Questions tagged [economics]

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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Leontief inverse in undirected network [closed]

I sort of understand how the Leontief inverse is measured and where it is used. Though it occurred to me whether it makes sense to use this approach in undirected networks (e.g. correlation matrix).
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Theorem of the Maximum for discrete sequences of constraint sets?

Suppose that $\{X_{n}\}_{n=1}^{\infty}$ is a sequence of sets that converges to $X$ in some sense. Let $f$ be a real-valued function. I am interested in conditions under which $$ \lim_{n \rightarrow \...
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How is dropshipping profitable if this Oberlo article says it costs $250 in marketing to generate 5 sales? Can someone help better explain this? [closed]

Under the headline, " Dropshipping marketing costs—the biggie", this Oberlo article calculates the hypothetical cost of generating 5 Facebook sales. The math includes the idea that it would ...
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-1 votes
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Microeconomics - utility function [closed]

Gracie has a flat she needs to furnish. She has £500 to spend. However, she would also like to buy some clothes for her new job. The cost of furniture f is £50 per unit and the cost of clothing c is £...
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Rearranging Annuity formula

Can someone please show me how this is rearranged/simplified from this: PV = CF[(1-(1+r)^-n)/r] to PV= CF(1/r)[1-(1/((1+r)^n)] with steps, will help me wrap my head around it. Also, how does it go ...
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Mechanism Design problem about IC and IR conditions

here I have some doubts about the mechanism-design exercise in the image. Since there are 2 options that B can choose to default, not default, and 2 types including type 1, type 2, and having loan, ...
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Solow residual with cost minimization, calculus

I am trying to get a good understanding of the steps involved in solving the dual of a maximization problem, namely cost minimization. At some point (last two steps), the author ends up with the ...
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1 answer
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Total derivation with respect to time.

Good evening everyone, I am trying to get a good understanding of total differentiation versus time. The problem I can't understand is the following. Starting with the basic national income accounting ...
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1 answer
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Game Theory - What is the equilibria?

I think i'm braindead from the amount of time i've stared at this. What is the equilibria in each of the scenarios in this? and preferably the subgame perfect equilibrium? Is there even any, as player ...
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1 vote
1 answer
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Economics profit optimisation problem with 2 products

I am struggling to solve this problem. I formulated my profit equation involving total revenues from both products and then subtracting the cost function from this, yet I do not get correct answers. I ...
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2 votes
1 answer
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How to graph the elasticity function ( knowing the - linear-demand function and the price function )? What goes wrong in my Desmos graph?

My goal is to visualize the graph of the elasticity function for a linear demand curve . The problem I face is that the elasticity function graph I came up with looks unfamiliar. I suppose my formula ...
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1 vote
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"Slope" in mathematics and " slope" in economics.

Note : I mainly consider the case in which demand curves are linear , to keep things simple. I'm having trouble in applying mathematics to (micro)economics due to the fact that in this discipline , ...
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Can a level curve of a function (given) with certain properties be discontinuous?

Consider the function $u : \mathbb{R}^2 \to \mathbb{R}$ that the following properties are satisfied: Every level curve is a function from $\mathbb{R}$ to $\mathbb{R}$. (That is, a level curve $U(x,y)=...
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What is the discounted (4%) difference in health outcomes between Treatment A and Treatment B using ICER, QALY and utility value?

I'm studying health economics and have been racking my brain trying to find the right answer to this problem, but I keep getting it wrong no matter what I do. I haven't had any trouble calculating ...
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Leading eigenvalue and Leontief inverse

Is it possible to get a Leontief inverse matrix $(I-C)^{-1}=I+C+C^2+....$ not equal to $I$ when the leading eigenvalue of matrix $C$, meaning the maximum of absolute eigenvalues, is zero? I am doing ...
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Utility function and Insurance

Bob is an expected utility maximizer with utility function $u(x) = −e^{−ax}$, where $a > 0$ is a parameter. Bob has wealth $w$. There are two states of the world, a good state and a bad state. The ...
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2 votes
1 answer
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Level curves representable by real-valued functions on $\mathbb{R}$

EDIT: I incorrectly interpreted the original question. The bounty has been awarded based on the (incorrect) interpretation I wrote here. The final version is posted here. Consider the function $u : \...
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1 vote
1 answer
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Level curves of $Q(x_{1},x_{2})=\min\{2x_{1};x_{2}\}+\min\{x_1;2x_{2}\}$

I started thinking of different cases for example suppose $2x_{1}<x_{2}$, then $x_{1}<2x_{2}$. So $Q(x_{1},x_{2})=2x_{1}+x_{2}=3x_{1}$, then $Q/3=x_{1}$. But I think this path is endless. How do ...
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Integrate a function with a power when knowing the integral without a power

So I have this function $f(i,t)$ which when integrated over $i$ gives: $$\int_0^Nf(i,t)di=F(t)$$ How then can I then integrate this: $$\int_0^Nf(i,t)^\frac{\epsilon-1}{\epsilon}di$$ To come out as ...
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1 vote
1 answer
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Discrete time forward rate

I'm reading Jarrow and Turnbull (1997) . They defined p(t,T) as the time t price of a default free zero coupon bond paying a sure dollar at time T where $0\le t \le T$ (in year) . They also defined ...
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on nested CES derivation

Embarrassingly, I am having a hard time deriving one equation from a paper and am wondering if someone can help. I have a nested-CES function $Q$ that is defined as $$ Q(S, M, L) = \left[\alpha S^{\...
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Discontinuous function $U$ with continuous preferences can be written as a composition of discontinuous & monotone function and a continuous function

Let $U : X \subseteq \mathbb{R}^n \to \mathbb{R}$; $n \geq 1$. Conjecture: Every discontinuous utility function $U$ representing continuous preferences can be written as $U = f \circ g$ for some ...
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Why Mr.Brown Still get the interest?

here is the example in broverman's book A promissory note is a short-term contract (generally less than one year) which requires the issuer of the note (the borrower) to pay the holder of the note (...
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Is there a math formula to calculate the following math problem? (Days of spending based on income)

I would like to learn how to calculate the following in the most efficient way possible. I guess there is a math function existing that could do that. Right now i am using google sheet functions, but ...
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HW Question Related to Derivatives

I believe this is asking us to do a partial derivative. I will include the questions below. As well as you'll see some of my work. If I'm able to complete this section, I should be able to do the rest....
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Is it possible that a convex level curve between two other level curves have higher utility than the other two?

Consider a differential function $U(x,y)$ such that $U(x,y) = t$ is convex for any $t \in \mathbb{R}$. Convexity is defined as: Given $t \in \mathbb{R}$, for any two points $x$ and $y$ such that $U(x) ...
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3 answers
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Compound interest formula is not understandable

I am struggling to understand the formula for compound interest. More specifically what the $n$ stands for. The formula is as follows according to the wikipedia: $$ A = P(1 + \frac{r}{n})^{nt} $$ ...
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3 votes
1 answer
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Line equation tangent to convex level curve

Suppose we are given a differentiable function $f(x,y)$ such that $\forall$ $t \in \mathbb{R}$, $f = t$ yields strictly convex level curves. If we are given a line equation $L:y = mx + c$ such that it ...
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3 votes
1 answer
108 views

Example of utility functions

I am working on an Economics problem and an example function of a graph that looks like this would be helpful. Suppose the straight line is $ax + by = c$, and the curvy lines (called Indifference ...
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3 votes
1 answer
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Name of the functional $p \mapsto P_X[p] = X\int_X^\infty p(x)\,dx$

Let $p(x): \mathbb{R} \rightarrow \mathbb{R}^+_0$ be a probability distribution with $\int_{-\infty}^\infty p(x)\,dx = 1$. Is there a special name for the parametrized functional $$p \mapsto P_X[p] = ...
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Difference between Pareto optimal redistribution and strict pareto optimal redistribution

Can someone explain the difference between Pareto optimal redistribution and strict pareto optimal redistribution? Because I know the definition but I do not understand it.
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Pareto optimal redistribution in binary exchange economy

Consider binary exchange economy with two goods and two agents, whose preferences are defined as follows: $\textbf{x}\succ \textbf{y}$ iff $x_{1}x_{2}>0 $ and $y_{1}y_{2}=0 $. In Edgeworth's box ...
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1 answer
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Best response to a given game matrix

Consider the following game matrix: $\begin{aligned}[] \begin{array}{|c|c|c|} \hline & A & B \\ \hline C & 5,0 & 1, 2 \\ \hline D & 1,2 & 7,4\\ \hline \end{array} \end{...
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1 vote
0 answers
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Beginner linear programming exercise help [closed]

Question i to v Question vi I want to ask how to solve question (v) or (vi) only (preferably both if possible) I did question i to iv (for reference) (i)$$min_{\lambda,v} \sum_{t=1}^T b_t\lambda_t + \...
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Lagrange Multiplierd for Economics

An individual purchases quantities a, b, and, c of three different commodities whose prices are p, q, and r, respectively. The consumer spends m dollars, where $m\gt2p$, and the utility function of ...
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-1 votes
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positive semidefinite

For general linear model : y=XB+u , u~N(0,(ssq)I) , u are i.i.d Let b* be the OLS estimator of B ,ie. b*=inv(X'X)X'y . Let b be any linear unbiased estimator of B having the form : b=Hy where H doesn'...
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4 votes
1 answer
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Geometric growth rate and Kelly's Criterion question

In the Wikipedia page about Kelly Criterion, the author calculated the expected wealth after N bets as $$W * (1+g)^N$$ where $W$ is the initial wealth, and $g$ is the expected geometric growth rate. ...
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2 votes
1 answer
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Demand function in Edgeworth box economy

Show in Edgeworth box economy, where $\omega_1=(3,3), u_1(x_1,x_2)=x_1+2x_2,\omega_2=(4,1), > u_2(x_1,x_2)=x_1+x_2$ that the following functions determine demand function of agents ($\lambda\in[0,...
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It is an economic optimization problem with monopoly

This is the first time I came to StackExchange! I have a problem dealing with this question. I do not know how to solve this surplus maximization with constraint. Currently, what I have found is the ...
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1 vote
1 answer
50 views

TMA — optimal and pessimal mating

In the Traditional Marriage Algorithm (TMA), where boys propose and girls reject, can we say that boys get their optimal mate because boys go first and the girls wait? Let's define ideal mate where ...
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0 votes
1 answer
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Forms of Nelson Siegel formula

Are these two forms of Nelson Siegel formula equivalent? $s_{m}(\beta )=\beta _{0}+\beta _{1}\frac{1-e^{\frac{-m}{\tau _{1}}}}{\frac{m}{\tau _{1}}}+\beta _{2}\left ( \frac{1-e^{\frac{-m}{\tau _{1}}}}{\...
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Proof of equivalence of NE for two games in extensive form with imperfect information and no chance moves

I have the following prompt: Let $\Gamma_2$ be an extensive-form game with imperfect information in which there are no chance moves, and assume that the game $\Gamma_1$ differs from $\Gamma_2$ only ...
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Help a noob with notation (I'm reading some Revenue Management literature) [SOLVED]

Kind of a disclaimer: I'm completely self-learning at the moment and need some feedback to stay on the right course. Intro So, I'm reading "Dynamic Pricing Without Knowing the Demand Function: ...
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4 votes
1 answer
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Game holder is always losing money in the St. Petersberg Paradox?

The St. Petersberg Paradox is described as follows: A gambler pays an entry fee $M$ dollar to play the following game: A fair coin is tossed repeated until the first head occurs and you win $2^{n-1}$ ...
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Weighted averages for microdata merging

I'm working with microdata files and would like to hear if any one may have a suggestion when merging the data. I'm concerned with making inferences on wages given specific character traits. I think I ...
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0 answers
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Bayesian Nash Equilibrium

Very simple question: Assume we are given a Bayesian game (in any form). Do we always find all Bayesian Nash equilibria by transforming the game into Bayesian normal form? I think so, why should it ...
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1 vote
1 answer
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Present value of all future costs associated with a policy of equipment replacement after time $T$.

It is required to find the optimal replacement time of a certain type of equipment. The initial cost of equipment is $C$. Salvage value and repair cost are given by $S(t)$ and $R(t)$ respectively. ...
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1 vote
1 answer
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Income and expenditure problem

The ratio of income of Anun and Hanun is 7 and 9. While the saving ratio of both is $4000$ and $6000$. If the expenditure of A is 83.3% of B then what is the total income of both. Here i am try by ...
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2 votes
0 answers
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Bayesian Nash equlibrium

Assume we have 3 types ($A$, $B$, $C$) each assigned probability $\frac{1}{3}$ and two players in a Bayesian game. Player 1 (Pl1) only knows if $A$ is played or not, Player 2 (Pl2) only knows if $B$ ...
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1 vote
1 answer
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What is the age of replacement?

The following problem is from 'Replacements of models'. The cost of a new machine is \$5000. The maintenance cost of the $n$th year is given by $C_n=500(n-1)$, $n=1, 2, \dots$. Assuming that the ...
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