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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Compound Interest similarity

You have just purchased a car with a $£20,000$ price tag. The dealer offers to let you pay for your car in $5$ equal annual instalments, with first payment due in a year. If the dealer finances your ...
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The correlation between alpha and beta

Consider the following 2-variable linear regression where error $e_i$'s are independently and identically distributed with mean 0 and variance 1; $$y_i=\alpha + \beta (x_i - \bar {x}) + e_i$$ where ...
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Effect on Minimizer of Tightening Constraints

The Statement of the Problem: Consider the minimization problem $f(x,y)=14x+20y$ under the constraints $x+2y \ge 4$, $7x+6y \ge 20$, and $x,y \ge 0$. Don't use the simplex method! (i) Draw the ...
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Convex combination and convex set

From where does $tx + (1-t)x'$ originate from? I am selfstudying an economists book, and this is popping up all of a sudden. I get that it's a line between $x$ and $x'$, but why? And is $tx' + (1-t)x$ ...
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Unknown functions yield a given determinant

I am trying to develop a nomogram which simultaneously shows the exact Fisher equation $(1+u) = (1+v)(1+w)$ and its linear approximation $u \approx v + w$. This amounts to finding twelve smooth ...
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Cournot competition: profit maximizer vs. market share maximizer

Today during an informal conversation with an established business researcher, I learned such a fact: In the classical Cournot competition model, if one player is a profit-maximizer, the other ...
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Econometrics/Statistics, variance and means

here's the problem I can't figure out on my own: The weight of a randomly selected student, (W), has a mean of $170$ and variance of $10$. Defining the new random variable ($Y$): the total weight of ...
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Gross Substitutes under continuous perturbations

Let $v_i(S)_{i \in [n], S \subseteq G}$ be a collection of Gross Substitute valuations. I am wondering if I can add a small perturbation to each valuation and still get Gross Substitute valuations. ...
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Profit Function where total revenue is re-spent on production?

I'm trying to find a function that finds the net profit gain over multiple iterations. For example, if I produce a unit for 5 dollars , and can sell it for 8 dollars, I would have a net gain of 3 ...
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Pricing a riskless asset in the Black & Scholes market

Consider a Black&Scholes Market where a risky asset evolves according to: $$\frac{dS_t}{S_t}=\mu dt+\sigma dB_t$$ $$S_o=s$$ Riskless asset is associated with risk free rate r. I want to represent ...
How would i go about solving the problem where i want to find $$max/min \quad \sum X_i$$ Where i have constraints which are $$M = P_1 X_1 + P_2 X_2+ P_3 X_3$$ and $$C_1 \geq X_1$$ $$C_2 \geq X_2$$ ...
Let $n$ be the number of voters and $A$ be the set of alternatives. For voter $i$, we denote by $a \succ_i b$, if $i$ prefers $a$ to $b$, where $a,b \in A$. Let $L(A)$ denote the set of all strict ...