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
82 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
224 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
32 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
119 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
116 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
103 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
159 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
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0answers
76 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
0answers
106 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
156 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 ...
1
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0answers
46 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
25 views

Properties of this set of functionals (mixed pairings)

(from the 4th page of http://www.math.toronto.edu/mccann/papers/econ.pdf) Let $X$ be a compact Hausdorff space, and let $\omega$ be a Borel probability measure on $X$. A Borel probability measure, ...
1
vote
0answers
19 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
24 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
54 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
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0answers
77 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
808 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
188 views

Stone-Geary utility function

$$ u(C_{t})=\frac{(C_{t}-\underline{C})^{1-\sigma }-1}{1- \sigma};\sigma > 0 $$ Does anyone know how to solve the utility maximization problem here and how consumption varies depending on ...
1
vote
0answers
61 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
50 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
82 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 ...
1
vote
0answers
90 views

Math model - constrain GDP given different growth rates of industries

ideas needed to model national GDP given different sector growth rates subject to some contraints Given: GDP equations for $n$ industries depend on growth rates and time i.e. $g(r_1,t), g(r_2, t), ...
1
vote
0answers
45 views

How is “index” at an Walrasian equilibrium proved? (in relation to Hopf-Poincare theorem)

So, the index of an (Walrasian/general equilibrium) equilibrium point is determined as the sign of $(-1)^{L-1} \times \det M$ where $M$ is a matrix and $M_{ij} = \frac{\partial{Z_i}}{\partial {p_j}}$, ...
1
vote
0answers
160 views

Econometrics Simultaneous equation Indirect Least Squares and Two Stage Least Squares

I still can't figure out this problem. PLEASE HELP! (1) $F_t = a_1 + a_2.C_t + a_3.P_t + e_t$ (2) $P_t = b_1 + b_2.F_t + b_3.S_t + b_4.I_t + u_t$
1
vote
0answers
61 views

Differentiation help

I recently got some lecture slides, but needed a little help understanding the maths behind them. (equations) (Working and Answer) Basically, I don't understand how to get from step (4) to (5). ...
1
vote
0answers
84 views

Game theory question- information quality maximisation, opinions of the question

I am developing a game theory question to help in deconstructing situations where information quality is comprimised and requires valuation against a set of criteria. I would be interested to know any ...
1
vote
0answers
24 views

Is there a trade model which takes in account credulity?

I have to admit I'm not to familiar with mathematical economics but, as a student in mathematics, I was trying to play a bit with a toy trade model I'm try to build over a finite population. My ...
1
vote
0answers
81 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 ...
1
vote
0answers
106 views

Trading price of 2 consumers with the same utility function

Say that two consumers, A and B, have the same utility function, just $u(x) = (x_1)^2 + (x_2)^2$ for simplicity. If consumer A has endowment $x_A = (4, 3)$, and consumer B has endowment $x_B = (3, ...
1
vote
0answers
370 views

Time flow analysis and theoretical flow time

I'm working for my program for economy where I have an example I try to solve. The flow rate is 0.15 units/min and A - 1 server: flow time = 5, capacity = 0.2 B - 2 servers: flow time = 9, ...
1
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0answers
122 views

Democratic central planning model

I want to model following situation: 1) There is a number of representatives of social groups (e. g. political parties). 2) Each of them devises an economic plan for the next year (N+1, N being ...
1
vote
0answers
383 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. ...
0
votes
0answers
103 views

preference relation.

In the exercise below I need to check whether the relation below is a preference relation ( need to be transitive (if $x>y$ and $y>z$ then $x>z$) and connected ). But I cannot find an ...
0
votes
0answers
51 views

Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and ...
0
votes
0answers
23 views

How do I express this profit function as a function of prices only?

How do I express this profit function as a function of prices only? The function is $(p-AC)q$, where $p$=price, $AC$=average cost (NOT marginal cost), and $q$=quantity sold. so in numbers ...
0
votes
0answers
62 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 ...
0
votes
0answers
27 views

Silly fraction question

I've got $$ MPK'=\frac{1-d}{1+r+x} $$ But I need it in the form $$ MPK'=d+r+x $$ How do I bring those up top?
0
votes
0answers
26 views

2 competitive or cooperative products?

I found this question in a calculus book and I'm not sure how to go about solving it: What exactly am I supposed to do to answer this? Do I need to find the first and second derivatives of each ...
0
votes
0answers
28 views

Spence signalling model question

My thinking: The unconditional expected marginal product = $1p_1+2p_2+3p_3$. I'm finding it hard to understand where the $y^*$ would lie.
0
votes
0answers
43 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 ...
0
votes
0answers
11 views

Maximizing Revenue in Relation to Occupancy Cost

I'm working on an expansion strategy for a retail client and I want to develop the ideal size space to occupy. We have several stores worth of data to pull and we know revenue, square feet, occupancy ...
0
votes
0answers
41 views

What quantity should the firm produce if it wants to maximize its profit given short run marginal coast and short run total cost function

A bicycle repair shop charges the competitive market price of 10 dollars per bike repair. The firms short run total cost is given by STC(Q)=$\frac{Q^{2}}{2}$ and the associated marginal cost curve is ...
0
votes
0answers
106 views

Computing the certainty equivalent for the lottery of infinite expected value

How can I compute the certainty equivalent for the lottery for someone whose Bernoulli utility function is $u(x)=\frac{x^{1-\gamma }}{1-\gamma }$ where $0< \gamma < 1$? Also, how much would the ...
0
votes
0answers
108 views

Robinson Crusoe economy problem

Consider the Robinson-Crusoe one-consumer, one-producer economy. Compute the equilibrium prices, profits and consumption when the production function is $f(L)=\sqrt{L}$, the utility function is ...
0
votes
0answers
34 views

Deriving the lagrangian multiplier

Could someone kindly help me with: 1. a step by step method of deriving the lagrangian multiplier 2. what are the uses of the lagrangian multiplier. I'm really new to this and your help will be ...
0
votes
0answers
28 views

Uncertainty and Strategy problem

Let $\delta _i$ denote the probability distribution (or lottery) that gives probability $1$ to obtaining the $i$th prize. In other words, $\delta _i$ is the $n$-element vector that has a $1$ in the ...
0
votes
0answers
21 views

Accounting for social costs in a CBA

I am writing a report regarding the cost-benefit analysis of installing a wind turbine. The report takes into account market (i.e.cost of purchasing the turbine) and non-market costs and benefits ...
0
votes
0answers
58 views

How are relative maximum problems solved?

I found this problem in an economics mathematics book self test and I really do not know how a person goes about solving a problem like this: I think there is differentiation involved but I'm just ...
0
votes
0answers
103 views

Question involving theory of the firm

Any ideas on how to help me get started on this question? A firm's technology possesses all the usual properties. It produces output using three inputs, with conditional input demands ...
0
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0answers
36 views

Optimizing revenue clicks CPC

I am quite new to optimization procedure and would like to get some hints here: I am work for a small business that offers a service of niche selling items where subribers pay for every item they ...