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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25 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 ...
-4
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0answers
24 views

Introduction to Economics [on hold]

please help, this is due in a couple hours and this is the the only question i can't figure out An economy's production possibility boundary is given by the mathematical expression 90 = 4 A + B, ...
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0answers
20 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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0answers
13 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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0answers
16 views

Conditional and simple correlation

While reading the article "Institutions Rule: The primacy of institutions over geography and integration in economic development" by Dani Rodrik I meet the notion "conditional correlation". There is ...
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0answers
22 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
53 views
+50

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
30 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
13 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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0answers
29 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
17 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
38 views

Squared of a summation? [on hold]

What is the squared of summation of ai times bi from i=1 to infinity? Is it correct to solve this question with (A+B)^2=A^2+2AB+B^2? Thanks
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1answer
27 views

Tax Receipts from Sin Taxes [on hold]

Assume Jack would purchase $10$ packs of cigarettes per week at a price of $\$1/$pack and $9$ packs if the price is $\$2/$pack and that he would buy $10$ lbs of carrots at a price of $\$1/$lb and ...
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0answers
10 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} ...
-1
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0answers
31 views

cash flow series [closed]

My econ skills are rusty so in terms of this questions is the following process correct to assume and follow: C = 1000(1.005)^-12 + 1200(1.005)^-24 + 1400(1.005)^-36 + 1600(1.005)^-48 C = about 4436 ...
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1answer
24 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
8 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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0answers
26 views

Basic economics question

Suppose a worker in Sylvania can produce 15 widgets or 5 tons of potatoes per month (or any linear combination in between). Suppose a worker in Atlantis can produce 4 widgets or 4 tons of potatoes ...
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0answers
34 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
28 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
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1answer
30 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
19 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
25 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
21 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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0answers
54 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
44 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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0answers
11 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
32 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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0answers
26 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 $$C_1 \geq X_1$$ $$C_2 \geq X_2$$ ...
0
votes
1answer
18 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
22 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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0answers
25 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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0answers
30 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
41 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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1answer
55 views

Leontief Input-Output Analysis demand given - econmic model! [closed]

here is my question regarding a task. An economy is based on two sectors, agriculture and manufacturing. Production of one monetary unit in agriculture requires an input of 1/6 from agriculture and ...
0
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2answers
34 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 ...
2
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1answer
51 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
42 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
2
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1answer
32 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
42 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 ...
1
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1answer
50 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
100 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
58 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 ...
3
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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
28 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
77 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 ...
2
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2answers
71 views

Find the consumer surplus, given supply and demand equations

Find the Consumer Surplus, given the demand and supply equations $$ D(x)=\frac{405}{\sqrt{x}} $$ $$ S(x)=5\sqrt{x} $$ The equilibrium point is $(81,45)$. I know the formula for consumer ...
3
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2answers
96 views

Claim: Mathematical models of the economy have thousands of variables

A quote from the book Linear algebra done right by Axler is as follows: "Mathematical models of the economy have thousands of variables" I find this hard to ...
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1answer
30 views

Showing public returns to be greater than private returns mathematically

Take this headline "OECD figures show public benefits more than individuals from tertiary education." How would I present this mathematically, to show that public returns are greater than private ...
1
vote
1answer
26 views

Finding Preto Optimal allocation if utlities are of the form $u_1=x_{11}x_{12}$ and $u_2=2x_{21}+x_{22}$

There are two persons and two goods in an exchange economy. Initial endowment is $$ \omega = (\omega_1,\omega_2) =\left((1,0),(0,1)\right)$$ The utilities of two agents are given by: ...