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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18k views

Deriving demand functions given utility

A consumer purchases food $X$ and clothing $Y$. Her utility function is given by: $U(X,Y) = XY +10Y$, income is $\$100$ the price of food is $\$1$ and the price of clothing is $P_y$. Derive the ...
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277 views

Deriving a demand curve intermediate microeconomics

The exercise says as follows: Zac consumes only pizza and Chianti in fixed proportions. 2slices of pizza per 1 glass of chianti. income is $100. Derive demand functions for pizza and Chianti. How do ...
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1answer
177 views

Preference Relation and Utility Function - Problem with inductive proof

I have a problem with an inductive proof of the following result. Theorem: If $X$ is a finite set, a binary relation $\succ$ is a preference relation iff there exist a function $u:X\rightarrow R$ ...
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63 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). ...
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1answer
149 views

Find profit maximizing profit and quantity given willingness to supply curves and a merger

This is a homework problem, but I'm at my wit's end. I don't even know where to start on this, but I've tried a number of strategies. Consider a regional market for wholesale electricity where ...
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2answers
3k views

Cournot-Nash Equilibrium in Duopoly

This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way of solving the following question: There are 2 firms in an industry, ...
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1answer
44 views

Cointegration for Price levels Time Series

I don't understand why is the difference between price levels is a stationary process while the time series of price levels themselves is a non-stationary process. For example: ...
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1answer
1k views

What is levy measure? Why is it needed, and what is $(1\wedge|x^2|)$?

A Borel measure $\nu$ on $\mathbb{R}$ is called a Lévy measure if $\nu({0})=0$ and $\int_\mathbb{R}(1\wedge|x^2|) \, \nu(dx) < \infty .$ ...
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1answer
100 views

Proving that a function is monotone

Here is the setting: We have a middleman that buys a product from the producers, and sells the product to the customers. The middleman charges a price $R$ to the customers, and pays a price $p(R)$ to ...
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1answer
606 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 ...
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90 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 ...
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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 ...
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1answer
427 views

Cobb-Douglas utility function

A simple Cobb-Douglas utility function: $$ U(X,Y)=\frac{X^{(1-\alpha)}Y^{\alpha}}{(1-\alpha)^{(1-\alpha)}\alpha^{\alpha}} $$ Here, I don't understand why we need the denominator: $ ...
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182 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 ...
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1answer
219 views

Normal distribution theoretical moments

how we can show that the following equality holds $E[(x-\mu)/\sigma]=0$ $E[(x-\mu)^2/\sigma^2-1]=0$ $E[(x-\mu)^3/\sigma^3]=0$ $E[(x-\mu)^4/\sigma^4-3]=0$
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973 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 ...
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2answers
290 views

Profit and Loss calculation: Fake currency

A store buys an item for $\$50$. They price it then, at $\$80$ ($\$30$ profit margin). A customer buys the item from them with a fake $\$100$ note. The store returns $\$20$ to the customer. My ...
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1answer
694 views

Mean preserving spread vs higher variance

In the Wikipedia article for mean-preserving spread, the following is claimed without citation: If B is a mean-preserving spread of A, then B has a higher variance than A; but the converse is not ...
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0answers
91 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 ...
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1answer
245 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 ...
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2answers
1k 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 ...
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2answers
63 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: ...
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2answers
385 views

Maximum feasible output of a company

Imagine, I have following model. There is a company X, which produces one unit of final output from 0.2 units of input A and 0.8 units of input B. Inputs A and B are bought from respective ...
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3answers
148 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 ...
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2answers
380 views

Game theory: Nash equilibrium in asymetric payoff matrix

I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
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1answer
62 views

Need to know how to inteprete an inequality

Pls have a look at this: http://imgur.com/FRfoP This is a screenshot of my lecture notes, from economics. I know that the LHS refers to the utility the agent thinks she will get if she consumes ...
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0answers
83 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 ...
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1answer
66 views

Price mechanism question (economics)

There are two goods in the market $X1$ and $X2$ and both of their prices are positive. If an agent's utility function is given as: Q1 = amount of X1 agent buys, Q2 = amount of X2 agent buys, $u = Q1 + ...
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1answer
47 views

Clarification of equations regarding capital switching and dated labor

Then, using this example (and further discussion), Samuelson demonstrates that it is impossible to define the relative "roundaboutness" of the two techniques as in this example, contrary to ...
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1answer
79 views

Why is profit of all firms zero in long-term?

I heard that profit of all firms in long-term becomes zero. But I am not convinced of why it is like that. Can anyone explain this mathematically?
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1answer
201 views

Input-output economics and stability of general equilibrium

Here, I will start with a simple expression for an input–output system with $x(t)$ representing the vector of outputs and $A$ the input–output matrix. Then, the simplest possible linear ...
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1answer
137 views

Mathematics behind Incentive Design

I was working on an Applied Math project on allocation and I had an interesting idea about extending it to providing incentives to different "players" in the allocation process. But I am clueless ...
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1answer
166 views

vickery auction question(second-price auction)

The question is as follow, Alice and Bob would both like to own the same manuscript. The manuscript is worth 5 million to Alice and worth 3 million to Bob. The present owner of the manuscript ...
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1answer
155 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 ...
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1answer
274 views

subgame perfect nash equilibrium for war of attrition

the question is as follow: suppose that two players are playing war of attrition, that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if ...
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2answers
4k views

cournot competition with N-firms

The question is as follow: Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q1, Firm 2 chooses Q2, and so on. The market ...
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1answer
160 views

Cournot-game problem

I'm so stuck with an exercise about Cournot game and was hoping if someone could help me out here. Would appreciate all the help. This is the exercise: Consider the market for Blue Turtle (a new ...
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1answer
215 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 – ...
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1answer
99 views

question on T period bargaining(alternating offers).

the following question is a kind of Rubinstein bargaining model: 2 players, A and B, have 100dollars to divide between them. They agree to spend T days negotiating over this division. The first day, ...
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1answer
128 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 ...
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1answer
815 views

Eigenvalues of matrix and stability

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 determined by the ...
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0answers
129 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 ...
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1answer
123 views

Find the real exchange rate

If the nominal exchange rate increases by 5%, while domestic inflation is 2% and foreign inflation is 3% then the real exchange rate changed by?
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1answer
237 views

Question on mixed nash equilibrium!

The question is as follows: Think of the Golden Ball game. Now player 1 is money-minded and jealous, and player 2 is very good-hearted, so the payoff matrix is follows: ...
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1answer
388 views

Arrow-Debreu model of general equilibrium having many equilibria

I am just beginning to study some stuffs outside introductory/sophomore(?) micro/macroeconomics. And I met with a stuff called Arrow-Debreu model. The question is, 1) What would be the proof that ...
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1answer
108 views

Understanding revenue and profit math stuffs in labor theory of value

In http://wrongarithmetic.wordpress.com/2010/08/22/keen-i/, it talks about how economists Steve Keen's argument against Labor Theory of Value (LTV) is wrong. What I do not get is from This ...
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1answer
118 views

long run equilibrium problem

Suppose the market for schools in a small town is of perfect competition. The market demand for school seats, $y$, is given by $y(p)$. The long run average cost function for each school is given by ...
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1answer
173 views

Net Present Worth Calculation (Economic Equivalence)

I'm currently doing some work involving net present worth analyses, and I'm really struggling with calculations that involve interest and inflation, such as the question below. I feel that if anyone ...
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1answer
83 views

Interpreting an integral/ probability

Think of two iid random variables $x$ and $y$ with density $f$ and CDF $F$ and a constant $c$. What could the qualitative meaning of the following expression be? ...
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1answer
3k views

Can someone explain what plim is?

In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor doesn't explain it well at all. Can someone tell me ...