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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8
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1answer
347 views

Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest ...
2
votes
1answer
41 views

Second price auction, page 82-84 of Osborne's An Introduction to Game Theory

Consider the second price auction defined and discussed on pages 82-84 of Osborne's An Introduction to Game Theory $($pages 80-82 here in this online draft version of the textbook: Martin J. Osborne, ...
-2
votes
0answers
30 views

Mean and variance of rank data with and without ties

My question has multiple parts, thanks for any help. With no ties, what would be the mean and variance of rank data 1 to n? Considering ties, would the mean increase/decrease...Would the variance ...
0
votes
0answers
31 views

Assigning value in a marketplace

In a marketplace where two parties come together for a transaction, both parties are necessary in order to create value for the marketplace. Where the marketplace is responsible for attracting both ...
1
vote
1answer
30 views

Deriving demand from quadratic utility function

How do you derive the demand for utility $u(x_1, x_2) = x_1^2 + x_2^2 $ and initial endowment is $\omega = (2,2) $? I believe this demand has three cases. Thank you
1
vote
1answer
40 views

Consumer Surplus

I am working on an economics problem where my solution is not correct, and I'd like to know why. Below is the question and my subsequent work/solution: The demand function for a particular ...
4
votes
1answer
23 views

Modified parcheesi game

A "modified Parcheesi" game starts with the following position: First $x$ flips a fair coin. If heads he can move two spaces or pass. If tails he can move one space or pass. If he occupies the ...
0
votes
2answers
81 views

Limit of CES function as $p$ goes to $- \infty$

I am trying to evaluate the limit of the CES Production function: $$Y=(aK^p + bL^p)^{1/p} $$ when $p$ goes to -infinity. It first yields the indeterminate form $0^0$. I tried solving the problem by ...
1
vote
1answer
29 views

Pure and mixed strategy in Nash Equilibria with n player

I got confused when I see the following problem: There are n staffs and they want to raise their salary, if any one or more than one of these staffs suggest their boss they want raise salary, all ...
0
votes
1answer
83 views

What is the pure strategy Nash Equilibria of asking your professor to cancel class?

Each student in a class has the option to remain silent or ask the professor to cancel class. If any students asks to cancel class, all students get a payoff of $r$. However, the student that asks ...
0
votes
2answers
346 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 ...
-1
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0answers
24 views

game theory atomic selfish routing

An asymmetric scheduling instance di ers from an atomic selfi sh routing instance in the following two respects. First, the underlying network is restricted to a common source vertex s, a common sink ...
3
votes
1answer
4k 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 ...
0
votes
2answers
37 views

How to make your own supply/demand graphs on a computer?

This is an econ question but I think you guys might have the solution. I am writing an economics paper and I need to show, in my theory, shifts in the supply and demand that I predict. I don't have ...
3
votes
1answer
149 views

Mistake in Wikipedia article on St Petersburg paradox?

I suspect that there is a mistake in the Wikipedia article on the St Petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...
3
votes
3answers
41 views

How does this derivative notation work?

Elasticity of substitution = $\dfrac{\mathrm d \ln(k/l)\;\;\;}{\mathrm d \ln(f_l/f_k)}$ This is type of notation I haven't really worked with before. Is this read as "The change in the natural log of ...
0
votes
0answers
25 views

Using Mean vs Median for Rapidly Changing Data

I am writing a report on global GDP per capita trends. As many of you know, were large shifts in the growth rates of these figures before and after the Great Recession. There has been some analysis on ...
0
votes
0answers
34 views

How to compute implicit rental rate?

I come across this question in my economics textbook, however I have no idea how to compute the implicit rental rate. Marc bought a new car last year for \$10,000. He can now sell the car for ...
0
votes
2answers
27 views

Interpretation of market completeness: full row rank payoff matrix

Suppose that there are $K$ assets and $S$ states of nature. The assets' payoff is represented by the matrix $$ \underbrace{R}_{S\times K}=\begin{pmatrix} r_{11}&\cdots& r_{K1}\\ ...
1
vote
1answer
62 views

Find consumer demand as a function of time, given the demand equation and price

An importer of Brazilian coffee estimates that local consumers will buy approximately $Q(p)= 4374/p^2$ kg of the coffee per week when the price is $p$ dollars per kg. It is estimated that $t$ weeks ...
0
votes
1answer
27 views

Showing public returns to be greater than private returns mathematically

Take this headline "OECD figures show public benefits more than individuals from tertiary education." How would I present this mathematically, to show that public returns are greater than private ...
3
votes
2answers
90 views

Claim: Mathematical models of the economy have thousands of variables

A quote from the book Linear algebra done right by Axler is as follows: "Mathematical models of the economy have thousands of variables" I find this hard to ...
2
votes
2answers
45 views

Find the consumer surplus, given supply and demand equations

Find the Consumer Surplus, given the demand and supply equations $$ D(x)=\frac{405}{\sqrt{x}} $$ $$ S(x)=5\sqrt{x} $$ The equilibrium point is $(81,45)$. I know the formula for consumer ...
0
votes
1answer
50 views

Optimization to minimize cost using the function C=Tq^(1/a)+F

I was given the function of $C=Tq^{1/a}+F$ where $C$ is total cost, $q$ is output, $a$ is a positive parametric constant, $F$ is the fixed cost, and $T$ measures the technology available (also a ...
2
votes
0answers
29 views

What are the most recent devopments with applying fractals to economics?

I was researching fractals for my senior mathematics presentation and discovered that one of the most recent pioneers in that section of the field was able to apply fractal mathematics to the field of ...
1
vote
1answer
24 views

Finding Preto Optimal allocation if utlities are of the form $u_1=x_{11}x_{12}$ and $u_2=2x_{21}+x_{22}$

There are two persons and two goods in an exchange economy. Initial endowment is $$ \omega = (\omega_1,\omega_2) =\left((1,0),(0,1)\right)$$ The utilities of two agents are given by: ...
0
votes
0answers
22 views

growing number of sample

The problem I have is as following, which I would like a solution to I am a tomato seller Everyday I sell tomatoes. I also have a demand forecast for tomatoes required everyday countrywide. I§m ...
-2
votes
1answer
47 views

maths- econA reasonably realistic model of a firm’s costs is given by the short-run Cobb- Douglas cost curve C=Tq^1/a+F w [closed]

A reasonably realistic model of a firm’s costs is given by the short-run Cobb- Douglas cost curve $$C=Tq^{1/\alpha}+F$$ where $C$ is total cost, $q$ is output, $\alpha$ is a positive parametric ...
0
votes
1answer
66 views

Maximizing total tax revenue with function Qs+-8+P and Qd=(80/3)-(1/3P)

The supply and demand equations of a good are given by Qs= -8+P Qd=(80/3) - (1/3)P P is measured in dollars. Suppose the government decides to impose a constant per unit tax of $t on the supplier. ...
0
votes
1answer
127 views

Von Neumann–Morgenstern independence axiom vs. Savage independence theorm

Von Neumann–Morgenstern independence axiom: Savage independence theorem: What is the difference between the two? I'm think Von Neumann is talking about the prizes (outcomes) and Savage is talking ...
0
votes
2answers
34 views

Chain rule using the expression F=150W^1/3

Suppose the attendence of a baseball game was denoted by W alone in the format F=(150W)^1/3. Is this function (strictly) concave or convex. Explain. To which I answered that it would be strictly ...
0
votes
1answer
21 views

Present Worth with Salvage Value

I would like to know how to consider the "Salvage Value" in the following question while calculating the present and future values. here is the question: We are planning to build a new bridge. ...
0
votes
1answer
489 views

Elasticity of demand given a quantity and a price function

I have a price function: $$ \frac{8,100,000}{q^2+8,100} $$ Where $q$ is quantity demanded. How can I find the price elasticity when $q = 30$? I know how to differentiate, but I'm just not sure what ...
0
votes
1answer
90 views

Partial Derivative Math Homework Help

The attendance (denoted by the variable F , measured in thousands of fans) at a blue Jays home game is approximated by F = 150W^(1/3)P^(2/3) Where W is the fraction of the games they have won so far ...
1
vote
1answer
103 views

How to find the price elasticity of demand?

I need help answering if this is demand elastic of inelastic. A policy adviser suggests that in order to improve its balance of trade with china, Canada should lower the price of some heavy ...
0
votes
0answers
29 views

Help with optimization and second-order conditions on area ):

If I wanted to enclose an area to have a total of 3000 square feet. I have two types of walls. Stone walls which cost 45 per foot. Stone walls must cover three walls. Wood walls cost 20 per foot. Wood ...
0
votes
2answers
54 views

Optimization across markets - How can I solve?

I am unsure how to solve problems involving several markets and optimizing the price across all my markets. Note: I am looking to be pointed in a specific direction of study, not a solution to the ...
0
votes
2answers
31 views

Finding the Maximum with Calculus, second order condition.

Question: "At a price of $8$ dollars per icket, a musical theatre group can fill every seat in the theatre, which has a capacity of $1,500$. for every additional dollar charged, the number of people ...
1
vote
2answers
58 views

Calculus of optimization help ):

If I need to sell 400 chairs. The price per chair is 90 dollars up to and including 300 chairs. Above 300, the price will be reduced by 0.25$ (on the whole order) for every additional chair over 300 ...
1
vote
3answers
61 views

Economics, numeraire, utility, demand, marginal rate of substitution

I typed my question in Microsoft Word and printscreen it instead of typing it, this is because I don't know how to type mathematical questions here, sorry for the inconvenience caused.
12
votes
0answers
321 views

Equilibrium existence proof

Problem: Let $J$ be an integer and let $I$ be an integer multiple of $J$. Let ${\cal I}= \lbrace 1,2,\ldots, I\rbrace$ and ${\cal J}= \lbrace 1,2,\ldots, J\rbrace$. The set $X_{I,J}$ of all ...
1
vote
1answer
46 views

Intemporal budget by lagrange

Assume that a representative agent lives forever and receives an endowment, denoted yt, in each period. The entire endowment sequence is known with certainty on date 0. The representative agent ...
0
votes
1answer
6k 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: ...
0
votes
1answer
40 views

Utility index function-would appreciate some clarification (confused about a log function)

I have already solved the problem but would appreciate a clarification in part (b). A has initial wealth w and faces a loss l with known probability pi. Insurance available at unit price p will ...
1
vote
1answer
26 views

Non strictly convex “singleton” preferences

A relation $\succeq $ over a vector space $X$ is rational if it is transitive and complete. We say $x\succ y$ iff $x\succeq y$ and NOT $y \succeq x$ Moreover $x\sim y$ iff $x\succeq y$ and $y ...
2
votes
1answer
49 views

quasi rationality, interesting axiom of revealed preferences

So imagine there is a notion of rationality that captures the idea of "thresholds in preference." For example, let $\mathbb{Z}$ be the integers: $\mathbb{Z} = \{\dots, -10, -9, \dots, 0, 1, 2, ...
0
votes
1answer
90 views

Easy (?) application of Lagrange multiplier

I am reading a book about utility theory and there is a exercise (without solution). I can't stop thinking about this, since the normal Lagrange multiplier approach seems not to work. We want to ...
0
votes
1answer
81 views

Help to solve this problem, the result doesn't seem right :/ silly mistake somewhere probably

Suppose that Coke and Pepsi are the only firms producing cola. Their products are not identical, but are very close substitutes. Let $P_c$ denote the price of Coke and $P_p$ the price of Pepsi. Demand ...
1
vote
1answer
50 views

How do I find if this estimator is unbiased and also its variance?

I need to find if the estimator $\tilde{\beta } _{2} = \frac{(y_{n}-y_{1})}{(x_{n}-x_{1})} $is unbiased given that i) $E(u_{i}\mid x)=0$ ii) $E(u_{i}\mid x_{i})=0$? I also need to calculate its ...
-2
votes
1answer
38 views

Optimization Problem with cost and profit [closed]

For the cost function $C(x)=3100+600x+0.6x^2$ and the demand function $p(x)=1800$. Find the production level that will maximize profit.