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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1answer
24 views

Given the utility function $U(F,G)=FG^2$, find the MRS

Intermediate Micro. My understanding for MRS conversions is that you find the derivative of each variable and place the former over the latter. That then in this case yields $\frac{1}{2G}$? Is this ...
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1answer
40 views

Corollary of the Frisch-Waugh Theorem

Consider the following linear regression model: $$y=X \beta + \epsilon = X_1 \beta_1 + X_2 \beta_2 + \epsilon $$ Where we have $n$ obsevations and $k$ variables, and hence $X$ is a matrix $nk$, and ...
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1answer
98 views

Is it true that everything that isn't linear is concave or convex (or both)?

In the conclusion of anti-fragile by Taleb, he claims that "everything non-linear is concave or convex, or both". Is the statement general, and if not, what are its limitations? I suppose he is ...
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0answers
26 views

General equilibrium econmy

I need to solve this problem. Any help there? Consider the economy consists of two and three goods. Consumers A and B have a preference on the consumption of goods 1 and 2 can be represented by the ...
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1answer
33 views

Is $f(g)$ homogeneous? If so, of what degree?

Given $f$ and $g$ are homogeneous functions of degree $k$. I have to show if $f(g)$ is homogeneous or not, and if so, of what degree. Definition (Homogeneous function). Let ...
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2answers
56 views

Preference Maximizing Choice Rule

Definition: A Choice Rule is a function $ C: \mathcal{P}(X) \to \mathcal{P}(X) $ such that $ C(B) \subset B, $ $\forall B \in \mathcal{P} (X) $ and $ C(B) \neq \emptyset $ if $ B \neq \emptyset $ The ...
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1answer
47 views

Using risk aversion

I'm trying to figure out what the non-stochastic equivalent payment is for someone who is risk-averse. Suppose we have a lottery that pays out\$100 with probability one half and \$0 with probability ...
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1answer
17 views

Maximum maintains order under limit in $\mathbb{R}^2_{+}$

I'm trying to show that if: $$ (a_{1n},a_{2n})\to (a_1,a_2)\\ (b_{1n},b_{2n})\to (b_1,b_2)\\ max\{a_{1n},a_{2n}\}\geq max\{b_{1n},b_{2n}\},\forall n\in\mathbb{N} $$ Then: $$ max\{a_1,a_2\}\geq ...
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2answers
40 views

If $x_i$ is from a random sample is $Var(\bar x \mid x_i)=0$?

If $x_i$ is from a random sample, is the conditional variance of the mean (or the sum of squares, really any statistic based on $x$) just treated as a constant? I saw this in a OLS variance of a ...
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0answers
34 views

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 ...
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0answers
26 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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1answer
33 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
123 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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1answer
65 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
84 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
90 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
78 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
107 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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0answers
96 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
158 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
65 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
33 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
62 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
53 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
75 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. ...
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1answer
51 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
243 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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0answers
75 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
42 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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0answers
133 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
17 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
27 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
32 views

Population and production in a dynamic system [on hold]

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 $t$. ...
3
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2answers
110 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
77 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 ...
2
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1answer
235 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
76 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
74 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
53 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
41 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 ...
3
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1answer
43 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
99 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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1answer
74 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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1answer
51 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
90 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
68 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
24 views

Percentage Increase and Dates

Suppose we have the following data: ...
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1answer
21 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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1answer
28 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
40 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 $l$ ...