Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

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How can I obtain Leontief and Cobb-Douglas production function from CES function?

In most Microeconomics textbooks it is mentioned that the Constant Elasticity of Substitution (CES) production function, $$Q=\gamma[a K^{-\rho} +(1-a) L^{-\rho} ]^{-\frac{1}{\rho}}$$ (where the ...
20k views

Fundamental equations in economics

For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important ...
548 views

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Hep with total differentiation of an AD function [closed]

Is there anyone who can help me with a total differentiation exercize. I am starting with the following formula for AD: $$x=\mu ^{-1}(g+i+e)$$ Where $\mu$ is the Keynesian multiplier. And have to ...
491 views

Question about budget constraint and utility maximization [closed]

I have also following budget set $$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$ where y is income. Assume that there are two stories. The agent can shop in both of them. The first store ...
392 views

Does the envelope theorem hold at a corner solution?

Suppose we have the following production function: $$F(L,K)=\max_{L_K}H(L,L_K,K)=\max_{L_K}\left[(L-L_K+1)^\alpha(L_K+K)^{1-\alpha}\right]=(L-L_K^*+1)^\alpha(L_K^*+K)^{1-\alpha}$$ With the ...
194 views

Multiple equilibria: which one to select?

There are two agents $i=1,2$. Consider the following programm \begin{align} &V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\ &V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}...
61 views

How to econometrically identify perfect complements in production?

The production $$f(x_i,...,x_n)=\min\{x_i,...,x_n\}$$ is pretty straight forward and usually with smaller size data sets and can usually be picked up on rather quickly in an intuitive sense. ...
564 views

Modifying Hotelling's lemma: Is this valid?

Hotelling's lemma is stated as: $$\frac{\partial \pi}{\partial p}=y$$ knowing however that on the more basic level, output $y$ is determined by the input(s) $x(p,w)$,let the profit function be ...
424 views

How does the companies set up utility function for its own purposes?

How does the companies set up utility function for its own purposes? In another word, what is the types statistics data that is usually consider and statistical method being used to set up these ...
1k views

list of math intense graduate level microeconomics books?

List of math intense graduate level microeconomics books? Except Reny's book, krep's books, varian's book and mas-collell's book books from subfields are acceptable, however by math intense i mean ...
105 views

Properties of orders and preference relations

Suppose I have alternatives $A$, $B$, and $C$. If I have strict preferences, that means that for any $x,y \in \{A,B,C\}$ such that $x \ne y$, either $x \succ y$ or $y \succ x$. Assume transitivity, ...
328 views

Correlated Equilibrium for Rock Paper Scissors

Consider the game of Rock, Paper, Scissors (RPS), with payoffs given as follows: Is there a correlated equilibrium in this game? Consider, for example the signal given to both players not to play ...
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Question on subgame perfect equilibrium

Consider a world of complete information with two agents X and Y and two time periods 1 and 2. Person X only lives in second period. Person Y lives in 1st and 2nd periods both. X and Y are each ...
104 views

Kuhn Tucker optimization problem and game theory [duplicate]

Consider a game with two players, where each player i= 1 ,2 has preferences $u_i$= $s_i^a$$c_i^{1-a}$, where c_i is the consumption and $s_i$ is social interaction. $s_i$ is given by : $s_i$ = $t_i$ + ...
315 views

What are some applications of Real Analysis in Graduate Economics?

I am interested as to what areas of masters/PhD coursework that learning the fundamentals of Real Analysis would be beneficial for? I am aware of its applications in Econometrics proofs and analysis, ...
I have a function: $u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.