I have strict preferences, that means that for any $x,y \in \{A,B,C\}$ such that $x \ne y$, either $x \succ y$ or $y \succ x$. Assume transitivity, ...
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1answer
608 views

Derive the demand functions: Hotelling-style Model

So I have this economics question that I have been trying for a while now and I can't seem to get the answer correctly. Below is the question and after I will show what I have so far. An explanation ...
6
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2answers
361 views

CES preferences intuition

I asked this question on math.stackexchange but deleted it from there and brought it here. I had a question about Constant Elasticity of substitution type preferences of the form: $$U=\int_{0}^{1}(c(\...
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2answers
180 views

Does it make sense to apply complex mathematics in economics given that the result can be off by substantial percentage points?

Complex mathematics make sense if the results can be calculated with precision. This applies for the physical sciences like physics and engineering. Economics is more of a social science subject. Does ...
6
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4answers
16k views

Calculating rate of growth of per capita income

Given this question: National income is increasing by 1.5% a year and population by 2.5% a year. What is the rate of growth of per capita income? Attempt: Since per capita income is GDP/ ...
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2answers
98 views

Risky Assets over Bernoulli Utility

My question is about 6.C.4. of Mas-Colell et.al.'s Microeconomic Theory book. We have N risky assets with returns $z_n, n = (1,...,N)$ per dollar invested which are distributed over $F(z_1,...,z_n).$ ...
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2answers
138 views

Finding an intercept on percentage based data and using dummy variables

How do I find an intercept on a percentage data? My data has percentage of grades ( I have converted to numbers where $A^*=8, A=7,B=6...U=0$) by ethnicity and other indicators which I want to test for ...
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1answer
662 views

Show that there is no continuous utility function which represents the lexicographic preferences [duplicate]

Show that there is no continuous utility function which represents the lexicographic preferences $\mathscr{L}$ given by $(x_1, x_2) \succeq (y_1, y_2)$ if and only if $x_1 > y_1$ or $x_1 = y_1$ ...
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2answers
5k views

What textbook can I use to really understand microeconomics, macroeconomics and mathematical economics [closed]

What textbook can I use to really understand microeconomics, macroeconomics and mathematical economics. It can be different textbooks. I'm in first year college taking introductory courses in ...
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3answers
1k views

CES Production Function with $\rho>1$

In using CES production functions of the form $f(x_1,x_2)=(x_1^\rho+x_2^\rho)^{1/\rho} $, we always assume that $\rho\leq1$. Why do we make that assumption? I understand that if $\rho>1$, the ...
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1answer
393 views

How does the companies set up utility function for its own purposes?

How does the companies set up utility function for its own purposes? In another word, what is the types statistics data that is usually consider and statistical method being used to set up these ...
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1answer
112 views

Stability analysis and dimension of a dynamic control system

I have an optimal control problem where I have two control and one state variable. $$max\int_{0}^{\infty}\left(u\left(c\right)-P_{M}M\right)e^{-\rho t}dt\tag{1}$$ where $P_{M}$ is the unit price of ...
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2answers
892 views

Constant Elasticity of Substitution: Special Cases

Take an $n$-commodity constant elasticity of substitution utility function, $$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho}$$ How do we show the following: Show that as $\rho \...
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1answer
1k views

Doing a PhD Economics without background in formal theorems?

I could really use some advice. I am a new PhD student in Economics and Finance. My background is in economics, and while I did mathematics in my Master's course, it was more data-analysis based ...
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1answer
3k views

What are the applications of complex numbers in modern economics? [duplicate]

I wonder what the most interesting applications of imaginary numbers in mainstream economics are. I read about the unit root test (Dickey-Fuller test) in time-series analysis; and I studied System ...
10
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3answers
2k views

Why is the derivative used to represent marginal cost instead of the difference?

Marginal cost is defined as "the change in the total cost that arises when the quantity produced is incremented by one unit." And given a total cost function $C(q)$ that's differentiable, the marginal ...
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1answer
223 views

Books about chaos theory

For someone who already knows micro and macro economics, are there any good books to understand chaos theory in economics and mathematical economics in general?
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58 views

What is the cumulative amount of working hours for consumer products?

Is there any research about the cumulative amount of working hours for consumer products like cars or mobile phones? With cumulative amount of working hours I mean the total amount of working hours ...
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2answers
3k views

Local Non-Satiation Proof

I have been having trouble with how to go forward with a proof for about three days now. I know the basic structure of the proof, but can't seem to construct it. Basically, I am trying to do a proof ...
4
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2answers
148 views

Good Site for Practicing Advanced Problems

In the past I have used Khan Academy to great success to practice advanced math problems. It is useful because it gives simple questions in a multiple choice fashion then it quickly tells whether your ...
5
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1answer
124 views

From Discrete to Continuous time: Total Differential

I'm trying to derive an HJB from a discrete time setting. At some point, I am left with $$ \lim_{\Delta\to 0} \frac{v(c_{t+\Delta}, u_{t+\Delta}, t+\Delta) - v(c_{t}, u_{t}, t)}{\Delta}$$ and am not ...
6
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3answers
573 views

Effect of a US Federal Reserve rate hike on the Dow Jones Industrial Average

There is speculation that the Federal Reserve of the United States will raise interest rates by 0.25% in the near future. What is the expected effect on the stock market if interest rates do rise by ...
1
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1answer
433 views

Does different Base Year in Price Index affected conversion of nominal value to the real value?

I do not have any economics background, but currently I have some data sets regarding price index. I have some doubts regarding if my way of conversion is correct? I have 4 data set. So let it be DS1,...
5
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1answer
490 views

Envelope Theorem

Say I'm solving for consumption given income, and we assume that an interior solution exists: $$ \max_c U(c, Y)\\ C(Y) = \arg\max_c U(c, Y)\\ $$ However, there is no closed-form solution for $C(Y)$. ...
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0answers
42 views

The mathematical model of integrated marketing communications

I am trying to generalize the media buying problem, the first steps are to use media buying approach to several advertising channels at once. But there should be next steps as well. Are there works ...
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0answers
68 views

Model for simple production chain economy

Given a simplistic economical model with a finite number of possible resources, and a set of machines that can be produced (with a cost) that that take some or none input, and give some output per ...
3
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1answer
45 views

Help understanding expression for continuous discounting

In footnote 3 of their paper "Patent Breadth, Patent Life, and the Pace of Technological Progress", O'Donoghue Scotchmer and Thisse take a discount rate of $r$ and write If the flow of profit $\...
3
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1answer
77 views

Conjecture Steady State from limit properties

The question is related to this thread. I'd like to derive a unique steady state for an optimal control problem. Consider the following programm \begin{align} &V(x_0) := \max_u \int^\infty_0 e^{-\...
3
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1answer
67 views

Econometric test for detecting change from trend stationary to stationary process

I am stuck with the following problem from research. Is there an econometric test which detects change from trend stationary to stationary process. I tried to search for this but the literature is ...
4
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1answer
217 views

Sequential games and Perfect Bayesian Equilibrium

Reading the paper http://www.sciencedirect.com/science/article/pii/002205319190155W I came up with the following question. Given that this paper deals with games in which players move simultaneously,...
6
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3answers
246 views

How to deal with a singular Leontiev inverted matrix?

I am currently studying and experimenting the input-output methodology. It is a 1930's method based on national accountings that allows to measure the interindustry flow of good and services. ...
5
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1answer
218 views

The Insane Sultan of Slickcrudistan: Calculating Currency Equilibrium

I work for a start-up that has encountered an economics problem no one on our team has been able to crack. A story form and a general form of the problem are below. I believe they are equivalent, but ...
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1answer
1k views

Solving the Hamilton-Jacobi-Bellman equation; necessary and sufficient for optimality?

Consider the following differential equation \begin{align} \dot x(t)=f(x(t),u(t)) \end{align} where $x$ is the state and $u$ the control variable. The solution is given by \begin{align} x(t)=x_0 + \...
6
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2answers
189 views

Multiple equilibria: which one to select?

There are two agents $i=1,2$. Consider the following programm \begin{align} &V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\ &V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}...
4
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1answer
392 views

Maximisation problem in a multiproduct firm

I am currently reading the book "Microeconomics: Principles and Analysis" by Cowell on my own. I'm interested in the section of the multiproduct firm, but i'm confused with the use of the profit ...
4
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3answers
228 views

What graph theory textbook should I use?

I'm doing my Msc dissertation on production networks and business cycles and I want to learn graph theory. I need to be able to model the evolution of the network and identify equilibrium graphs. ...

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