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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2
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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
votes
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. ...
0
votes
1answer
52 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, ...
0
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0answers
248 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 ...
0
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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 ...
0
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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 ...
0
votes
1answer
18 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....
1
vote
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 ...
-1
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1answer
32 views

Population and production in a dynamic system [closed]

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
votes
2answers
120 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
votes
2answers
79 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$ $\forall y\in Y\exists\epsilon>0\ N_{\epsilon}^{X}(y)\subseteq Y$,...
2
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1answer
236 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: $c'(...
0
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0answers
81 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 ...
-2
votes
1answer
75 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
1
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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
votes
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 y_{t-1})^...
2
votes
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 ...
0
votes
1answer
101 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 ...
1
vote
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 necessary)...
1
vote
1answer
96 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
votes
0answers
70 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
24 views

Percentage Increase and Dates

Suppose we have the following data: ...
0
votes
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 ...
0
votes
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 $l$ ...
0
votes
1answer
76 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 ...
0
votes
1answer
30 views

Compound Interest similarity

You have just purchased a car with a $£20,000$ price tag. The dealer offers to let you pay for your car in $5$ equal annual instalments, with first payment due in a year. If the dealer finances your ...
0
votes
0answers
37 views

The correlation between alpha and beta

Consider the following 2-variable linear regression where error $e_i$'s are independently and identically distributed with mean 0 and variance 1; $$ y_i=\alpha + \beta (x_i - \bar {x}) + e_i$$ where ...
1
vote
2answers
56 views

Effect on Minimizer of Tightening Constraints

The Statement of the Problem: Consider the minimization problem $f(x,y)=14x+20y$ under the constraints $x+2y \ge 4 $, $7x+6y \ge 20$, and $x,y \ge 0$. Don't use the simplex method! (i) Draw the ...
1
vote
0answers
55 views

Show that if A and B are strictly convex, then A + B is strictly convex or provide a counter example.

We have: If A is open: $\exists x,y \in A,$ $x \neq y$ such that $\lambda x+(1-\lambda y)\in \dot A $ (the interior) and $\exists u,v \in B,$ $x \neq y$ such that $\lambda u+(1-\lambda v)\in \...
1
vote
1answer
29 views

A risk neutral individual chooses among a pair of gambles.

I'm a little confused about the following lecture slide, which is written as follows. A risk-neutral individual chooses among pairs of gambles ...
0
votes
0answers
103 views

How CES function with integral becomes min function in the limit

I wonder how a CES function over a continuum of goods, $$\left(\int_1^\infty c(\theta)^\delta g(\theta) \mathrm{d}\theta\right)^\frac{1}{\delta}$$ where $c(\theta), g(\theta)>0 \forall \theta\in\...
1
vote
1answer
26 views

Convex combination and convex set

From where does $tx + (1-t)x'$ originate from? I am selfstudying an economists book, and this is popping up all of a sudden. I get that it's a line between $x$ and $x'$, but why? And is $tx' + (1-t)x$ ...
1
vote
0answers
27 views

Unknown functions yield a given determinant

I am trying to develop a nomogram which simultaneously shows the exact Fisher equation $(1+u) = (1+v)(1+w)$ and its linear approximation $u \approx v + w$. This amounts to finding twelve smooth ...
2
votes
0answers
161 views

Cournot competition: profit maximizer vs. market share maximizer

Today during an informal conversation with an established business researcher, I learned such a fact: In the classical Cournot competition model, if one player is a profit-maximizer, the other ...
0
votes
1answer
30 views

Econometrics/Statistics, variance and means

here's the problem I can't figure out on my own: The weight of a randomly selected student, (W), has a mean of $170$ and variance of $10$. Defining the new random variable ($Y$): the total weight of ...
0
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0answers
17 views

Gross Substitutes under continuous perturbations

Let $v_i(S)_{i \in [n], S \subseteq G}$ be a collection of Gross Substitute valuations. I am wondering if I can add a small perturbation to each valuation and still get Gross Substitute valuations. ...
0
votes
1answer
119 views

Envelope Theorem and Static Optimization

The Statement of the Problem: For fixed $r \gt 0$ and $m$, find the maximum value of $1-rx^2-y^2$ on the constraint set $x+y=m$. Find the value function $f^*(r,m)$ and compute $\frac{\partial f^*}{\...
0
votes
3answers
180 views

How much is 6% a year in months?

I am currently in high school where we are learning about present value. I struggle with task like these: Say you get 6% interest each year, how much interest would that be each month?
2
votes
1answer
161 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 ...
1
vote
1answer
85 views

Can I embed $\mathbb R^{\mathbb N}$ with a partial order into $^\ast\mathbb{R}$ with the linear order?

Define a relation $\prec$ on $\mathbb R^{\mathbb N}$ as, For all $f, g \in \mathbb R^{\mathbb N} $, $f \prec g$, if for all $n \in \mathbb N$, $f(n) \leq g(n)$, and there exists a $m \in \mathbb ...
1
vote
1answer
14 views

Profit Function where total revenue is re-spent on production?

I'm trying to find a function that finds the net profit gain over multiple iterations. For example, if I produce a unit for 5 dollars , and can sell it for 8 dollars, I would have a net gain of 3 ...
0
votes
2answers
430 views

Using Lagrange for finding Marshallian Demand

I want to find the marshallian demand function for the user function $u(x_1,x_2) = x_1^ax_2^{1-a}$ where $a \in (0,1)$. This is what I have so far: $$L = x_1^ax_2^{1-a} - \lambda(p_1x_1 + p_2x_2 - y)$...
0
votes
1answer
449 views

Does one necessarily need an MS in Math before taking a PhD in Math? [closed]

I finished bachelor's in mathematical finance and am nearly finished with master's in mathematical finance (I am already done with thesis), and I plan to pursue a PhD not in mathematical finance but ...
1
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0answers
36 views

Quasiconcavity of $g(x)=xf(K-x)$

The function $f(x)$ is strictly increasing, finite, positive and twice continuously differentiable on the compact interval $[0,K]$, and $f(0)=0$. I'm trying to either find a counterexample to, or a ...
4
votes
1answer
132 views

Core vs. Strong Core in Housing Allocation Games

I am presently reviewing the course notes for my Game Theory course, and I'm struggling with the concepts of the core vs. the strong core. In the notes, we have three players, with preferences ...
2
votes
1answer
50 views

Mathematical question about currencies

I've tried to get an answer for this question elsewhere but with no luck, so I would appreciate a mathematical analysis of it. Assume $0\%$ commission. Consider three currencies, let's say the Zong, ...
2
votes
0answers
38 views

Average Cost of Obtaining in game Item

I know this will sound like a trivial maths problem, but recently I've been playing a game in which you can pay 5 in game gems to get a Rare (R), Super Rare (SR), and Ultra Rare (UR) characters ...
1
vote
1answer
45 views

Endogenous covariate in first-difference panel data model

I have a linear panel data set (murder.dta, standard STATA dataset). First I estimate a first difference model. An assumption from this model is that the first differences of the covariates and the ...