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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-9
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0answers
27 views

Qd=1200-6P+0.5M-10Pb+4T+2Pe+3N [closed]

Qd=1200-6P+0.5M-10Pb+4T+2Pe+3N I need some help on this problem... a) Good A is a(n)_____good because the slope parameter on _____ is _____. b) Goods A and B are _____ because the slope parameter on ...
0
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0answers
31 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 ...
0
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0answers
37 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 ...
1
vote
2answers
51 views

income distribution from N, min,max and mediansalary, and total compensation

My goal is to obtain a reasonable approximation of the Gini index of a company (UBS). I need to obtain an estimate of the salaries distribution from publicly available data: Nuber of employees=60205 ...
2
votes
1answer
54 views

What is this subclass of the class of monotonic transformations?

Let $u$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$. Then $v$ is called a positive monotonic transformation of $u$ if $u(x) < u(y)$ if and only if $v(x)<v(y)$ and similarly for ...
-4
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0answers
22 views

Uniform distribution in Economics (price dispersion) [closed]

In the Salop-Stiglitz Model of price dispersion, Consumers are heterogeneous, with search costs uniformly distributed between 0 and 8. If y=G(c*)=G((1-x)*1) how would i work this out, as I am very ...
-2
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0answers
45 views

I don't understand how to compute the equation below

What I really don't understand is how to enter this equation (picture below) into a calculator, more specifically I would like some clarification as to what the significance of the (3 4) and (1 4) ...
3
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0answers
49 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 ...
1
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1answer
319 views

What is my unit of observation for this time series data set?

My professor gave us a data set to run a regression and I have a data set which lists years from 1959-2007, gross private investments (in billions of dollars), and gross private savings (in billions ...
1
vote
1answer
50 views

From utility function (3 products) to demand function (2 products)

I am struggling with this exercise and would appreciate some help. Consider two goods and a representative consumer whose utility is given by: $U(q_{0}, q_{1}, q_{2})= ...
0
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0answers
30 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) = ...
0
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1answer
25 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. ...
0
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1answer
13k views

Microeconomics: Calculating Tax Revenue and Tax incidence

Australian Government has imposed a tax on Beer. Assume that the tax on Beer is $20 per unit (a unit is a carton of drinks) Assume the demand and supply functions for cartons of Beers per week are: ...
1
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1answer
25 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 ...
0
votes
1answer
30 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, ...
4
votes
1answer
37 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 ...
2
votes
1answer
43 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. ...
2
votes
2answers
78 views

Measuring how “connected” nodes are in a network

I am an undergraduate studying economics and mathematics. I've never studied graph theory formally (only briefly in my spare time) and as such I don't have formal terms for what I'm clumsily trying to ...
3
votes
1answer
66 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. ...
1
vote
2answers
246 views

Third and average price auction

Third price auction: the winner is the highest bidder but this time instead of paying the second highest bid, he would pay the third highest bid. -assume there are at least 3 bidders. - Average price ...
0
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0answers
58 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 ...
1
vote
2answers
42 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 ...
0
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0answers
14 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, ...
0
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0answers
122 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 ...
0
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1answer
34 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 ...
0
votes
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 ...
1
vote
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 ...
3
votes
3answers
2k views

Using the definition of a concave function prove that $f(x)=4-x^2$ is concave (do not use derivative).

Let $D=[-2,2]$ and $f:D\rightarrow \mathbb{R}$ be $f(x)=4-x^2$. Sketch this function.Using the definition of a concave function prove that it is concave (do not use derivative). Attempt: ...
2
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1answer
91 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: ...
0
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1answer
21 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: ...
7
votes
2answers
4k views

Understanding the Leontief inverse

What I remember from economics about input/output analysis is that it basically analyses the interdependencies between business sectors and demand. If we use matrices we have $A$ as the input-output ...
3
votes
2answers
48 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 ...
0
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0answers
34 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 ...
0
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0answers
47 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 ...
-1
votes
1answer
47 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
2
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3answers
82 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 ...
4
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1answer
32 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 $l$ ...
1
vote
2answers
108 views

Proving that a function is monotone

Here is the setting: We have a middleman that buys a product from the producers, and sells the product to the customers. The middleman charges a price $R$ to the customers, and pays a price $p(R)$ to ...
1
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0answers
34 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 ...
10
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3answers
997 views

Can someone explain Cremer-Mclean's astonishing result in auction theory?

In mechanism design/auction theory, there is a famous result by Cremer and Mclean that if agents'/bidders' valuations are even slightly correlated, then all the surplus can be extracted by the ...
3
votes
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 ...
0
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0answers
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: ...
0
votes
1answer
27 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 ...
0
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0answers
9 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 ...
1
vote
1answer
36 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 ...
1
vote
1answer
25 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 ...
0
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0answers
26 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 ...
0
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0answers
20 views
17
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4answers
9k views

What exactly does it mean for a function to be “well-behaved”?

Often in my studies (economics) the assumption of a "well-behaved" function will be invoked. I don't exactly know what that entails (I think twice continuously differentiability is one of the ...
2
votes
2answers
1k views

derivative with respect to $\log(x)$

I have a dynamic equation, $$ \frac{\dot{k}}{k} = s k^{\alpha - 1} + \delta + n$$ Where $\dot{k}/k$ is the capital growth rate as a function of savings $s$, capital $k$, capital depreciation rate ...