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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1answer
37 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 ...
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181 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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30 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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69 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 ...
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1answer
29 views

micro economics [closed]

If production function is linear and given by: $Y=3K +L$ Find the marginal rate of technical substitution. If price of capital equals the price of labour what is the best combination of capital ...
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35 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... ...
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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 ...
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15 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 ...
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22 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 ...
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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 ...
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2answers
49 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 ...
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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?
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24 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 ...
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30 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 ...
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1answer
103 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 ...
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0answers
36 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 ...
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1answer
17 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 ...
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1answer
59 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 ...
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1answer
27 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 ...
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0answers
21 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} ...
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1answer
34 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 ...
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0answers
10 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 ...
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394 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 ...
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39 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 ...
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1answer
35 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 $10$ ...
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1answer
40 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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21 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
30 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 ...
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0answers
25 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 ...
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164 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, ...
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1answer
53 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 + ...
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14 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 ...
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1answer
36 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 ...
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27 views

What is the solution to this maximization/minimization problem.

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 $$C_1 \geq X_1$$ $$C_2 \geq X_2$$ ...
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1answer
25 views

Understanding the proof of Gibbard-Satterthwaite theorem

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 ...
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1answer
26 views

Manipulating a summation expression for Future Value (Annuities)

I've been given the following expressions for regular payments with regular annual compounding (Annuities): (1) $$ F - (1 + r)F $$ (2) $$ F = d \sum^T _{t=1} (1+r)^{T-t}$$ where: ($F$) is a Future ...
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36 views

Optimization - economics application, density functions and optimal labour supply

Assume and individuals preferences over consumption (c) and leisure ($l$) are described by the function: $u_i=c_i-a(b-l_i)^2$ The government provides lump-sum transfers to its citizens ($f$) ...
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48 views

Optimization (economics application) - Optimal tax rate and levels of education and housing

Every family has a preference over education (E) and housing (H) defined by the function: $U(E,H) = E^\alpha H^{1-\alpha}$ Households differ only with respect to income where household i's income is ...
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2answers
87 views

Implicit function theorem in comparative static problem

The individual lives for two periods. He has a utility function $u(c_{1} )+ bu(c_2)$. His budget constraint requires that his period I consumption be his period I endowment minus any savings, $c_1 = ...
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2answers
37 views

Adding interest and saving to principal

I know the formula $$ K_n = K_0 \cdot (1+r)^n $$ to get the balance after $n$ years with an interest rate $r$. What if I'm adding 5 dollars to the principal each day. How can I find the balance ...
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1answer
61 views

Second price auction, page 82-84 of Osborne's An Introduction to Game Theory

Consider the second price auction defined and discussed on pages 82-84 of Osborne's An Introduction to Game Theory $($pages 80-82 here in this online draft version of the textbook: Martin J. Osborne, ...
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1answer
61 views

Deriving demand from quadratic utility function

How do you derive the demand for utility $u(x_1, x_2) = x_1^2 + x_2^2 $ and initial endowment is $\omega = (2,2) $? I believe this demand has three cases. Thank you
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1answer
36 views

Modified parcheesi game

A "modified Parcheesi" game starts with the following position: First $x$ flips a fair coin. If heads he can move two spaces or pass. If tails he can move one space or pass. If he occupies the ...
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1answer
45 views

Consumer Surplus

I am working on an economics problem where my solution is not correct, and I'd like to know why. Below is the question and my subsequent work/solution: The demand function for a particular ...
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1answer
76 views

Pure and mixed strategy in Nash Equilibria with n player

I got confused when I see the following problem: There are n staffs and they want to raise their salary, if any one or more than one of these staffs suggest their boss they want raise salary, all ...
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1answer
109 views

What is the pure strategy Nash Equilibria of asking your professor to cancel class?

Each student in a class has the option to remain silent or ask the professor to cancel class. If any students asks to cancel class, all students get a payoff of $r$. However, the student that asks ...
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2answers
145 views

How to make your own supply/demand graphs on a computer?

This is an econ question but I think you guys might have the solution. I am writing an economics paper and I need to show, in my theory, shifts in the supply and demand that I predict. I don't have ...
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3answers
46 views

How does this derivative notation work?

Elasticity of substitution = $\dfrac{\mathrm d \ln(k/l)\;\;\;}{\mathrm d \ln(f_l/f_k)}$ This is type of notation I haven't really worked with before. Is this read as "The change in the natural log of ...
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0answers
30 views

Using Mean vs Median for Rapidly Changing Data

I am writing a report on global GDP per capita trends. As many of you know, were large shifts in the growth rates of these figures before and after the Great Recession. There has been some analysis on ...
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1answer
96 views

Find consumer demand as a function of time, given the demand equation and price

An importer of Brazilian coffee estimates that local consumers will buy approximately $Q(p)= 4374/p^2$ kg of the coffee per week when the price is $p$ dollars per kg. It is estimated that $t$ weeks ...