# Tagged Questions

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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### What is my unit of observation for this time series data set?

My professor gave us a data set to run a regression and I have a data set which lists years from 1959-2007, gross private investments (in billions of dollars), and gross private savings (in billions ...
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### Economics maximization problem linear activity

Consider the vectors: $a_1 = \begin{pmatrix} 0 \\ -1 \\ 1 \\0 \end{pmatrix}, a_2 = \begin{pmatrix} 0 \\ 0 \\ -1 \\1 \end{pmatrix}, a_3 = \begin{pmatrix} 2 \\ 0 \\ 0 \\ 1\end{pmatrix}$ Find a single ...
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### Could math have predicted with certainty the banking crisis? (Why did it happen?) [closed]

The economics I do understand seem like trivial mathematics. Complex proofs are required for engineering involving safety - algorithm running times for pacemakers, strengths of physical structures ...
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### Which derivative is correct?

Consider the following expressions: $$C_{i}=\sum_{j=1}^{N_i}v_{j}, \quad v_j \in \mathbb{R}, \quad N_i \in \mathbb{N}$$ $$x_{i}=\frac{C_{i}}{N_i}$$ I want to obtain an ...
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### Applying Slutsky's Equation

Note: I asked in the Mathematics Meta regarding if it is permitted to ask Mathematics questions of economic nature. I also posted this question in the Economics Stackexchange but have not got any ...
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### Economics : Game-theory (Nash equilibrium)

This is a homework question, but resources online are exceedingly complicated, so I was hoping there was a fast, efficient way to solving following question. Question: Six students are going on a ...
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### The simplest, advanced optimal pricing problem

Consider an arbitrary distribution, $F(x)$, with density $f(x)$ and the property of increasing hazard rate: ${f(x)\over1 - F(x)}$ increasing in $x$. Let $p^*$ maximize $p(1-F(p))$. Show that $p^*$ ...
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### Applied Rational Choice Theory

I am a programmer researching the application of Rational Choice Theory. I have found many links to the philosophical nature of it. And fewer documents formalizing it's mathematical principles. ( ...
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### Calculate future price with continuous compounding

A forward contract for 4 months is entered into when a stock index is at 1000. If the risk free interest rate is 3% per year (with continuous compounding) and the dividend yield on the index is 2% ...
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### Normalization in Economics (relative price)

I am reading a textbook in Economics and realized normalization of price is extremely common. (Reference: Microeconomic Theory (MWG, p 24)) Can somebody please help me understand two things: (1) ...
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### Euler Equation and Marginal Rate of Substitution

I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well ...
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### Maximize firm's profit

Please give me any advices how to solve this. I'm good in maths, but I just don't understand these economical issues A firm's profit is given by the function: $PROFIT(L,K) = 50 L^{0.2} K^{0.8}$, ...
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### Find change in gross profit after price change

How do you solve this question? A company has 3 products. They contribute to 30%, 30% and 40% of sales respectively. They have profit margins of 15%, 30%, and 50% respectively. If the ...
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### Replication a options portfolio

I'm not too sure I'm going about answering this question correctly. I have used the following to derive my answer. I see that the portfolio above is a combination of a short-call(strike price 20) ...
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### help for an integral

I need help calculating this integral: $$\int_0^x \frac{2(e^{\gamma u}-1)}{(\gamma+\kappa)(e^{\gamma u}-1)+2\gamma} du$$ I tried with the integration by parts but the situation seems to get ...
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### What is this subclass of the class of monotonic transformations?

Let $u$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$. Then $v$ is called a positive monotonic transformation of $u$ if $u(x) < u(y)$ if and only if $v(x)<v(y)$ and similarly for ...
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### Counterexample to each Arrow's axiom

I am trying to find ways that combine group preferences which hold for 3 out of the 4 Arrow's axioms. Here is what I have come up with so far: Unrestricted Domain Not sure what scheme would ...
I' trying to solve this problem but would need some help: Let $N=N(t)$ denote the size of a certain population, $X=x(t)$ the total product and $y(t)=X(t)/N(t)$ the product per capita at time $t$. ...