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
5k views

An algorithm for arbitrage in currency exchange

I found a really interesting problem and I wanted to hear people's opinion. It has to do with currency exchange rate. If we are give some coins $c_1,c_2,\dots,c_n$ and an array $R$ that keeps the ...
2
votes
1answer
297 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
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3answers
146 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 ...
10
votes
2answers
866 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
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1answer
2k 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?
1
vote
1answer
495 views

How to show that Roy's identity holds in the case of a monotonic increasing transformation?

I know that by Roy's identity, the Marshallian demand for a good (i) is $x^*_i = -\frac{V_i}{V_y}$, where $V(Y,P)$ is the indirect utility function, $V_i=\frac{\partial V}{\partial P_i}$, and ...
0
votes
2answers
6k views

Given supply and demand curves, and a tax, how can I find the tax burdens and revenue?

Suppose we have the following system of equations: $Q_s=-20+3P$ $Q_d=-220-5P$ $Q_s=Q_d$ Say we want to find the tax burden of the consumer, the tax burden of the firm, and the total revenue ...
1
vote
1answer
304 views

Optimization price per unit

I have no idea how to do this, I tried a lot of things but they don't make sense and I have too many variables. A manufacturer has been selling lamps at the price of \$6/lamp, and at this price ...
0
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2answers
374 views

What can I deduce from the graph of marginal value?

Homework problem: We have a graph of value: x coordinate number of widgets made. y coordinate value in $. For the first 5 widgets the value greatly increases to $100 and then after 5 ...
3
votes
1answer
560 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
1answer
69 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. ...
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1answer
1k views

Proof involving a convex set

So, the problem is actually from a microeconomics class. The problem is this: If preferences are represented by a utility function $u(x,y)=xy$, show that these preferences are convex. Now in case ...
1
vote
1answer
303 views

Economic optimisation problem

Here is the question: Consider a car-owning consumer with utility function $$u (x) = x_1x_2 + x_3 (x_4)^2 ,$$ where $x_1$ denotes food consumed, $x_2$ denotes alcohol consumed, $x_3$ denotes kms of ...
1
vote
1answer
2k views

How do I graph this budget constraint?

How do I graph the following conditions? We are in two good life, spinach and sprouts, spinach on x axis, sprouts on y axis. If you consume 10 or less servings of spinach, you pay \$5 for each. Above ...
0
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3answers
851 views

Economics supply and demand question

If the market demand for shoes is given by $QD = 10000-250P$ and the supply is $QS = 5000$, what is the equilibrium price of shoes? How many pairs of shoes will be sold? Thanks in advance.
2
votes
1answer
659 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 ...
10
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5answers
3k 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 ...
1
vote
2answers
494 views

Engineering Economics - Annual Cost Question

My question is as follows: 1.) An earth compactor costs $38,000 and has an economic life of 9 years. However, the purchaser needs it for only 1 project that will be completed in 3 years. At the end ...
3
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0answers
126 views

Optimal tax rate

Suppose you have two countries A and B, with a tax rate $T_A$ and $T_B$, respectively. The tax is redistributed to all people equally. Hence if you live in A and you make $I$ as income then you will ...
2
votes
1answer
430 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 ...
10
votes
1answer
397 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 ...
1
vote
0answers
433 views

Maximizing two codependant profit equations for Bertrand Model Oligopolies

For this problem I was given the Fixed Cost, Marginal cost, and demand curves for two firms (x and y). So far, from this information I derived the profit (π) function for each firm. ...
3
votes
2answers
595 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 ...
0
votes
1answer
156 views

Optimizing Group Spending

I have always thought that groups of individuals that spend more money(as opposed to save) have more money in the long run. My reasoning is that if a particular group spends money, then each dollar ...
1
vote
1answer
286 views

Find a price vector p for various prices of industries.

( Leontief input-output model ) Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according to the $3 \times 3$ consumption matrix A = ...
0
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1answer
3k views

Computing the break-even point

Problem The Lake Shore Inn is trying to determine its break-even point. The inn has 50 rooms that are rented at $60 per night. Operating costs are as follows, in dollars ...
1
vote
1answer
170 views

Normal distribution probability

just a quick question dealing with probability. The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal ...
5
votes
1answer
232 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 ...
4
votes
2answers
469 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 ...
5
votes
1answer
700 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 ...
13
votes
11answers
7k 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 ...
17
votes
4answers
8k 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 ...