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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0answers
28 views

References for the following functional

In many of the types of problems Ive looked at the following quantity keeps arising and I was wondering if anyone knew any references I could look at to learn some its properties. Take any function ...
3
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1answer
38 views

partial derivative of a sum 1

This is part of a much bigger question I am working on, but I dont understand how I would differentiate a finite sum of the form: $$\frac{\partial}{\partial \phi} \sum_{t=2}^{T} (y_t - \phi ...
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2answers
59 views

economist puzzle for

Mr. White and Mr. Black agreed on the plan to average the wealth by pairs of economic classes, but they differed on the order. Averaging means that the total wealth of the two classes is ...
-2
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1answer
20 views

consumer’s utility function question [closed]

A consumer’s utility function is given by U=4xy where x is the amount of good one and y is the amount of good two. Suppose the consumer has £40 to spend. Let the price of good one be £1 and the ...
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0answers
15 views

If the null hypothesis is true, how will the test statistic be distributed?

I went with T~(50-6) The question goes.... "A regression is estimated with 50 observations, five explanatory variables and with a constant. Suppose You want to test the following hypothesis $H_0: ...
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1answer
23 views

If $\ln(y) = 5 - 0.1X $what is the elasticity of $Y$ with respect to $X$, when $X=10$?

So i got the following model $\ln(y) = 5 - 0.1* X$ The elasticity of Y with respect to X, when $X=10$ i said -0.1 but apparently i'm wrong Isn't the coefficient of X the elasticity of y when the ...
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0answers
9 views

the test statistic of the sum of a multiple regression

ok so model is... $$ y = −3.33846 + 1.49877 x_1 + 0.489858 x_2 $$ $$se(B_2)= 0.539803 , se(B_3)= 0.102043$$ So the test statistic is $$H_0: B_2 + B_3 =1$$ $$H_0: B_2 + B_3 \ne 1$$ so test ...
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1answer
29 views

Nash equlibrium game theory

Given the following game: Find nash equilibrium (NE) Find subgame perfect nash equilibrium. Main problem i have is with converting this to normal form of the game (because this is i think ...
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0answers
28 views

Maximizing revenue [closed]

The marginal revenue for green ink pads is given as follows: MR=2500-5Q, while the marginal cost of green ink pads is 5Q. How many ink pads will be produced to maximise revenue
1
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1answer
24 views

Interpretation or definition of “shadow prices”

I do understand that shadow price associated to a resource is the marginal profit you would get if you buy one more unit of that resource. I also know that it is the minimum profit you would accept to ...
0
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0answers
18 views

What does it mean to set the technology matrix of the Leontif Input Output Model to 0?

I'm just beginning to learn about Leontif Input Output Systems and Linear Algebra. What is the significance of the solution if I set the technology matrix equal to the trivial solution (make the ...
2
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1answer
35 views

Numerical Reasoning EPSO Ratio Question DGB

I would appreciate if anyone can please help me on this task please. If germany's DGP increased by 3% between 2000 and 2003, how much did government R&D spending increase during this period? ...
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0answers
19 views

Percentage Increase and Dates

Suppose we have the following data: ...
0
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1answer
13 views

Demeaned fixed effects invariant to base category

Consider the following regression equation: $\gamma_{ib}=\beta_{b}+\alpha_{i}$. Where $\gamma_{ib}$ is matched bank-firm loan growth between $t$ and $t-1$. $\beta_{b}$ is a set of $B$ dummies (one for ...
0
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0answers
9 views

State space form

I want to write the following equations on state space form, but I am unsure how it looks. $u_t=u_t^*+u_t^*+\epsilon_t^1$ $u_{t+1}^*=u_{t}^*+\epsilon_t^2$ $u_{t+1}^c=\lambda_1 u_{t}^c+\lambda_2 ...
0
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1answer
21 views

Expectation vs Variance in Economics

When deciding between two projects available, where E[ReturnB] > E[ReturnA] but Var[B] > Var[A], why would this not be a clear case and rather look at the principle of maximization of expected return? ...
4
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1answer
29 views

A Question about Nested Maximizations

I am working on labor demand models where firms have to choose the optimal level of employment by maximizing profits. In particular, I have faced the following problem: Maximize with respect to $l$ ...
0
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1answer
51 views

Game theory question- no idea how to proceed

A monopolist sells two products, X and Y . There are three consumers with asymmetric preferences. Each consumer buys either one unit of a product or does not buy the product at all. The per-unit ...
0
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1answer
18 views

graph theory, economics and learning prerequisites

I'm a undergraduate student of economics and I"d like to know which classes I have to take to get in in graph theory with the purpose to apply it to economic theory. Undergraduate math is sufficient ...
0
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1answer
26 views

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 ...
0
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0answers
18 views

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 ...
1
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2answers
39 views

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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0answers
46 views

Show that if A and B are strictly convex, then A + B is strictly convex or provide a counter example.

We have: If A is open: $\exists x,y \in A,$ $x \neq y$ such that $\lambda x+(1-\lambda y)\in \dot A $ (the interior) and $\exists u,v \in B,$ $x \neq y$ such that $\lambda u+(1-\lambda v)\in ...
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1answer
25 views

A risk neutral individual chooses among a pair of gambles.

I'm a little confused about the following lecture slide, which is written as follows. A risk-neutral individual chooses among pairs of gambles ...
0
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0answers
52 views

How CES function with integral becomes min function in the limit

I wonder how a CES function over a continuum of goods, $$\left(\int_1^\infty c(\theta)^\delta g(\theta) \mathrm{d}\theta\right)^\frac{1}{\delta}$$ where $c(\theta), g(\theta)>0 \forall ...
1
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1answer
11 views

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 $tx' + (1-t)x$ ...
1
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0answers
26 views

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 ...
2
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0answers
50 views

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 ...
0
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1answer
21 views

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 ...
0
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0answers
15 views

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. ...
0
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1answer
48 views

Envelope Theorem and Static Optimization

The Statement of the Problem: For fixed $r \gt 0$ and $m$, find the maximum value of $1-rx^2-y^2$ on the constraint set $x+y=m$. Find the value function $f^*(r,m)$ and compute $\frac{\partial ...
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3answers
42 views

How much is 6% a year in months?

I am currently in high school where we are learning about present value. I struggle with task like these: Say you get 6% interest each year, how much interest would that be each month?
2
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1answer
39 views

What is this subclass of the class of monotonic transformations?

Let $u$ be a continuous function from $R$ to $R$. Then $v$ is called a positive monotonic transformation of $u$ if $u(x) < u(y)$ if and only if $v(x)<v(y)$ and similarly for greater than and ...
1
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1answer
66 views

Can I embed $\mathbb R^{\mathbb N}$ with a partial order into $^\ast\mathbb{R}$ with the linear order?

Define a relation $\prec$ on $\mathbb R^{\mathbb N}$ as, For all $f, g \in \mathbb R^{\mathbb N} $, $f \prec g$, if for all $n \in \mathbb N$, $f(n) \leq g(n)$, and there exists a $m \in \mathbb ...
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0answers
9 views

Supply Curve and Consumer's Surplus Help

The following information is given: p=S(x)= 80e^(0.05x) ¯x=15 What I am struggling to figure out is how to obtain the value of ¯p I set S(x)=15 and got that ¯p was -33.47952, but am unsure if this ...
1
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1answer
7 views

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 ...
0
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2answers
36 views

Using Lagrange for finding Marshallian Demand

I want to find the marshallian demand function for the user function $u(x_1,x_2) = x_1^ax_2^{1-a}$ where $a \in (0,1)$. This is what I have so far: $$L = x_1^ax_2^{1-a} - \lambda(p_1x_1 + p_2x_2 - ...
0
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0answers
14 views

Calculating the conversion factor for a bond

It is june 25 2005. The futures price for the June 2005 CBOT bond futures contract is 118-23. Calculate the conversion factor for a bond maturing on Jan. 1, 2021, paying a coupon of 10% : since the ...
0
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1answer
272 views

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 ...
1
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0answers
27 views

Quasiconcavity of $g(x)=xf(K-x)$

The function $f(x)$ is strictly increasing, finite, positive and twice continuously differentiable on the compact interval $[0,K]$, and $f(0)=0$. I'm trying to either find a counterexample to, or a ...
3
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1answer
49 views

Core vs. Strong Core in Housing Allocation Games

I am presently reviewing the course notes for my Game Theory course, and I'm struggling with the concepts of the core vs. the strong core. In the notes, we have three players, with preferences ...
2
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1answer
44 views

Mathematical question about currencies

I've tried to get an answer for this question elsewhere but with no luck, so I would appreciate a mathematical analysis of it. Assume $0\%$ commission. Consider three currencies, let's say the Zong, ...
2
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0answers
31 views

Average Cost of Obtaining in game Item

I know this will sound like a trivial maths problem, but recently I've been playing a game in which you can pay 5 in game gems to get a Rare (R), Super Rare (SR), and Ultra Rare (UR) characters ...
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0answers
12 views

Endogenous covariate in first-difference panel data model

I have a linear panel data set (murder.dta, standard STATA dataset). First I estimate a first difference model. An assumption from this model is that the first differences of the covariates and the ...
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0answers
49 views

Personal Experiences with Probability Simulation

Simulations methods are increasingly used in theoretical and (especially) applied probability. Personally, I have used simulation for purposes that range from recreational Q&A to applications of ...
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0answers
29 views

When the company will stop production?

Given total costs function $C(q)=100+10q-6q^2+3q^3$. For which price the company will stop production given that all of the fixed costs are sunk? Do not know how to approach those type of questions, ...
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0answers
14 views

Assistance with exponential inflation equations

We are trying to model an exponentially inflationary currency exchange, let's say converting dollars into clams, based on a compounding rate. Our cost equation looks like this: c = b(b*r)^e Where: c ...
0
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0answers
58 views

Finding the equilibrium quantity of goods produced

Consider a market with 3 types of goods, $a$, $b$ and $m$. There are two types of consumers: 100 consumers of type X and 100 consumers of type Y. All consumers of the same type are identical to each ...
3
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1answer
76 views

Given domain and range of a monotone function, what is the maximum slope?

I'm looking for a reference in answer to one of the following questions: Is there a general result out there that will give the maximum possible slope of a monotone function, given its domain and ...
0
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0answers
30 views

How to calculate the max home purchase price based on a maximum Debt to Income ratio?

I'm trying to calculate the maximum home purchase price a home buyer can afford given their annual salary, monthly debt, and a maximum debt to income ratio of 44%. I am not super familiar with ...