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.

learn more… | top users | synonyms

1
vote
2answers
28 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
70 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
votes
0answers
12 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 ...
0
votes
1answer
22 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
0answers
23 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
votes
1answer
14 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}\\ ...
-2
votes
1answer
42 views

maths- econA reasonably realistic model of a firm’s costs is given by the short-run Cobb- Douglas cost curve C=Tq^1/a+F w [closed]

A reasonably realistic model of a firm’s costs is given by the short-run Cobb- Douglas cost curve $$C=Tq^{1/\alpha}+F$$ where $C$ is total cost, $q$ is output, $\alpha$ is a positive parametric ...
0
votes
0answers
34 views

Minimizing average cost through optimization [closed]

A reasonably realistic model of a Firms cost is given by the short-run Cobb-Douglas cost curve: C=T(q^1/a)+F where C is total cost, q is output, a is positive parametric constant, F is the fixed cost, ...
0
votes
1answer
43 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
49 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
votes
2answers
32 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 ...
-4
votes
0answers
33 views

Economics home work help with math ): [closed]

The supply and demand equations of a good are given by Qs = - 8 + P Qd = (80/3) - (1/3) P respectively. P is mesured in dollars. Suppose the government decides to impose a constant per unit tax of ...
0
votes
1answer
18 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
85 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 ...
-3
votes
0answers
47 views

Partial Derivative and Elasticity Help! [closed]

The attendance (denoted by the variable F, measured in thousands of fans) at a blue jays home game is approximated by: $F=150\cdot W^{1/3}\cdot P^{-2/3}$ where W is the fraction of the games they have ...
1
vote
1answer
86 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 ...
-1
votes
0answers
14 views

Effect of excise tax on american goods? [closed]

Usual demand and supply curve for cars in U.S cross at the price of 10000 dollars. Suppose US car producers can freely sell their cars at 20000 dollars in international market and US government ...
0
votes
2answers
28 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
1answer
23 views

Help with optimization and second-order conditions on area ):

If I wanted to enclose an area to have a total of 3000 square feet. I have two types of walls. Stone walls which cost 45 per foot. Stone walls must cover three walls. Wood walls cost 20 per foot. Wood ...
0
votes
1answer
42 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
49 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
52 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
43 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
18 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
86 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
40 views

Utility index function-would appreciate some clarification (confused about a log function)

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 p will ...
-2
votes
1answer
28 views

Optimization Problem with cost and profit [closed]

For the cost function $C(x)=3100+600x+0.6x^2$ and the demand function $p(x)=1800$. Find the production level that will maximize profit.
1
vote
1answer
41 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
47 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 ...
0
votes
0answers
39 views

Is this derivative of $\frac{\partial x}{\partial P}$ correct?

By IFT, let $x^* + \Phi \left (\frac{f(x)+\check{G}}{a(\hat{G}+f(x))} \right ) - 1 = 0 \equiv F$. $P=f(x)$ is a convex function, where $f'<0$, and $f''>0$. I want to find $\frac{\partial ...
0
votes
1answer
36 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
48 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
vote
0answers
24 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
0answers
294 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
33 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
26 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
15 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
37 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
1answer
34 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
76 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
59 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
21 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
37 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
25 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
14 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
30 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
19 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 ...
2
votes
1answer
47 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
44 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
54 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 ...