# 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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### If you have two envelopes, and …

Suppose you're given two envelopes. Both envelopes have money in them, and you're told that one envelope has twice as much money as the other. Suppose you pick one of the envelopes. Should you switch ...
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### Lower hemicontinuity of the intersection of lower hemicontinuous correspondences

I have been stumped for long by this exercise (3.12(d)) from Stokey and Lucas's Recursive Methods in Economic Dynamics. Would greatly appreciate any hints. Let $\phi: X \to Y$ and $\psi: X \to Y$ be ...
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### 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), 405â€“428. The setting is as follows: A finite set ...
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### Limit of CES function as $p$ goes to $- \infty$

I am trying to evaluate the limit of the CES Production function: $$Y=(aK^p + bL^p)^{1/p}$$ when $p$ goes to -infinity. It first yields the indeterminate form $0^0$. I tried solving the problem by ...
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### Can I get a PhD in Stochastic Analysis given this limited background?

General advice on PhD apps welcome Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic? 1/4 I ...
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### Matrix question: implication of $\frac{1}{n}X'X\to M$

Suppose $K$ is fixed and consider a matrix $X$ that is $n\times K$ and has full column rank. Assume that we know $$\frac{1}{n}X'X\to M\text{ as } n\to\infty.\tag{i}$$ That is, as $n$ becomes larger, ...
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### Third and average price auction

Third price auction: the winner is the highest bidder but this time instead of paying the second highest bid, he would pay the third highest bid. -assume there are at least 3 bidders. - Average price ...
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### Mistake in Wikipedia article on St Petersburg paradox?

I suspect that there is a mistake in the Wikipedia article on the St Petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...
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### How can a social welfare function be a linear combination of von Neumann-Morgenstern utility functions?

The von Neumann-Morgenstern axioms were an attempt to characterize rational decision-making in the presence of risk. The von Neumann-Morgenstern utility theorem says that if someone is vNM-rational, ...
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### 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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### 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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### Does one necessarily need an MS in Math before taking a PhD in Math? [closed]

I finished bachelor's in mathematical finance and am nearly finished with master's in mathematical finance (I am already done with thesis), and I plan to pursue a PhD not in mathematical finance but ...
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### Existence of a utility function on the reals

Suppose I have $\preceq$, a total order on $\mathbb R^n$. I wish to show that there is a utility function $u:\mathbb R^n\to\mathbb R$ such that $x\preceq y \leftrightarrow u(x)\leq u(y)$. I came up ...
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### Is the standard definition of vector wrong?

The definition of a vector is usually something like "a quantity that has both a magnitude and a direction". But, in the context of, say, economics rather than physics, does this definition make ...
We are given players 1, 2 and their respective strategies (U, M, D for player 1, L, C, R for player 2) and the corresponding pay-offs through the following table: $\begin{matrix} 1|2 & L & C ... 2answers 598 views ### Geometric series to calculate price I decided to add my extension to this question as a new question here. I am trying to represent the following as a geometric series equation: ... 0answers 65 views ### Follow-up on solution to Markov process equation I asked a question here about solving a system related to an absorbing Markov chain. I now have a variation where there are$m$types (of student, job seeker, etc) each of which applies to ... 1answer 43 views ### (Proof) Representing preorder$\succsim$as a real-valued function. I am reading a proof and having a hard time understanding on some parts. In math language, the proof is trying to show the existence of continuous preorder$\succsim$(i.e. preserved under limits, ... 1answer 80 views ### Suppose that the sequence of prices{$p_k$} converges to a limiting price$\bar p$. What must$\bar p$be? We let$Q_k$denote the supply of commodity,$D_k$the demand for the commodity, and$p_k$the price at$k$-th time. The demand depends on the current price,$D_k = a + b p_k$and the supply depends ... 1answer 95 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 ...
Each student in a class has the option to remain silent or ask the professor to cancel class. If any students asks to cancel class, all students get a payoff of $r$. However, the student that asks ...