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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2
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1answer
46 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
67 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 ...
0
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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
vote
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
44 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
18 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
295 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
29 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
52 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
votes
1answer
46 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 ...
1
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0answers
18 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 ...
1
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0answers
60 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 ...
0
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0answers
30 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
17 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
63 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
votes
1answer
80 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
34 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 ...
1
vote
1answer
39 views

Stochastic dominance characterization

Consider two probability measures on $\Bbb R$ given by $\mu$ and $\nu$. We write $\mu\leq \nu$ if there exists a joint distribution $P$ with the latter marginals such that $P(x\leq y) = 1$. In ...
0
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0answers
361 views

How to calculate $p_i$ in Blau's Index of Heterogeneity

I came across this: "Therefore, board gender diversity and board racial diversity are calculated using Blau's index of heterogeneity $(1 - \sum p_{i}^2)$, where $p_i$ is the proportion of group ...
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0answers
37 views

From utility function (3 products) to demand function (2 products)

I am struggling with this exercise and would appreciate some help. Consider two goods and a representative consumer whose utility is given by: $U(q_{0}, q_{1}, q_{2})= ...
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0answers
70 views

Utility maximization of n goods

I have a question that involves finding the optimal demand of n goods for a consumer. However, I haven't anything like this before and I'm not sure how to proceed. The consumer has a utility ...
0
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0answers
36 views

how to solve a simplex with n variables

I don't know how to resolve a simplex with n variables I have this primal problem \begin{cases} \text{min}& z=-x_1 - x_2 -... - x_n\\ &a_1x_1 + a_2x_2 +... + a_nx_n \le 1\\ &x_1... ...
-1
votes
1answer
18 views

I need som help with price ratios.

Okay, so I'm doing some econ. homework and I'm supposed to draw a graph where the relative price of $P$ is $4 T/P$. Thing is that my brain stops working anytime I try to think about ratios. I know ...
0
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0answers
17 views

Engel Curve in Economics

I have a utility function in the form $U = B^{.67}Z^{.33}$ I am supposed to find an Engel curve assuming that the price of goods B and Z are $P_b$ and $P_z$ respectively with income level $Y$. I can ...
0
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0answers
25 views

Density - Excess Bunching - Bunching Estimator

Saez defines excess bunching at the kink as the area under the density in the dominated region: $$ B = \int^{z^*+d z}_{z^*} h(z)dz \approx h(z^*)dz^* $$ where income $z$ is distributed according to a ...
0
votes
1answer
24 views

About uniqueness of interest yield

I am not sure this belong to this site, in case I will post it elsewhere. Let $P$ be the price of a bond, let $C_k$ the promised cash flow in year $k$. Then we define the interest yield $y$ as the ...
0
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2answers
62 views

dynamical systems applied to economics

I'm ending my undergraduate economics course and I'd like to extend my MA research program to dynamical economic systems. Knowing that my mathematical basis is calculus of 1 and 2 variables, linear ...
1
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0answers
28 views

Convolution of which distribution will give a uniform distribution?

Suppose there are two IID random variables x1 and x2. What should be the distribution of these random variables so that the distribution of x1-x2 is a uniform distribution?
0
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0answers
27 views

Proving the expenditure function $e(p,u)$ is strictly increasing in $u$ when $u$ is not assumed to be an increasing function.

Hello I am wondering how best to prove that the expenditure function $e(p,u)$ is strictly increasing in $u$ assuming that $u$ itself is not an increasing function (which is the opposite of what $u$ is ...
0
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0answers
32 views

Submodular function of 2 variables with specific properites

For an application in economics, I am looking for an example function with the following properties: Function of 2 variables on the unit interval, i.e., $f : [0,1]\times[0,1] \rightarrow ...
3
votes
1answer
120 views

Reference Request - Introductory book on Mathematical Modelling in Economics and Business

I have to take a compulsory course named Mathematical Modelling in Economics and Business this semester and have absolutely no background on the subject. I also noticed there is no post on this site ...
0
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0answers
37 views

Optimal choice of job based on multiple ranks

First of all I should state that I am a non-mathematics student but am pretty mathematically-inclined. I have a problem that I can't find a solution to on Google. Here is the hypothetical: I have ...
1
vote
1answer
19 views

Find the OLS estimator $β_1$ when a new variable is added to the regression

Suppose $y_t$ = $β$$x_t$ + $u_t$ , where t = 1, 2, ..., n. We know, in this case, the OLS estimator is $\hatβ$ = ∑$x_t$$y_t$ / ∑$x_t^2$ . Now suppose one more observation $x_{n+1}$ is added. At the ...
0
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1answer
64 views

Optimization of utility function with Lagrange multiplier

Let u: ${\mathbf R^n_+ \rightarrow \mathbf R}$ be a utility function of n goods which you buy in quantities $x_1,…,x_n$ to the prices $p_1,…,p_n$ under the budget K. So maximize $u(x_1,…,x_n)$ subject ...
0
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1answer
31 views

State the likelihood function and the appropriate objective function which must be maximized for maximum likelihood estimation

Consider a simple exponential employment duration model where $t_j$ is length of the employment and $x_j$ is a suitable economic explanatory variable. The distribution of $t_j$ is assumed to be ...
0
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0answers
26 views

Solving the production scheduling problem using optimal control

I want to solve the production scheduling problem with quadratic production costs and no inventory costs using optimal control without discounting. My work: The quadratic production cost is $c_{1} ...
0
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1answer
41 views

Simple PPF question

Econoland and Free Enterprise are two economies each producing two goods: airplanes (A) and grains (G). Currently the two economies do not trade with one another. The table below provides ...
0
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0answers
11 views

Quasilinear Utility

We know if the utility function is quasilinear(QL) w.r.t say good 1, then the demand for other goods is independent of income (no income effect for goods 2...N). But is the reverse implication also ...
3
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0answers
453 views

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 ...
0
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0answers
40 views

Implicit differentiation: Differentiating function with respect to integral

I am stuck on a simple problem and would highly appreciate your opinion. I have a optimization problem over $x$ with the objective function $$F=aG(x,y)+ (1-G(x,y))(1-x)$$ So the first order condition ...
1
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1answer
38 views

Hypothetical scenario with economics

You have been assigned to purchase a new molding machine. One vendor offered a machine that will cost $200,000$, with an estimated installation of $10,000$. The machine has an expected life of $10$ ...
0
votes
1answer
47 views

cash flow diagram, in/outflow series

I have a econ midterm coming up soon and stumbled upon this question. I know this is the math section but it appears not many use the finance one. My approach is: 2C=800/(1.12^2)+1200/(1.12^6)=125.71 ...
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0answers
22 views

House allocation with existing tenants

In a house allocation with existing tenants model using the TTC mechanism, consider the incentive of an agent to misreport his/her preferences. Can it ever be that misreporting the true preferences by ...
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0answers
32 views

Nash equilibrium in marriage market stable matching

Consider a marriage market where matchings are formed using the DA women-proposing algorithm. However, there is an additional constraint that only matches among agents that have previously gone out on ...
0
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0answers
26 views

length plus width equals price, factoring?

im trying to grasp what this means as I usually work with areas (L x W = A) or perimeters (2L + 2W = P)... This problems was presented to me by a colleague and i'm just trying to wrap my head around ...
0
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0answers
189 views

Positive/Negative Definite Bordered Hessian?

I understand how to check a function for concavity and convexity using the Hessian matrix and the rules for the determinants of the leading principal minors. I understand if these rules are violated, ...
0
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1answer
61 views

How can I find the sum of an infinite series of products?

Background Today in my macroeconomics class my teacher taught us three concepts. The first is very simple: consumption $c$ is a linear function of national income $y$. Mathematically, $$c = My + ...
0
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0answers
18 views

dF(x,a,b)/dy>0 iff x<g(x,a,b) then can we say that there is a upper bound on x to ensure dF/dy>0

Suppose df(x,a,b)/dy>0 iff x where g(x,y,a,b) and f(x,y,a,b) are implicit solutions to an optimization problem and x,y,a,b are parameters, then can we say that there is a upper bound on x to ensure ...
2
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1answer
37 views

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 ...