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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2answers
128 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
votes
2answers
100 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 ...
0
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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
32 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: ...
2
votes
1answer
50 views

What are the most recent devopments with applying fractals to economics?

I was researching fractals for my senior mathematics presentation and discovered that one of the most recent pioneers in that section of the field was able to apply fractal mathematics to the field of ...
0
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2answers
111 views

Interpretation of market completeness: full row rank payoff matrix

Suppose that there are $K$ assets and $S$ states of nature. The assets' payoff is represented by the matrix $$ \underbrace{R}_{S\times K}=\begin{pmatrix} r_{11}&\cdots& r_{K1}\\ ...
0
votes
1answer
64 views

Optimization to minimize cost using the function C=Tq^(1/a)+F

I was given the function of $C=Tq^{1/a}+F$ where $C$ is total cost, $q$ is output, $a$ is a positive parametric constant, $F$ is the fixed cost, and $T$ measures the technology available (also a ...
0
votes
1answer
307 views

Maximizing total tax revenue with function Qs+-8+P and Qd=(80/3)-(1/3P)

The supply and demand equations of a good are given by Qs= -8+P Qd=(80/3) - (1/3)P P is measured in dollars. Suppose the government decides to impose a constant per unit tax of $t on the supplier. ...
0
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2answers
37 views

Chain rule using the expression F=150W^1/3

Suppose the attendence of a baseball game was denoted by W alone in the format F=(150W)^1/3. Is this function (strictly) concave or convex. Explain. To which I answered that it would be strictly ...
0
votes
1answer
32 views

Present Worth with Salvage Value

I would like to know how to consider the "Salvage Value" in the following question while calculating the present and future values. here is the question: We are planning to build a new bridge. ...
0
votes
1answer
103 views

Partial Derivative Math Homework Help

The attendance (denoted by the variable F , measured in thousands of fans) at a blue Jays home game is approximated by F = 150W^(1/3)P^(2/3) Where W is the fraction of the games they have won so far ...
1
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1answer
126 views

How to find the price elasticity of demand?

I need help answering if this is demand elastic of inelastic. A policy adviser suggests that in order to improve its balance of trade with china, Canada should lower the price of some heavy ...
0
votes
2answers
47 views

Finding the Maximum with Calculus, second order condition.

Question: "At a price of $8$ dollars per icket, a musical theatre group can fill every seat in the theatre, which has a capacity of $1,500$. for every additional dollar charged, the number of people ...
0
votes
2answers
130 views

Limit of CES function as $p$ goes to $- \infty$

I am trying to evaluate the limit of the CES Production function: $$Y=(aK^p + bL^p)^{1/p} $$ when $p$ goes to -infinity. It first yields the indeterminate form $0^0$. I tried solving the problem by ...
1
vote
2answers
80 views

Calculus of optimization help ):

If I need to sell 400 chairs. The price per chair is 90 dollars up to and including 300 chairs. Above 300, the price will be reduced by 0.25$ (on the whole order) for every additional chair over 300 ...
1
vote
3answers
111 views

Economics, numeraire, utility, demand, marginal rate of substitution

I typed my question in Microsoft Word and printscreen it instead of typing it, this is because I don't know how to type mathematical questions here, sorry for the inconvenience caused.
1
vote
1answer
54 views

Intemporal budget by lagrange

Assume that a representative agent lives forever and receives an endowment, denoted yt, in each period. The entire endowment sequence is known with certainty on date 0. The representative agent ...
0
votes
0answers
25 views

growing number of sample

The problem I have is as following, which I would like a solution to I am a tomato seller Everyday I sell tomatoes. I also have a demand forecast for tomatoes required everyday countrywide. I§m ...
0
votes
1answer
131 views

Easy (?) application of Lagrange multiplier

I am reading a book about utility theory and there is a exercise (without solution). I can't stop thinking about this, since the normal Lagrange multiplier approach seems not to work. We want to ...
0
votes
1answer
59 views

Was my inference regarding $u(z)=log(z)$ correct?

I have already solved the problem but would appreciate a clarification in part (b). A has initial wealth $w$ and faces a loss $l$ with known probability $\pi$. Insurance available at unit price ...
1
vote
1answer
51 views

Elasticity of demand the idea behind it.

I have been looking at elasticity of demand, but I am struggling to understand the concept. Now I have taken a simple example in hope of beeing able to understand what is going on. Eliacticity of ...
1
vote
1answer
52 views

How do I find if this estimator is unbiased and also its variance?

I need to find if the estimator $\tilde{\beta } _{2} = \frac{(y_{n}-y_{1})}{(x_{n}-x_{1})} $is unbiased given that i) $E(u_{i}\mid x)=0$ ii) $E(u_{i}\mid x_{i})=0$? I also need to calculate its ...
1
vote
1answer
138 views

Finding the optimal combination for the Cobb-Douglas function given a budget

I am trying to figure out to find the optimal combination of the Cobb-Douglas function given some budget. An example question is: Output can be produced with labour and capital according to $Q = ...
1
vote
1answer
87 views

Why is the Stochastic Process in the HJM model non-Markovian?

I want to understand exactly what my title asks "Why is the Stochastic Process for the short rate in the HJM model of interest rates non-Markovian?" That process is the following: ...
1
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0answers
27 views

A sufficient condition for a good to be normal

Context: there are $2$ goods with prices $P_1$ and $P_2$ and the decision maker has the utility function $U(C_1,C_2)$. Denote $U_j=\frac{\partial U(C_1,C_2)}{\partial C_j}$ for $j\in\{1,2\}$. A good ...
12
votes
1answer
357 views

Equilibrium existence proof

Problem: Let $J$ be an integer and let $I$ be an integer multiple of $J$. Let ${\cal I}= \lbrace 1,2,\ldots, I\rbrace$ and ${\cal J}= \lbrace 1,2,\ldots, J\rbrace$. The set $X_{I,J}$ of all ...
0
votes
1answer
57 views

Expected Return, Expected Value, and an Ito Process

I am reading John Hull's "Options, Futures, and Other Derivatives". I am currently in Ch. 31 on the HJM Model. Hull makes a statement which a need an explanation for. First, some notation. Let ...
1
vote
1answer
33 views

Non strictly convex “singleton” preferences

A relation $\succeq $ over a vector space $X$ is rational if it is transitive and complete. We say $x\succ y$ iff $x\succeq y$ and NOT $y \succeq x$ Moreover $x\sim y$ iff $x\succeq y$ and $y ...
0
votes
0answers
20 views

Aggregated demand function for several similar offers?

I want to generate a realistic demand function for a service, depending on the price and properties of offers. The service is passenger travel, for whatever purpose. There are several companies that ...
0
votes
0answers
54 views

A linear algebra textbook that is advanced enough as a prerequisite to read time series and econometric textbook?

A linear algebra textbook that is advanced and comprehensive enough as a prerequisite to read time series by Hamiliton and econometric by Hayashi? If possible, please also answer on which statistics ...
4
votes
2answers
89 views

Applications of information theory in economics?

What are some direct applications of information theory in economics theory and/or finance? Any relevant articles, surveys, or book references are appreciated (especially if they are targeted to ...
1
vote
1answer
173 views

Marriage Market Proof (Alternative Proof of Rural Hospitals Theorem)

How do I get (a) + (b) + (c) $\implies$ (d) $\implies$ (e)? (a) Show that for each $m \in M$, if $\mu(m) = \emptyset$ for some stable matching $\mu$, then for the woman-optimal matching, $\mu_W$, ...
0
votes
1answer
64 views

Spotting mistake: unnecessary given condition

I have solved the following problem without using a given premise. Could someone please spot whether I have done something wrong? Suppose we have a relation $\geq$ that is transitive, but not ...
0
votes
1answer
27 views

Is there a mistake with this national income model Mik. Wisniewski Intro to Math Methods in Econ pg. 61

I can't figure out the steps to this equation for the national income model. It seems simple, but I don't see why in step 4 I don't get Y-bY+tY I thought it was a mistake in the book at first, but ...
0
votes
4answers
39 views

Can someone walk me through how this expression simplifies to y/x?

I am just wondering how this equation comes to be: it is from an economics problem involving marginal utilities. I have my two variables, $x$ and $y$. Intuitively, how does $$\frac{0.5\times ...
0
votes
1answer
28 views

Confused by informal math: total differentiation

I'm reading these notes that say: total differentiation gives $$ P=a_LW+a_KR\implies dP=a_LdW+a_KdR+[Wd(a_L)+Rd(a_K)]\tag{i}. $$ Please let me explain the notation: we can think of $R,W$ and $P$ as ...
0
votes
0answers
32 views

Reasoning for the Shape of MRTS line

I was looking to understand better the shape of the MRTS curve (Marginal rate of technical substitutes for A production function with 2 inputs). So I know that for 2 inputs in production function they ...
1
vote
2answers
37 views

How to analyze convergence of non-linear difference equation (recurrrence relations)

I've a couple of functions, such as: $Y(t+1)=2-\ln(Y(t))$ $Y(t+1)=(Y(t))^{-2}$ $Y(t+2)=e^{-Y(t)}$ and I need to analyze stability and convergence. No problem with stability, but I can't figure out ...
1
vote
1answer
31 views

Functions of 2 variables and applications to economics

Given the production function $Q := \sqrt K + L^2$, determine the optimal level of production and the relative demand of the two inputs capital $K$ and work $L$. The cost of a unit of capital ...
1
vote
1answer
55 views

quasi rationality, interesting axiom of revealed preferences

So imagine there is a notion of rationality that captures the idea of "thresholds in preference." For example, let $\mathbb{Z}$ be the integers: $\mathbb{Z} = \{\dots, -10, -9, \dots, 0, 1, 2, ...
3
votes
1answer
73 views

A simple dual problem in economics: profit v.s. cost

The setup is simple but a bit lengthy. Please bear with me. Suppose that I have a production function $F(K,L)$ that is: constant return to scale; increasing in each factor: $F_K>0$, $F_L>0$ ...
0
votes
2answers
60 views

Optimization across markets - How can I solve?

I am unsure how to solve problems involving several markets and optimizing the price across all my markets. Note: I am looking to be pointed in a specific direction of study, not a solution to the ...
4
votes
2answers
208 views

If you have two envelopes, and …

Suppose you're given two envelopes. Both envelopes have money in them, and you're told that one envelope has twice as much money as the other. Suppose you pick one of the envelopes. Should you switch ...
0
votes
1answer
46 views

Does maximizing an increasing function of two variables in more favorable conditions always increase both inputs?

Consider the problem of maximizing $\sqrt{x}y$ such that $x+y=10$. By basic calculus we can show that the maximum occurs at $x=10/3$, $y=20/3$. If we loosen the constraint to $x+y=12$ then the maximum ...
1
vote
1answer
31 views

Verifying a production set is a convex cone

This comes from a paper that I am reading: For $i=1,2$, suppose that $F_i(\cdot,\cdot)$ satisfies the assumption: $F_i(K_i,L_i)$ is defined for all $K_i\geq 0$, $L_i\geq 0$. $F_i(0,0)=0$. ...
1
vote
1answer
40 views

Statistica Significane of the Slope Coefficient

Can someone please help me with this? Consider that you are examining the relationship between the height of children and their parents. You decide to collect data from 110 college students, and ...
0
votes
0answers
60 views

Convergence of probability

So I am getting ready for my first econometrics exam, and we have a lot of these plim (probability limits). Looking at the definition, I have that as n goes to infinity, ...
1
vote
1answer
83 views

Looking for resources for understanding derivation of demand from utility

I am struggling with my homework and would very much appreciate a rundown of the math or pointers to where I can find help otherwise. Quoting from the assigment: There are $n$ sectors in the ...
0
votes
1answer
60 views

Econometrics Question

Can someone please help explain this (or provide a website link). I know the answer is (a). To decide whether or not the slope coefficient is large or small, a) you should analyze the economic ...
3
votes
1answer
69 views

Matrix question: implication of $\frac{1}{n}X'X\to M$

Suppose $K$ is fixed and consider a matrix $X$ that is $n\times K$ and has full column rank. Assume that we know $$ \frac{1}{n}X'X\to M\text{ as } n\to\infty.\tag{i} $$ That is, as $n$ becomes larger, ...