# 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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### How to find unkown height of triangle without hyptenuse

I been trying to solve this question and have tried to solve it for many days, but do not know how, any help would be much oblidged. A cable company owns the roads marked with the dotted lines in ...
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### Calculus for Economics

Please suggest me a good book for Calculus. I am a beginner. It would be better if you tell me which book would be appropriate for learning Calculus for understanding Economics.
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### Auction Design : Multiple lots, one win max per bidder, not regret

This is a real life game theory problem. I have to organize an auction. There is a finite number of lots, which are not equivalent. There is a finite number of bidders; the number of bidders is ...
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### Underlying utility function behind a linear two-product demand curve

I am trying to find the underlying utility function behind a linear two-product demand model. For that, I use two methods considering the following utility function: U(q_1,q_2) = \...
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### Consumer surplus for multiple products

I want to extend the classical definition of consumer surplus to multi-product case. For a single product, consumer surplus is given as CS=\int_ {p_{market}} ^ {p _{\max}}D(p)dp. \end{...
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### computing a fixed interest rate

I've been struggling for hours now with understanding a Topcoder problem, Autoloan , but i cannot grasp the way of computing it from a mathematical point of view. The excerpt goes as follows: A ...
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### Same Expected Value but different variances. Is $E[U(X)] \ge E[U(Y)]$?

Let $U: \mathbb R -> \mathbb R$ be a concave function, and let $X$ be a random variable with a normal distribution, expected value $\mu$, and standard deviation $\sigma$. Let $\lambda \gt 1$, and ...
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### Prove that $E[U(X)] \ge E[U(Z)]$

Let U: $\mathbb R$ -> $\mathbb R$ be a concave function, let X be a random variable with a finite expected value, and let Y be a random variable that is independent of X and has an expected value 0. ...
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### Graph Theory text for social scientist.

I am a graduate student in Economics. I have a decent grounding in maths, but I've never studied graph theory or combinatorics. I need to study graph theory in order to analyse production networks. ...
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### Is 2nd-price with a discount auction truth-telling?

I know that 2nd-price auction is truth-telling, but 3rd-price auction is not. What If I run the regular 2nd-price auction, in the end, the winner is charged at the 2nd bidding price with a discount, ...
268 views

### Market Equilibrium & Calculus

I am a math nerd, but I'm working on my majorly lacking derivative analysis calculus. Trying to break into better understanding market equilibrium. I found some example questions that I am working ...
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### I need something like “how to calculate equilibrium price for complete idiots”

My grandfather rises, sells and resells livestock and I want to help him by calculating when and for what price to (re)sell or buy livestock. As far as I understand(although I have a hunch that I need ...
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### Arrow’s Theorem

Suppose $k ≥ 3$ Recall that Arrow’s Theorem shows that any function $F:(S_k)^n\to S_k$ (the input is composed of n permutation of $[k]$ and the outcome is a single permutation of $[k]$ that satisfies ...
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### Scaling value based on a variable range

I'm looking for a formula that produces a predictable and scaling result based on an initial input variable. The initial input will be between 0 and 48, and needs to return a number between 0.8 and 1....
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### Need help understanding a simplification in a simultaneous search model.

The problem I am trying to solve is $\max_{k \in \mathbb{N}} \int_0^1 u d F(u)^k - ck$, where the associated utility is an iid random variable U following $F(\cdot)$ on [0,1]. $c > 0$ is the ...
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### Population and production in a dynamic system [closed]

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 $t$. ...
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### Percentage change relationship

Given $Z=X^{\alpha}$ how can one prove that the percentage change in $Z$ is simply $\alpha$ times the percentage change in $X$? This was given as a 'simple mathematical rule' in an economics text ...
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### Y open relative to X

I'm trying to prove the following theorem: Let $X\subseteq\mathbb{R}^{k}$, $Y\subseteq X$. Then $Y$ is open relative to $X$ $\iff$ $\forall y\in Y\exists\epsilon>0\ N_{\epsilon}^{X}(y)\subseteq Y$,...