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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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Finding the Dictator in Arrow's Impossibility Theorem

Arrow's Impossibility Theorem states that if we have at least three different social states and a finite number of individuals (voters), any social welfare function that satisfies the conditions of ...
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0answers
17 views

Choquet Integral - literature and papers

I'm currently looking for some books, articles and lectures about Choquet integral, it's applications (mainly in actuarial office) and everything connected to this (rather something practical than ...
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3answers
40 views

Percentage Plateau

We're trying to figure out something, and things aren't adding up. The senario is that you make $\$ 50,000$ a year. Every year you get a $15\%$ bonus of that income, which then gets added to your next ...
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2answers
67 views

Can you solve this stolen money riddle?

So, a basic word problem has gone viral on FaceBook quite a few times now and many people remain convinced of their own incorrect answers. Suppose a man walks into a store to steal a $\$100$ bill ...
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2answers
46 views

Explaining Why the Zero Conditional Mean Assumption is Important

I am currently relearning econometrics in more depth than I had before. One thing I am trying to make sense of currently is why it is necessary for the assumption of: $$E(u\mid x)=E(u) $$ to be true (...
6
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1answer
72 views

Players A and B repeatedly flip a (possibly unfair) coin until one loses everything. Each starting with a different amount of money

There are two players $A$ and $B$. At the beginning $A$ has $a_0 ∈ [0,1]$ amount of money and $B$ has $b_0 = 1 - a_0$ amount of money. They have one possibly unfair coin which they flip repeatedly. $A$...
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2answers
55 views

Solution to a problem of equilibrium

I am not sure how to write this problem. But here it goes. I have a fixed amount of money. I want to distribute it in three different jackpots. Each one with a unique way of payout. Jackpot1 pays the ...
2
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1answer
28 views

First-Order Stochastic Dominance

Consider two cumulative distribution functions $F(x)$ and $G(x)$ for $x\in[a,b]$ where $G(x)$ has the first-order stochastic dominance over $F(x)$. That is, $F(x)>G(x)$ for all $x\in(a,b)$. We ...
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2answers
48 views

Intermediate Economics

This question refers to a market in which quantity demanded is given by $q = a - bp$ and quantity supplied by $q = c + dp$. In this market, an increase in the parameter $a$ would: a. increase ...
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2answers
53 views

Demand Function

A consumer has the utility function over goods X and Y, $U(X; Y) = X^{1/3}\cdot Y^{1/2}$ Let the price of good x be given by $P_x$, let the price of good $y$ be given by $P_y$, and let income be ...
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1answer
24 views

What is an example of a situation that uses the kinematic equations that isn't motion through space?

The kinematic equations describe the relationship between a variable $x$ and its first $\frac{dx}{dt}$ and second $\frac{d^2x}{dt^2}$ derivatives, assuming its second derivative is constant. This does ...
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0answers
48 views

Subgame perfect equilibrium question

There are two neighboring towns, Alfa and Beta. Firm A is located in Alfa, firm B in Beta. The two firms produce and sell identical goods, with fixed marginal costs of c. The two firms simultaneously ...
2
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1answer
63 views

What is this curve called?

This curve can be easily generated with a spreadsheet. You can set cell A1 to be 100 and then B1 will be this formula =A1×(100+RAND()×10−5)÷100 And fill down about 150 or more cells. Then copy row ...
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0answers
31 views

Burdett and Mortensen (1998), Equation (22), Integral by parts question.

Suppose $F(x)$ and $H(x)$ are both cumulative prob dist functions on the support of $[b_0,b_1]$ and we know followings: $u(x|F)=\int_{b_0}^{x}\frac{m}{1+k[1-F(b)]} dH(b)$ and from this $[1+k(1-F(x))]...
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0answers
42 views

Given the Marginal Cost Function, Calculate Marginal Profit

A friend of mine is having a bit of difficulty with their calculus homework and came to me for help, but I'm stumped at this point. The question is asking for the marginal profit of the 31st unit of a ...
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0answers
10 views

Importance of uniqueness of recursive utility

I am working with recursive utilities generated by aggregators at the moment. Can someone explain why it is important that an aggregator generates a unique recursive utility as opposed to multiple?
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0answers
25 views

Aggregating Using Integrals

I am working with the following Economic model of labour and consumption decisions: I have a population whose mass is normalized to one of consumers. They derive utility from consumption $c$,...
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1answer
27 views

Finding price for desired margin

My algebra is rusty, I'm trying to rearrange an equation, the purpose of which is to calculate the price that would result in a desired margin. Here are my workings: ...
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0answers
40 views

A gap in a game theory derivation

Consider an $n$-player game exerting effort to increase their probability of winning. Let $x_i$ denote $i$'s probability of winning and $e_i$ $i$'s effort: $$x_i=\frac{e_i}{\sum_{j\in N}e_j}$$ $i$'s ...
1
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1answer
41 views

Finding best response function

Consider two players Player 1 choose $x_1$ Player 2 choose $x_2$ $x_1, x_2 \in [0,b]$ and $b>0$ The payoffs for players 1 and 2 are identical and equal $$Z=u(x_1+x_2)+v(2b-x_1-x_2)$$ $u$ ...
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2answers
38 views

How to derive the growth rate rules from the log growth equation?

These are approximations, which, I guess, only apply for small growth rates $g$ ($g$ is a function that denotes the change in its argument). $$\begin{align} g(xy) &= g(x) + g(y) \\ g(x/y) &= g(...
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0answers
11 views

Prediction Interval for the Sum of Multiple Probits

Say I have N draws all from the same random sample. Given a fixed multivariate probit model, trained on some sample of the population that does not overlap with the N observations, $\Phi(X_i \beta)$ ...
2
votes
1answer
42 views

Difference between Arrow and Gibbard-Satterthawite theorem

I have a question related to two very important theorems from Social Choice Theory. What is the difference between Arrow Theorem and Gibbard-Saterthwaite theorem? I mean, the obvious one is that in G-...
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1answer
48 views

Equality of the two definitions of Gini index

Assume $p$ to be a finite measure on $\mathbf R_+$ for the distribution of wealth among a group of people and $\pi$ its normalization to $1$ (ie $\pi(\mathrm d r) = p(\mathrm d r)\left(\int_0^\infty p(...
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1answer
24 views

How to find initial values for calculating IRR manually?

I want to calculate the IRR manually (as in writing the algorithm) by using the method that is described on Wikipedia. It says I can use the secant method to numerically compute the value. For the ...
3
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0answers
27 views

Is this random generation of a distribution over the [0,1] interval measurable?

So this is basically from an economics lecture (the lecturer introduced the voting model from myerson 1993). I have this feeling that the lecturer simplified this model though, so this might not be ...
1
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1answer
46 views

Logarithmic differentiation with respect to time

I have a question regarding a logarithmic differentiation with respect to time. I would highly appreciate it if you might help me with this matter. Here is the set-up. All starts with a production ...
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3answers
52 views

How to explain the equation about summation?

$$\frac{\sum_{i=0}^nx_iy_i-\bar y\sum_{i=0}^nx_i}{\sum_{i=0}^nx_i^2-\bar x\sum_{i=0}^nx_i}= \frac{\sum_{i=0}^n(x_i-\bar x)(y_i-\bar y)}{\sum_{i=0}^n(x_i-\bar x)^2}$$ Maybe it refers some calculation ...
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0answers
18 views

Leontief model table

please can somebody help me to understand how to solve this Leontief input-output exercise. Im trying from days to make this exercise without success Questions are: 1) What wil be the value of TOTAL ...
0
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1answer
35 views

Take the partial derivative of $P_F$ divided by partial derivative of $M$

I have calculated the following Marshallian demand functions Additionally, I have calculated the indirect utility function for this question Question: If you take the partial derivative of Pf and ...
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0answers
46 views

Question on first and second price sealed bid auction

I’m studying on auction. But I couldn’t understand some questions about this topic. And I cannot solve such type questions. For example, I know that a set of symmetric and risk neutral bidders ...
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1answer
39 views

Proove that $\operatorname{supp}(\sigma^{*}_{i})\subset B_{i}(\sigma^{*}_{-i})\Rightarrow \sigma ^{*}$ is N.E

PROBLEM Proof if mixed strategy $\sigma^{*}\in \sum$ is s.t $\forall i\in N : \operatorname{supp}(\sigma^{*}_{i})\subset B_{i}(\sigma^{*}_{-i}) \Rightarrow \sigma^{*}$ is Nash Equilibrium. ...
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1answer
45 views

Acidifying Water: Calculating the best bang-for-the-buck

I have water that is at a pH of 8.0. I want to acidify the water to a pH of 4.0. I have two products that I can use to acidify the water: Lemon Juice: ...
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1answer
41 views

strictly dominated strategy

PROBLEM Proof that if a pure strategy is strictly dominated, then any mixed strategy that assigns positive probability will also be strictly dominated by some other mixed strategy. i.e If $s_{i}\in ...
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37 views

Finding bet response function for mixed Nash strategy.

Consider the following static game I want to plot the graph that shows each players’ best response to the opponents mixed Nash strategy choince. ————————————- my solution Firstly, I find pure ...
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1answer
43 views

Finding mixed Nash equilibrium

I have following simultaneous move game table Game table Player 1 can take one of three actions A,B,C and player 2’s possible actions are D,E,F. First of all I found pure Nash equilibrium And (B,...
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0answers
29 views

Finding Bertrand equilibrium with no demand function explicitly given

Two cell phone companies A and V are located at the extremes of a line of length one and transportation cost t = 4. Consider an initial situation where both firms offer a generic phone that consumers ...
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1answer
51 views

Consider the following Matrix, are the conditions satisfied?

I am trying to solve the following questions however i am having little lucky. I have searched online and consulted my textbook however neither are proving to be helpful. These types of questions ...
0
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1answer
32 views

Find price, income & cross elasticity with demand function

Demand Function for $X$ is $$ Q_x=420 - 7P_ye^{P_x} + 0.06Y^2+390P_y^3 $$ Find price, cross and income elasticites of demand at $P_x = 7.1$, $Y=1764$, $P_y = 8.2$ Explain. Here is my workings: $...
2
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0answers
28 views

Derivation of a parameter in optimization problem

My question The solution for first part $$L=(aq+1-a)x1x2+\lambda (y-(a(p1+c)+(1-a)p1)x1-x2p2)$$ As a result after FOCs $$x1=\frac {y}{2(a(p1+c)+(1-a)p1)}$$ $$x2={y\over 2*p2}$$ The solution ...
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0answers
26 views

Unique optimal solution for optimization problem.

I have such a function $$F(e,a,b)= (1-p(e))f(a)+p(e)f(a+b)-c(e)$$ Where $p’(e)>0$ and $p”(e)<0$ and $c(e)$ is strictly increasing and convex f is strictly increasing and strictly concave. ...
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1answer
34 views

Writing down income

Consider a welfare system under which a single cash transfer (a guaranteed income) is given to every citizen. Then for each dollar the person earns, this payment is reduced by $\alpha$ dollars, where $...
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0answers
51 views

No pure-strategy Nash equilibrium in all-pay auction

In an all-pay auction (i.e. everyone pays their bid, but only the highest bidder gets the good), why is there no pure-strategy Nash equilibrium?
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1answer
29 views

Writing The Budget constraint

My answer For state 1: $$C1= (100*q_1+200*q_2)-150(q_1+q_2)$$ So $$C1= 50q_2-50q_1$$ For state 2: $$C2= (200*q_1+100*q_2)-150(q_1+q_2)$$ So $$C2= 50q_1-50q_2$$ As a result, the state ...
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1answer
27 views

Econometrics- Multiple Regression

I have conducted a multiple regression analysis online, however, I'm having a hard time understanding the results. can someone please explain them to me. Im actually doing a research paper which ...
2
votes
1answer
87 views

Deriving a parameter in optimization problem

My question: [![enter image description here][1]][1] My solution for the part (i) [![enter image description here][2]][2] Hopefully my solution is correct. Especially check the budget constraint. ...
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1answer
104 views

Profit maximization question

I have the following question A monopolist has a cost function, $\textrm{c}(q)=q$. It faces the following demand function: $$ q(p) = \begin{cases} \frac{100}{p} & \textrm{if } p \leq 20 \\ 0 ...
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0answers
48 views

Profit maximizing with demand function

Cost function is $c(q)=q$ Demand function is $q(p) = 100/p$ for $p\le 20$. And $q(p)=0$ for $p>20$. In order to calculate profit maximizing output and price $$max [p(q)*q-q]$$ And marginal ...
0
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1answer
25 views

Conditional expectation and conditional median

Suppose $(x_i,y_i)$ are random draws from the population and $\alpha, \beta$ are scalars. Let $u_i$ be unobserved effects(residuals). Consider the model $y_i=\alpha+\beta x_i +u_i$. By Law of Iterated ...
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0answers
29 views

How do I approach this dynamic discrete choice model?

I'm working through an old problem set (that sadly I don't have solutions for) and I got stuck. It is a dynamic model of entrepreneurship and invention. I'm looking for guidance on this model as well ...