For questions regarding the mathematical analysis of economic models and problems. This includes questions about the formulation or solution of models from microeconomics or macroeconomics.

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On properties of linear orders

I have a simple question. Let A={a,b,c,...} be a set and > a total strict order on $2^A$. Total strict order means that for any two subsets of A, say S and S', either S>S' or S'>S but not both. The ...
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0answers
21 views

Annunity calculation with and without tax

I'm doing a annunity calculation: payment = 331880*( 0,002458333 /( 1-(1+0,002458333)^-84) ) This will return me the payment per. month of the loan ...
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0answers
20 views

Calculate the excess burden (deadweight loss) of as a function of t [closed]

Consider a consumer whose utility is given by $U(x,y)=x+y$. She spends her income, given by $I=10$, on two consumption goods, $x$ and $y$, the prices of which are given, respectively, ...
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1answer
18 views

Partial Derivative Problem ( Two Variable Function).

Two commodities $Q_1$ and $Q_2$ are said to be substitute commodities if an increase in the demand of either results in a decrease in the demand of the other. Let $D_1(p_1,p_2)$ and $D_2(p_1,p_2)$ be ...
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2answers
73 views

Is the standard definition of vector wrong?

The definition of a vector is usually something like "a quantity that has both a magnitude and a direction". But, in the context of, say, economics rather than physics, does this definition make ...
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0answers
38 views

Options Pricing / Delta -Mathematical Finance

Consider Apple Inc. as the underlying asset, use its daily adjusted closing prices from August 12, 2014 to August 12, 2015 as historical data to estimate standard deviation. Use the rate r = 0.005 as ...
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1answer
28 views

Rate of Return / Standard Deviation / Correlation Coefficient - Mathematical Finance

Consider these two stocks: AT&T Inc. (T) and Verizon Communications Inc. (VZ). Use the daily adjusted closing prices from March 1, 2015 to August 12, 2015 as historical data. Estimate the mean ...
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1answer
35 views

Application of convex functions in economy [closed]

I have read in some texts that convex functions has application in economy. I want to see some clear examples of such applications.
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1answer
75 views

Is there a concept already for $\frac{f'(x)}{f(x)/x}$?

Given a differentiable real function $y=f(x)$, is there a math concept/terminology already defined for $$\frac{f'(x)}{f(x)/x}?$$ This quantity is inspired from price elasticity of demand. Thanks.
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2answers
63 views

System of Differential Equations- Asymmetric First-Price Auction

I am working on a problem in my Auction Theory textbook regarding a two-player asymmetric first price auction. Assume the bidders are risk neutral. The problem statement is as follows: ...
3
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1answer
73 views

How to find unkown height of triangle without hyptenuse

I been trying to solve this question and have tried to solve it for many days, but do not know how, any help would be much oblidged. A cable company owns the roads marked with the dotted lines in ...
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2answers
34 views

Calculus for Economics

Please suggest me a good book for Calculus. I am a beginner. It would be better if you tell me which book would be appropriate for learning Calculus for understanding Economics.
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36 views

Monthly Vs. Per Month

I am not a native English speaker so I have some difficulty absorbing the topics in economics. One example is this. If the problem says the interest rate is 15 percent semiannually, that means ...
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0answers
46 views

Chaos theory in stock market

I am doing an IB Extended Essay on chaos theory and fractals in the consumer stock market. It is a high school level essay (4000 words) and should be understandable for a calculus student. I'm having ...
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0answers
55 views

Auction Design : Multiple lots, one win max per bidder, not regret

This is a real life game theory problem. I have to organize an auction. There is a finite number of lots, which are not equivalent. There is a finite number of bidders; the number of bidders is ...
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1answer
51 views

Underlying utility function behind a linear two-product demand curve

I am trying to find the underlying utility function behind a linear two-product demand model. For that, I use two methods considering the following utility function: \begin{equation} U(q_1,q_2) = ...
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1answer
28 views

Consumer surplus for multiple products

I want to extend the classical definition of consumer surplus to multi-product case. For a single product, consumer surplus is given as \begin{equation} CS=\int_ {p_{market}} ^ {p _{\max}}D(p)dp. ...
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1answer
27 views

computing a fixed interest rate

I've been struggling for hours now with understanding a Topcoder problem, Autoloan , but i cannot grasp the way of computing it from a mathematical point of view. The excerpt goes as follows: A ...
4
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1answer
38 views

Same Expected Value but different variances. Is $E[U(X)] \ge E[U(Y)]$?

Let $U: \mathbb R -> \mathbb R$ be a concave function, and let $X$ be a random variable with a normal distribution, expected value $\mu$, and standard deviation $\sigma$. Let $\lambda \gt 1$, and ...
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1answer
46 views

Prove that $E[U(X)] \ge E[U(Z)]$

Let U: $\mathbb R$ -> $\mathbb R$ be a concave function, let X be a random variable with a finite expected value, and let Y be a random variable that is independent of X and has an expected value 0. ...
3
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1answer
72 views

Graph Theory text for social scientist.

I am a graduate student in Economics. I have a decent grounding in maths, but I've never studied graph theory or combinatorics. I need to study graph theory in order to analyse production networks. ...
0
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1answer
32 views

Is 2nd-price with a discount auction truth-telling?

I know that 2nd-price auction is truth-telling, but 3rd-price auction is not. What If I run the regular 2nd-price auction, in the end, the winner is charged at the 2nd bidding price with a discount, ...
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0answers
78 views

Market Equilibrium & Calculus

I am a math nerd, but I'm working on my majorly lacking derivative analysis calculus. Trying to break into better understanding market equilibrium. I found some example questions that I am working ...
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19 views

Calculating present worth for benefits/cost analysis

I need some help solving an example question that I found in book. The example is Ex 9.3 from Engineering Economy 7th edition by Blank and Tarquin. Whenever I calculate the PW of investment, costs, ...
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1answer
35 views

I need something like “how to calculate equilibrium price for complete idiots”

My grandfather rises, sells and resells livestock and I want to help him by calculating when and for what price to (re)sell or buy livestock. As far as I understand(although I have a hunch that I need ...
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125 views

Arrow’s Theorem

Suppose $k ≥ 3$ Recall that Arrow’s Theorem shows that any function $F:(S_k)^n\to S_k$ (the input is composed of n permutation of $[k]$ and the outcome is a single permutation of $[k]$ that satisfies ...
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1answer
13 views

Scaling value based on a variable range

I'm looking for a formula that produces a predictable and scaling result based on an initial input variable. The initial input will be between 0 and 48, and needs to return a number between 0.8 and ...
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1answer
22 views

Need help understanding a simplification in a simultaneous search model.

The problem I am trying to solve is $\max_{k \in \mathbb{N}} \int_0^1 u d F(u)^k - ck$, where the associated utility is an iid random variable U following $F(\cdot)$ on [0,1]. $c > 0$ is the ...
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1answer
22 views

Population and production in a dynamic system

I' trying to solve this problem but would need some help: Let N=N(t) denote the size of a certain population, X=x(t) the total product and y(t)=X(t)/N(t) the product per capita at time t. Suppose: ...
3
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2answers
51 views

Percentage change relationship

Given $Z=X^{\alpha}$ how can one prove that the percentage change in $Z$ is simply $\alpha$ times the percentage change in $X$? This was given as a 'simple mathematical rule' in an economics text ...
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2answers
44 views

Y open relative to X

I'm trying to prove the following theorem: Let $X\subseteq\mathbb{R}^{k}$, $Y\subseteq X$. Then $Y$ is open relative to $X$ $ \iff$ $\forall y\in Y\exists\epsilon>0\ N_{\epsilon}^{X}(y)\subseteq ...
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1answer
101 views

Calculus in Economics

A company is planning to manufacture and market a new headphone set. After conducting extensive market surveys, the research department provides the following estimates: Marginal costs function: ...
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0answers
38 views

How can I draw an edgeworth box in 3 dimensions

If there are 3 types of goods(x,y,z) and 2 consumers (a,b) how can I draw the Edgeworth box? It must be 3 dimensional, right? Is there a software or online tool that I can use to draw a 3D Edgeworth ...
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1answer
50 views

Find the equation of a budget hyperplane in R4, from an endowment point and a price vector [closed]

http://imgur.com/ofDS6MO Its been a while since I had to deal with vectors, if someone could help me along with 1.1 that would be very much appreciated
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0answers
50 views

Heteroskesdacity

Consider the following model for real estate values applied to a cross-section of homes: $Price = \beta_0 + \beta_1\cdot SQFT_i + \beta_2 \cdot YARD_i + \beta_3 \cdot POOL_i + \epsilon_i$ where ...
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0answers
36 views

References for the following functional

In many of the types of problems Ive looked at the following quantity keeps arising and I was wondering if anyone knew any references I could look at to learn some its properties. Take any function ...
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1answer
41 views

partial derivative of a sum 1

This is part of a much bigger question I am working on, but I dont understand how I would differentiate a finite sum of the form: $$\frac{\partial}{\partial \phi} \sum_{t=2}^{T} (y_t - \phi ...
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3answers
85 views

economist puzzle for

Mr. White and Mr. Black agreed on the plan to average the wealth by pairs of economic classes, but they differed on the order. Averaging means that the total wealth of the two classes is ...
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16 views

If the null hypothesis is true, how will the test statistic be distributed?

I went with T~(50-6) The question goes.... "A regression is estimated with 50 observations, five explanatory variables and with a constant. Suppose You want to test the following hypothesis $H_0: ...
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1answer
30 views

If $\ln(y) = 5 - 0.1X $what is the elasticity of $Y$ with respect to $X$, when $X=10$?

So i got the following model $\ln(y) = 5 - 0.1* X$ The elasticity of Y with respect to X, when $X=10$ i said -0.1 but apparently i'm wrong Isn't the coefficient of X the elasticity of y when the ...
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0answers
10 views

the test statistic of the sum of a multiple regression

ok so model is... $$ y = −3.33846 + 1.49877 x_1 + 0.489858 x_2 $$ $$se(B_2)= 0.539803 , se(B_3)= 0.102043$$ So the test statistic is $$H_0: B_2 + B_3 =1$$ $$H_0: B_2 + B_3 \ne 1$$ so test ...
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1answer
39 views

Nash equlibrium game theory

Given the following game: Find nash equilibrium (NE) Find subgame perfect nash equilibrium. Main problem i have is with converting this to normal form of the game (because this is i think ...
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1answer
27 views

Interpretation or definition of “shadow prices”

I do understand that shadow price associated to a resource is the marginal profit you would get if you buy one more unit of that resource. I also know that it is the minimum profit you would accept to ...
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0answers
28 views

What does it mean to set the technology matrix of the Leontif Input Output Model to 0?

I'm just beginning to learn about Leontif Input Output Systems and Linear Algebra. What is the significance of the solution if I set the technology matrix equal to the trivial solution (make the ...
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0answers
21 views

Percentage Increase and Dates

Suppose we have the following data: ...
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1answer
17 views

Demeaned fixed effects invariant to base category

Consider the following regression equation: $\gamma_{ib}=\beta_{b}+\alpha_{i}$. Where $\gamma_{ib}$ is matched bank-firm loan growth between $t$ and $t-1$. $\beta_{b}$ is a set of $B$ dummies (one for ...
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0answers
10 views

State space form

I want to write the following equations on state space form, but I am unsure how it looks. $u_t=u_t^*+u_t^*+\epsilon_t^1$ $u_{t+1}^*=u_{t}^*+\epsilon_t^2$ $u_{t+1}^c=\lambda_1 u_{t}^c+\lambda_2 ...
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1answer
26 views

Expectation vs Variance in Economics

When deciding between two projects available, where E[ReturnB] > E[ReturnA] but Var[B] > Var[A], why would this not be a clear case and rather look at the principle of maximization of expected return? ...
4
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1answer
33 views

A Question about Nested Maximizations

I am working on labor demand models where firms have to choose the optimal level of employment by maximizing profits. In particular, I have faced the following problem: Maximize with respect to $l$ ...
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1answer
64 views

Game theory question- no idea how to proceed

A monopolist sells two products, X and Y . There are three consumers with asymmetric preferences. Each consumer buys either one unit of a product or does not buy the product at all. The per-unit ...