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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82 views

Economic Elasticity: where elasticity-equation come from?

I know the equation for economic elasticity is: $$\varepsilon = \frac{\%\,\Delta Y}{\%\,\Delta X}\frac{X}{Y} = \frac{\partial Y(X)}{\partial X}\frac{X}{Y} = \frac{\partial \log(Y)}{\partial ...
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1answer
21 views

Change in the price of an item based on a group's need for the item.

Okay so this is likely to be confusing to read, please bear with me. The base price of an item is 1440. There are only 6 of these items and there is a population of 20. 10 of the population want or ...
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1answer
183 views

When do $\epsilon$-Nash equilibrium strategies converge to Nash equilibrium strategies?

Suppose I have a game on $n$ players and a sequence of strategy profiles $(s_1^{(1)},\dots,s_n^{(1)}), (s_1^{(2)},\dots,s_n^{(2)}), (s_1^{(3)},\dots,s_n^{(3)}), \dots$. Each ...
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1answer
124 views

Existence of asymmetric equilibria in the dollar auction game

Consider a game in which an auctioneer sells one dollar to the highest bidder. The high bidder wins the dollar, but every bidder pays their bid. Concretely, assume that there are two bidders ...
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1answer
119 views

Wealth indicator function for bidder agent logic

I want to create a wealth indicator function used by the logic of a bidder agent, that tells the agent if he's rich (in comparison to others). Given: Total number of competitors $n$ Amount of all ...
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1answer
2k views

L'hopital's rule in deriving Cobb-Douglas function from CES production function

$$ \ln(Y) = \ln(A) + \frac{\ln[\alpha K^\gamma + (1-\alpha) L^\gamma]}{\gamma}$$ can be taken to the limit by applying l'Hôpital's rule: $$\lim_{\gamma\rightarrow 0} \ln(Y) = \ln(A) + ...
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0answers
174 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) $P_t = b_1 + b_2.F_t + b_3.S_t + b_4.I_t + u_t$
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231 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 ...
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1answer
189 views

Random walk serial correlation

Given a model $$Y_t =b_0 + b_1 \cdot X_t + b_2 \cdot Z_t + e_t,$$ where the error term $e_t$ follows a random walk form of serial correlation $e_t = e_{t-1} + u_t$. Further assume $u_t$ has zero mean ...
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1answer
74 views

Stability under supremum of sets of social choice function with single peaked preferences

Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455. The setting is as follows: A non-empty finite set of ...
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2answers
364 views

Endowments & Utility Function to get Demand Function

We have two people, $A$ and $B$, A has $200$ units each of both good $X$ and $Y$ and $B$ has $100$ units each of both good $X$ and $Y$. $A$ has tastes providing a utility function such that $u(X,Y) = ...
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1answer
47 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
64 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
219 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
95 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 ...
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1answer
119 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
159 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
22 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
68 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
48 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 ...
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1answer
303 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 ...
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2answers
105 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
128 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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83 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
177 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 ...
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1answer
141 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
11k 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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1answer
213 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
140 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
62 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
131 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
2k 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
97 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
484 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
85 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
371 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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0answers
168 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
197 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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1answer
737 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
240 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
583 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
85 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
226 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
789 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
61 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
307 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
146 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 ...