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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1answer
54 views

How to build (and maximize) this equation

I'm trying to solve an economics problem but I cannot figure out how to build the equation system, or how to find the maximum in a piecewise function. A simplified version of the function would be ...
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1answer
80 views

Find the transaction cost-adjusted expected return of the stock

Let $W^b_i$ denote the weight of stock i in the existing portfolio and $W^a_i$ denote the weight of stock i in the new portfolio to be created. Let $c_i$ denote the transaction cost of stock $i$. If ...
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2answers
354 views

Geometric series to calculate price

I decided to add my extension to this question as a new question here. I am trying to represent the following as a geometric series equation: ...
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1answer
107 views

Using limit argument with non-continuous social-choice functions

This question is related to another question of mine Invariance of strategy-proof social choice function when peaks are made close from solution, and it revolves around the use of limit arguments with ...
6
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1answer
149 views

Invariance of strategy-proof social choice function when peaks are made close from solution

A question emerging from reading Schummer, J., & Vohra, R. V. (2002). Strategy-proof Location on a Network. Journal of Economic Theory, 104(2), 405–428. The setting is as follows: A finite set ...
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2answers
299 views

Solving for steady state in macro model, probably just simple calc problem…

I am building a macroeconomic model and I am having trouble calculating the steady state. GDP in the model is determined by Y(L,B,K) = x*L+y*B+z*g*K where (x,y,z) are known constants, L is the ...
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1answer
24 views

Finding the most profitable option

Right now, I have 1€. And I know exactly how to invest that euro to make profit, but I have 3 options: Invest the euro, and win exactly 1€ (I'd have 2€ then) Invest the euro, and earn some money ...
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1answer
76 views

Compound discount

I am trying to construct an equation for calculating a price, that takes into account compound interest of 10%. 1 item = $10 2 items = $19 3 items = $27.1 so ...
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1answer
59 views

Concept of efficiency in auctions

I have some confusions about the concept of "efficiency" in auction theory. One interpretation is that an auction is efficient if it maximizes the social-welfare. But social-welfare is not well ...
2
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1answer
304 views

What kinds of sets are reasonable to place on the continuum?

Warning: I don't know anything about set theory so I wouldn't really know how to spot an existing answer if it were around. Suppose I want to model some economic good or product. I would like to ...
4
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2answers
119 views

Does Arrow's Theorem apply when choosing a single best candidate?

According to Wiki, Arrow's Impossibility Theorem proves that we cannot create a social welfare function that obeys unanimity, non-dictatorship, and IIA. However, in real elections, we want to choose ...
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1answer
183 views

Minimizing total cost function

In today's test (question c) I had to minimize equation $(3)$ and solve for N*. I did it through deriving, setting to $0$ and solve for N (no doubts about that). My question is, in this image it ...
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1answer
102 views

Calculating the bank multiplier.

The question is as follows: In a simple close economy, banks are required to maintain a liquidity ratio of 8%. An additional £15 billion of currency is deposited in the banking system. Calculate the ...
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1answer
253 views

Relation between quasilinear utility and quasilinear function

When we say Quasilinear utility, it is known that function is linear in numeraire. It is expected to be linear in one argument and hence it can be called *quasi*linear. Can any one tell me if there is ...
0
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1answer
169 views

Quasilinear utility functions

Is the utility function below quasilinear? $U(X,Y)=XY+10Y$ I know that an equation of the form $U(X,Y)=f(X)+Y$ is quasilinear but I'm not sure about functions of the form $U(X,Y)=f(X,Y)+Y$.
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1answer
23k 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 ...
0
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1answer
357 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
208 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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0answers
67 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
171 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 ...
2
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2answers
4k 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
45 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: ...
2
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1answer
2k 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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2answers
107 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 ...
4
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1answer
794 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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0answers
92 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
25 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 ...
0
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1answer
495 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: $ ...
2
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0answers
196 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
239 views

Normal distribution theoretical moments

how we can show that the following equality holds $E[(x-\mu)/\sigma]=0$ $E[(x-\mu)^2/\sigma^2-1]=0$ $E[(x-\mu)^3/\sigma^3]=0$ $E[(x-\mu)^4/\sigma^4-3]=0$
6
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1answer
1k 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
339 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
855 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
109 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
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1answer
281 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 ...
2
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2answers
65 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
510 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
154 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
401 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
64 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 ...
2
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0answers
87 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
75 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
50 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
80 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?
1
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1answer
231 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 ...
1
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1answer
147 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 ...
2
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1answer
185 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 ...
2
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1answer
174 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
312 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 ...