The economics tag has no wiki summary.
14
votes
4answers
3k 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 ...
10
votes
10answers
2k views
Which 4 maths courses to take as an Economics PhD student?
I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...
10
votes
2answers
304 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 ...
10
votes
1answer
298 views
A (mathematically) sound investment strategy
It is common wisdom in the investment community that a long-term investor saving for his future would do well to invest in high-risk/high-return assets when he is young, slowly switching his portfolio ...
8
votes
5answers
1k views
Motivating linear algebra for economics students?
I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors.
This is a typical ...
6
votes
1answer
58 views
Invariance of strategy-proof social choice function when peaks are made close from solution
A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428.
The setting is as follows:
A finite set ...
5
votes
1answer
678 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 ...
5
votes
1answer
221 views
Measure of value of resources in a competitive game
Let we have a competitive survival game in which a player has choice between different resources to earn. The question here is which resource should he prefer to maximize the chance of survival. I ...
5
votes
0answers
175 views
Olympic Badminton, or How to Design a Tournament
Hearing the recent news about disqualified Badminton players in the ongoing 2012 London Olympics got me wondering about how best to design tournaments to avoid situations where players are ...
4
votes
2answers
67 views
Does Arrow's Theorem apply when choosing a single best candidate?
According to Wiki, Arrow's Impossibility Theorem proves that we cannot create a social welfare function that obeys unanimity, non-dictatorship, and IIA.
However, in real elections, we want to choose ...
4
votes
2answers
1k views
Cournot Nash Equilibrium Between Two Firms
Suppose we have two firms with specialized, but similar products. Suppose market demand for the two products is:
$$p_1(q_1,q_2)=a-bq_1-dq_2$$
$$p_2(q_1,q_2)=a-bq_2-dq_1$$
where $d \in (-b,b)$. Suppose ...
4
votes
2answers
112 views
Slope of a nonlinear curve at a single point
This part of my microeconomics lesson plan has me baffled.
Consider for example the nonlinear continuous and differentiable function Y = f(X) = X 2 + 4. Suppose we want to know its slope at the ...
4
votes
1answer
81 views
Gibbard–Satterthwaite Theorem versus Arrow Theorem
Arrow Theorem is a very classical result in social choice theory, stating very roughly that any reasonable voting procedure is either dictatorial or subject to tactical voting. More precisely, there ...
4
votes
1answer
90 views
Is functional integration useful in theoretical economics?
Definition of functional integration here
Functional integration is a collection of results in mathematics and
physics where the domain of an integral is no longer a region of
space, but a ...
4
votes
1answer
468 views
Lower hemicontinuity of the intersection of lower hemicontinuous correspondences
I have been stumped for long by this exercise (3.12(d)) from Stokey and Lucas's Recursive Methods in Economic Dynamics. Would greatly appreciate any hints.
Let $\phi: X \to Y$ and $\psi: X \to Y$ be ...
4
votes
0answers
92 views
Open Problem in Fixed Point Theory [Prize]
This open problem appeared on the bulletins of Evans Hall at Berkeley this week.
I hope this doesn't violate StackExchange policy (the solution carries a $500 prize), but I thought why not re-post ...
4
votes
0answers
59 views
How to minimize game night transactions?
Me and a number of friends occasionally met up and play some game (often pool or some card game) and play for small stakes to give the game a little extra spice. After each round we jot down the ...
3
votes
3answers
324 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:
...
3
votes
2answers
192 views
Majoring in maths
Does majoring in mathematics with economics (with emphasis on mathematics) have good career prospects? Does anyone know something about this course?
3
votes
1answer
380 views
What's the most straight-forward way to prove Walras's Law?
Walras' Law states that summation of pi Ei(p) = 0 for all pi.
We define Ei(p) = xi(p) - qi(p) - Ri.
What are the next steps that I should take?
3
votes
2answers
294 views
Finding best response function with probabilities (BR) given a normal-matrix representation of the game
We are given players 1, 2 and their respective strategies (U, M, D for player 1, L, C, R for player 2) and the corresponding pay-offs through the following table:
$\begin{matrix}
1|2 & L & C ...
3
votes
1answer
36 views
Stability under supremum of sets of social choice function with single peaked preferences
Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455.
The setting is as follows:
A non-empty finite set of ...
3
votes
1answer
129 views
Finding mixed Nash equilibria in continuous games
I'm taking my first (graduate-level) game theory class. I understand how to find Nash equilibria in simple games, such as those given in finite tables, and can see (usually) how to find the mixed ...
3
votes
0answers
55 views
How many dollars does it take to be rich?
This is probably a dumb economics question since I don't know anything about that subject beyond a few buzzwords (but I do know a little math). I'm trying to figure out how many dollars it takes to ...
2
votes
2answers
96 views
From which areas of mathematics does consumer theory in microeconomics spawn?
In my intermediate microeconomics class last year, I was rather surprised by the math involved in building consumer theory. In consumer theory you do things like define a binary relation $\succsim_a$ ...
2
votes
2answers
105 views
How can I reconcile these two different equations for “Arc Elasticity”?
Well, I've encountered a problem which seemed me like a wrong answered one so, I Google'd for the formulas of both "Arc Elasticity" and "Arc Elasticity of Demand" So far, I've found myself in some ...
2
votes
3answers
98 views
Problem relating convex sets and optimization
I am working on a microeconomics problem, but I have just kind of just boiled down to the following problem involving convex sets. I have a convex set of vectors in $\mathbb{R^n_+}$ of the form ...
2
votes
2answers
342 views
Are the Karush-Kuhn-Tucker conditions applicable when one or more of the constraints are nonlinear?
I am just beginning to read about the use of "Concave Programming" methods and use of the Karush-Kuhn-Tucker conditions to identify the maximum value of a non-linear objective function subject to ...
2
votes
1answer
82 views
Stability of a system that has (Jacobian-like) matrix with eigenvalue of less than 1 that has $x$ as non-eigenvector
This is about general equilibrium:
Suppose that $x(t)$ represents outputs of all sectors and parts of the
whole economy - represented as matrix. How outputs evolve to $x(t+1)$
is ...
2
votes
1answer
200 views
Solving a Maximum Likelihood Estimation with an exponential distribution
I need someone's insight on applying a MLE for an exponential distribution. In a finance paper, I have the following:
$\displaystyle d_i \sim \frac{\epsilon_i}{\lambda_i}$ where $\epsilon_i$ is ...
2
votes
1answer
215 views
How to find Pareto-improvements with maths?
I hope this is not off topic.
I've got two utility functions for two different kinds of agents, A and B, and their endowments ($w_1$ and $w_2$) of the (2) goods ($x_1$ and $x_2$).
The utility ...
2
votes
1answer
131 views
Application of the Factor–Price equalization theorem (Samuelson) on trade?
I'm trying to understand the factor price equalization theorem by Samuelson. I came across this graph but I don't know how to interpret it. Could anyone give me a short resume on what the graph is ...
2
votes
1answer
224 views
Statistics with overlapping periods
I've been having a lot of discussions about finance recently in which people will point to some results using overlapping time periods and claim a high degree of statistical significance. For ...
2
votes
1answer
75 views
Elasticity of Substitution (CES)
This appears to be a nice forum. I just registered since I have a question...
I have a CES aggregator-function
$$
f(c,q) = (r c^{a} + b q^{a})^{1/a}.
$$
It is postulated that it can be rewritten as
...
2
votes
1answer
47 views
A question about infinite utility streams
At the end of Diamond's Evaluation of Infinite Utility Streams he proves a theorem (which he doesn't give a name to, but it's at the very end of the article). There is a step in which he jumps from ...
2
votes
1answer
117 views
Economics: two rival firms in two countries
I am currently working on a paper in macroeconomics, where I found a result that I cannot manage to understand. Since we don't have a macroeconomic site yet, and this is mostly game theory, I will ...
2
votes
1answer
97 views
How to prove that there exist a concave function and $\gamma\in[0,1]$ and some other numbers which satisfy an inequality
I'm working on an economics paper, and in the model I've made I've basically gotten myself a little bit stuck. I need to show that there exists a nondecreasing concave function $u$ and numbers $P$ and ...
2
votes
1answer
65 views
Incomplete “round trip” of taking a minimum, then a maximum, from a positively skewed distribution
Let's say you have a distribution that is either symmetric or positively skewed (and defined over 0-1). Call it F.
Then, you find the distribution of the minimum of n>1 draws from F. Call it Fmin.
...
2
votes
1answer
234 views
Production Function
Yes.. I know this is a math forums but there is no economics.stackexchange.com :(.
Since this is also a math problem, I thought I'd post it here. Please help.
An undeveloped economy produces goods ...
2
votes
0answers
45 views
What kinds of sets are reasonable to place on the continuum?
Warning: I don't know anything about set theory so I wouldn't really know how to spot an existing answer if it were around.
Suppose I want to model some economic good or product. I would like to ...
2
votes
0answers
80 views
What is the (expected) outcome of this hybrid auction?
A certain hybrid auction can be accurately modelled as follows.
There are $n$ risk-neutral, rational participants $i=1,2,\ldots,n$, and a guy called Zerro: $i=0$.
Each, except Zerro, has a private ...
2
votes
2answers
57 views
Creating indices
Is there a "proper" formula for creating indices? I need to compute series of numbers into a KPI that can be tracked over time.
Example dataset is like this:
...
2
votes
0answers
42 views
Constructing and understanding stock-flow model
Suppose that $\textbf{x} = A\textbf{x} + B\dot{\textbf{x}}$ where
$\textbf{x}$ is vector of economic output level, $A$ is input-output
matrix, $B$ is stock-flow matrix. The system represents ...
2
votes
1answer
67 views
Applied Math for economics question: mostly algebra help
I am teaching myself the calulus component necessary to get thorugh an econ based stats and applied math class. My algebra is killing me please help - the practive problem is given
$y = –x^3 + 7x – ...
2
votes
0answers
66 views
Optimal strategy in a VCG auction with partial collusion?
Suppose you control the bid prices in a multiple-item VCG auction for a partial coalition of bidders. Each bidder is only allowed to win one item out of the set of multiple items, which are all ...
2
votes
1answer
62 views
Non-core allocations in the 2-fold replica of an economy.
Here's the definitions I'm using, just in case.
Let $E$ be the exchange economy given by agents $A,B$, starting allocations $x_A=(0,1)$, $x_B=(1,0)$ and utility functions given by $u_A=x+y$ and ...
2
votes
0answers
89 views
proof using (fixed point theorem)
I am seeking to solve for a Nash equilibrium in pure strategies $(d_2,d_2)$ involving two players, $1$ and $2$. Given that $h'(.)$ is s strictly decreasing and continuous function, $\Phi(d_1-d_2)$ ...
2
votes
0answers
211 views
Nash equilibrium question
(Hotelling’s voting model) Consider a population of voters uniformly distributed along the ideological spectrum from left (x = 0) to right (x = 1). There are two candidates i = 1,2 for a single
office ...
2
votes
0answers
83 views
Optimal tax Rate
Assume you have two countries A and B, with a tax rates $T_A$ and $T_B$. The tax is redistributed to each people equally. Hence if you live in A and you make $I$ as income then you will finally ...
1
vote
3answers
142 views
My brothers share from income.
My brother is driving a limo with his partner who told him that they will go 50-50 on income and also 50-50 on gas.
So if my brother earns \$1000 by spending \$200 on gas, what will be my brothers ...
