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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6
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0answers
117 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 ...
5
votes
0answers
318 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
921 views

Can I get a PhD in Stochastic Analysis given this limited background?

General advice on PhD apps welcome Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic? 1/4 I ...
4
votes
0answers
176 views

How to solve a non-homogeneous second-order linear difference equation with both a forward and a backward difference?

Quite a long title for this: I'm looking for the general solution of the following difference equation: $$ax_{t+1} -bx_t + x_{t-1} = c + u_t$$ where $a,b,c$ are real constants and $u_t$ is a bounded ...
3
votes
0answers
31 views

Calculating the equilibrium price. ( Theory- whith no smooth supply and demands curves)

I was looking for a theory wich explain the following problem: I have the next , demand, supply curve: The book didn't explain how to compute the equilibrium price with this market (only was ...
3
votes
0answers
96 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 ...
3
votes
0answers
166 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 ...
3
votes
0answers
180 views

economic modelling asked for

I am putting together a proposal for a system of economic exchange which links a transaction of money through a period of time, and subjective relationship evaluation between two people. How can it be ...
3
votes
0answers
132 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
0answers
39 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
2
votes
0answers
42 views

How to differentiate without knowing the function, only the inputs?

Given a function $f(p, \alpha w)$, where $\alpha > 0$, how do I differentiate with respect to $\alpha$ ? The answer is supposedly $ w D_w f(p,w) $ (it says that it differentiated with respect to ...
2
votes
0answers
153 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 ...
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 ...
2
votes
0answers
282 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
2
votes
0answers
227 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
0answers
123 views

Suggestions for projects in mathematics of finance

I am looking for computational projects related to mathematics of finance suitable for a senior level independent study for a student who has seen the green light, (or the light of the green!). I had ...
2
votes
0answers
96 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 ...
1
vote
0answers
12 views

Infinite Horizon Transversality Condition

I am an economics student, and I have run into a question where I must apply a transversality condition in order to prove that we have a balanced growth path (all variables grow at the same constant ...
1
vote
0answers
9 views

Bayes risk and Bayes decision

We are considering a sample of size $n$ from an exponential distribution, with parameter $w >0$. We wish to produce an estimate for $d$, for $w$ , with loss function: $L(w, d)=w(w-d)^2$ The prior ...
1
vote
0answers
111 views

Question on economics (monopolist) (will involve simple calculus)

QUESTION: Consider the problem of a monopolist that sells its product on two different markets $m$, with $m=1,2$. Each market has an aggregate demand function given by $1200−α_mp_m$, where $p_m$ ...
1
vote
0answers
40 views

Basic optimization question

A teacher put this problem up the other day and I'm confused about how he got to the answer. Can you explain it to me? Job $X$ provides $20$ vacation days and $143,000$ euro annual salary. Job $Y$ ...
1
vote
0answers
20 views

Envelope theorem for Conditional value at risk

Let $X$ be a Gaussian random variable and suppose $f(p,X)$ is a strictly increasing and continuous function in $p \in \mathbb R$. Conditional value at risk is defined in the following way ...
1
vote
0answers
18 views

Difference between Sequential and Weak Sequential Equilbria

This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. ...
1
vote
0answers
38 views

Kuhn Tucker condition is sufficient for a global optimum?

$L$ is the variable and $s,r$ are parameters. The question asks to solve $max_{L\geq0}rf(L)-wL$ where $f(L)$ is twice continuously differentiable, strictly increasing and strictly concave. Then how ...
1
vote
0answers
16 views

R squared conceptual question with respect to number of observations.

The following statement is true. However, I have difficulties to understand why. I would appreciate if someone could explain it conceptually or perhaps with or without reference to any formula. In a ...
1
vote
0answers
15 views

consistency of variance MM estimators residuals

How can I prove with $Var(\hat{u})_t= E(\hat{u}^2_t)= (1- h_t)\sigma^2_0$ that MM estimator $\hat{\sigma}^2 \equiv \frac{1}{n} \sum_{t=1}^n \hat{u}_t^2$ is consistent? I can may assume that a LLN ...
1
vote
0answers
55 views

Unique Nash Equilibrium

If a game has a unique Nash Equilibrium, then does it have a unique Mixed Nash Equilibrium as well, where this MNE is the unique NE? The game I have in mind is the following (but I am more curious ...
1
vote
0answers
19 views

Quasiconvexity analog for function with an integer domain.

Suppose I have a function that is not quasiconvex, as in the graph below, but would be quasiconvex if we cared only about integer points. That is, $f:X \subset \mathbb{Z}\rightarrow \mathbb{R}$ ...
1
vote
0answers
34 views

On properties of linear orders

I have a simple question. Let $A=\{a,b,c,...\}$ be a set and $>$ a total strict order on $2^A$. Total strict order means that for any two subsets of $A$, say $S$ and $S'$, either $S>S'$ or ...
1
vote
0answers
26 views

Annunity calculation with and without tax

I'm doing a annunity calculation: payment = 331880*( 0,002458333 /( 1-(1+0,002458333)^-84) ) This will return me the payment per. month of the loan ...
1
vote
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 ...
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
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 ...
1
vote
0answers
35 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 ...
1
vote
0answers
95 views

Personal Experiences with Probability Simulation

Simulations methods are increasingly used in theoretical and (especially) applied probability. Personally, I have used simulation for purposes that range from recreational Q&A to applications of ...
1
vote
0answers
89 views

Utility maximization of n goods

I have a question that involves finding the optimal demand of $n$ goods for a consumer. However, I haven't anything like this before and I'm not sure how to proceed. The consumer has a utility ...
1
vote
0answers
35 views

Convolution of which distribution will give a uniform distribution?

Suppose there are two IID random variables x1 and x2. What should be the distribution of these random variables so that the distribution of x1-x2 is a uniform distribution?
1
vote
0answers
24 views

House allocation with existing tenants

In a house allocation with existing tenants model using the TTC mechanism, consider the incentive of an agent to misreport his/her preferences. Can it ever be that misreporting the true preferences by ...
1
vote
0answers
28 views

A sufficient condition for a good to be normal

Context: there are $2$ goods with prices $P_1$ and $P_2$ and the decision maker has the utility function $U(C_1,C_2)$. Denote $U_j=\frac{\partial U(C_1,C_2)}{\partial C_j}$ for $j\in\{1,2\}$. A good ...
1
vote
0answers
65 views

Follow-up on solution to Markov process equation

I asked a question here about solving a system related to an absorbing Markov chain. I now have a variation where there are $m$ types (of student, job seeker, etc) each of which applies to ...
1
vote
0answers
67 views

Application of a general “Weierstrass theorem”

http://books.google.at/books?id=9OSrV73a40gC&pg=PA45&lpg=PA45 gives a general Weierstrass theorem. Are there notable applications of this theorem, say in the calculus of variations? (I could ...
1
vote
0answers
27 views

Optimize profit given complete market information

Assume there are $N$ market participants (on the order of several hundred), and $M$ items (several thousand) being bought and sold on a market. For each participant/item pair, you know how many units ...
1
vote
0answers
39 views

Introductory book about economic models with deterministic chaos

I'm looking for introductory textbook about economic models (micro/macro/finance) which incorporate deterministic chaos. Models could be with or without random noise. By introductory I meant master ...
1
vote
0answers
368 views

Put-Call-Parity of Asian Options

I could need some help with deriving the put-call-parity for asian options. Let $S_t$ be the price of the underlying asset at time $t$ and set $Y_t = \int_0^t S_t dt$. Then the payoff of an asian ...
1
vote
0answers
110 views

Using data points and a best-fit to find a function for quantity with respect to price

So I'm taking an entrepreneurship class, and we're doing a simulation where we run a donut shop. My math is pretty strong (integral and differential calculus level), so I'm trying to use my math ...
1
vote
0answers
153 views

Solving the General Equilibrium with $4$ equations and $4$ unknowns

I have to solve four equations to solve the equlilibrium prices for the two countries: $\frac{2p_1}{w_1} + \frac{p_1}{w_2}= \frac{48w_1^2 + 4p_1^2+p_2^2}{8p_1w_1}+ ...
1
vote
0answers
3k views

Profit Maximization Question of a Leontief (Perfect Complements) Production Function?

This is a question from my intermediate micro economics text book. Any help is very appreciated! Given Info: Company ST (a company which offers custom travel-planning services) is a ...
1
vote
0answers
71 views

what is a connection between two simple yet important economics and math formula: elasticity

what makes it interesing to define them in mathematics? what is a connection between two simple yet important economics and math formula: elasticity? Something interesting to read: ...
1
vote
0answers
66 views

$\frac{\partial}{\partial\theta}\phi'\mu+\frac{\alpha\phi'\Sigma\phi}{2}=0$

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
1
vote
0answers
129 views

Optimal auction for risk averse seller

Consider an auction of a single unit of indivisible good. There are $n$ buyers whose values of the object is drawn independently from the uniform distribution on $[0,1]$. The buyers have interim ...