The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [mathematical-economics]

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

Filter by
Sorted by
Tagged with
0
votes
1answer
105 views

How is it economically responsible to destroy proprty which has value? [closed]

precursor: bitcoin.stackexchange.com/q/1851 How can it be economically responsible to destroy property which has value? If a property is destroyed (which is the right of the property holder in most ...
3
votes
1answer
160 views

Euler equation through tangency conditions

I am rather new to economics in general and to the Neoclassical Growth Model in particular and I was wondering if there was a way to get the Euler equation for consumption without using the Lagrangian ...
7
votes
2answers
3k views

Why is Roy's Identity so important?

I've been reviewing some of my microeconomics theory and have been reading up on Roy's Identity. Recall that Roy's identity is defined as: $$x^*_{i}(\text{p},m)=-\frac{\frac{\partial v}{\partial p_{i}...
3
votes
2answers
236 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 ...
4
votes
1answer
2k views

Mixed strategy Nash equilibrium in 3x3 game

What is the MSNE for the following game? I think you can eliminate strategies $A$ for player 1 and $C$ for player $2$, as these will are weakly dominated by all other strategies. Then, the game ...
6
votes
2answers
1k views

In auction theory, why is my own valuation a random variable?

Auction theory typically (always?) begins by assuming that each bidder's valuation is a random variable. Now, it might seem reasonable (at least from a Bayesian perspective) for you to treat other ...
3
votes
4answers
133 views

Lotteries and expected utility

Suppose we have the following four lotteries: $L_{1}=[(1,\$1)]$ $L_{2}=[(0.01,\$0),(0.89,\$1),(0.1,\$5)]$ $L_{3}=[(0.9,\$0),(0.1,\$5)]$ $L_{4}=[(0.89,\$0),(0.11,\$1)]$ If our agent says that he ...
0
votes
1answer
50 views

Compute the average income and the average utility

I don't know how to compute the average income and the average utility for the second case. It is confused because I have to consider two densities $[0,0.5]$ and $[0.5,1.2]$.Can anybody tell me how to ...
1
vote
1answer
42 views

What is the name and the mathematical model of this effect

Consider the case when some economic variable affects some another (for example, interest rate affects price index) because it involves human decisions. The effect is not immediate and would take some ...
2
votes
0answers
94 views

Use of the Lagrangian in empirical work

In my own studies I have noticed that many of the constrained optimization type questions that are often covered in intermediate/advanced microeconomics courses are seldom seen in more empirical types ...
1
vote
0answers
83 views

Risk Dominance on a Network

Suppose there are players on the network illustrated on the right (with 1 player on each vertex). There are two players $H$ and $J$ that are on the ends of the green line. $H$ plays $A$ and player $...
1
vote
1answer
50 views

Finding a stable equilibrium

I'm trying to determine which strategy is stochastically stable. In my lecture notes, we assign probabilities $a$, $b$ $1-a-b$ to player 2 strategies $T,M,B$ resp. Hence we have the payoffs $$u(t)=...
0
votes
1answer
46 views

Deriving support in bidding strategy

I'm considering some question, and I'm not sure what it asks me to do: Consider a two-bidder auction with two types of players, high type and low type ($v_h>v_l$). The probability of a low ...
3
votes
1answer
73 views

When can tit-for-tat be sustained?

Consider the following infinitely repeated hawk-dove game: $\hspace{1cm}\hspace{1cm}\hspace{1cm}$ For what discount rate $\delta$ can tit for tat sustain $D,D$? My professor says the answer is $\...
1
vote
0answers
23 views

Markov switching

I want to build some kind of two-stage Markov switching model but with two time-series. My general idea was to calculate some kind of dependence between two time-series in two different periods of ...
1
vote
1answer
59 views

Simple arbitrage model of a single commodity

Maybe, my question is a little chaotic. I want a mathematical model to describe the arbitrage of a single commodity. As I know , if I have much money, I can buy out or buy most of some commodity, ...
4
votes
1answer
45 views

One-step Binomial model's Radon-Nikodym derivative

In the one-step binomial model... For $\frac{d \mathbb Q}{d \mathbb P}$, I think it's $\frac{d \mathbb Q}{d \mathbb P} = \frac{q_u}{p_u}1_u + \frac{q_d}{p_d}1_d$, so it's some asset with payoffs $\...
5
votes
1answer
94 views

Quasiconcavification

Let $f_1, f_2$ be two smooth strictly-quasiconcave functions. Do there always exist monotone transformations $g_1,g_2$ such that the sum $g_1\circ f_1 + g_2 \circ f_2$ is ​a strictly-​...
4
votes
3answers
175 views

What are some important mathematics results that were first developed in Economics?

Economics is known to import mathematical methods that were proven to be useful in other areas. There is any important result in mathematics that was first developed in the context of Economics ...
2
votes
1answer
70 views

Term for perfect symmetric asymmetry

Let $x \in [0,1]$ denote some state (e.g. market share). Let $i \in \{1,2\}$ denote an agent (e.g. firm). Im considering a model where payoffs $F_i(x)$ are perfectly invertible in the sense that the ...
1
vote
0answers
256 views

Why use geometric mean for GDP when calculating the credit-to-gdp ratio?

I have a question regarding the difference between stock and flow variables. I know that a stock variable is measured at a specific point in time $t$ and the flow of this variable is measured over ...
0
votes
1answer
51 views

Levelized cost of electricity, to calculate the absolute costs?

I'm doing my master thesis about the renewable energies. So my goal is to calculate how much it will cost to switch our fuel based energy generation to renewable energy generation. So my first thought ...
0
votes
1answer
256 views

Debt accumulation equation derivation: valid given that it rests on calculus and the time period is a year? (nowhere near infinitesimal?)

Above is an image of what I’m referring to. The top ‘rule of thumb’ is derived using calculus, and hence is only valid for infinitesimal changes in t. However, this equation is considered over the ...
4
votes
1answer
137 views

Understanding the Zellener-Revankar Production Function

I took out a book from my university library called Econometric Modelling with Time Series: Specification Estimation and Testing in an attempt to understand the importance of MLE in Econometrics. ...
2
votes
1answer
793 views

How was the CES production function derived?

The Constant Elasticity of Substitution production function is defined as: (Taken from Wikipedia) $$Q=F \boldsymbol{\cdot}\left(a\boldsymbol{\cdot}K^r+(1-a)\boldsymbol{\cdot}L^r \right)^{1\over{r}}$$...
0
votes
1answer
77 views

Utility Functions: Implying endless consumption?

Do utility functions imply that if a consumer's income infinite, his consumption should also be infinite? The reason why I'd think this is the case is based on my basic understanding of utility ...
1
vote
1answer
2k views

How to derive the Indirect Utility Function from the Marshallian Demand Function?

I have been trying to derive the indirect utility function $(V(p,y))$, where $p$ is price and $w$ is wage, given the Marshallian demand functions $x(p,y)$ with the help of Roy’s identity (the utility ...
0
votes
1answer
86 views

Is there any good textbook for theoretical economics mathematical modelling? [duplicate]

I am currently reading some theoretical economics books and, of course, many mathematical expressions appear. I kind of guess their meaning, but it takes a lot of time and, after all, my guesses are ...
4
votes
1answer
138 views

Karush-Kuhn-Tucker in infinite dimension

Does the Karush-Kuhn-Tucker theorem on sufficient conditions for optimality of a convex program apply in countable dimension? For precisions, see Definition 4.1.1 and Theorem 4.1.4 of this course. ...
6
votes
1answer
273 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 ...
2
votes
0answers
381 views

Second order condition for symmetric game

Denote by $i \in \{1, \ldots, n\}$ an economic agent. Let $\mathbf x \in \mathbb R^n$ denote a vector of actions and $x_i \in \mathbf x$ a typical element. Let further $f_i : \mathbb R^n \to \mathbb ...
0
votes
1answer
110 views

Variance of $\hat{\beta _0}$ in case of homoskedasticity

Stock and Watson express the variance of $\hat{\beta _0}$ like $\hat{\sigma }^2_\hat{\beta _0}=\frac{E({X_{i}}^{2})}{n\sigma _{X}^{2}}\sigma ^{2}$, but starting from variance of $\hat{\beta _1}=\frac{...
1
vote
2answers
59 views

How to model spendthrift behavior

First, I'll introduce the observation and then ask the question. I have a brother-in-law who has a quirk: given the same product and two prices for it in different stores, he's willing to pay the ...
6
votes
1answer
212 views

Envelope theorem for discrete choice sets?

If we have a function $$f(x)=\max_yg(x,y)$$ Then we can find the derivative $d/dx \ f(x)$ by realizing that $$(1): \quad \frac {\partial }{\partial y}g(x,y^*)=0$$ because of the first order ...
2
votes
1answer
400 views

mathematical marxian models

Ive been doing some superficial reading on Feldman-Mahalanobis Model and have been wondering what other equations and "brand name" models that have been prodouced by marxist economists? What other ...
1
vote
1answer
66 views

Why $v_i=(X_i-\mu _X)u_i$ is i.i.d?

I don't understand. Ok, we have $\beta_1-\hat{\beta }_1=\frac{\frac{1}{n}\sum_{i=1}^{n}v_i}{(\frac{n-1}{n}){s_{X}}^{2}}$. So, for the first OLS assumption results that $E(v_i)=E((X_i-\bar{X})u_i\...
0
votes
2answers
169 views

Unconstrained Optimization:Why is there no “profit style” function in consumer theory?

When being exposed to your equations for profit maximization you have an equation of: $$\pi=pf(x)-c(x)$$ with this you can solve for the optimal input(s) $x$ from the first order conditions and some ...
2
votes
1answer
2k views

intuition behind the blanchard kahn conditions?

In order for a DSGE model to have a unique solution, it is required to satisfy the Blanchard Kahn conditions. However, these conditions seem very abstract to me. Is there an intuition behind the ...
1
vote
0answers
122 views

Deriving a Best Response Function in Baik (1994)

I'm reading a game-theory related paper*, and I'm not following the derivation of some property of the best-response functions. Suppose I have two players $1$ and $2$, whose strategies are ...
6
votes
2answers
98 views

Does every allocation have a maximal Pareto-improvement?

Consider an economy with a finite number of goods and a finite quantity of each good. Each agent $i$ has a preference-relation $\succeq_i$ which is a total, reflexive and transitive relation over the ...
3
votes
0answers
61 views

Mathematically optimal age to begin drawing Social Security retirement benefits as a function of expected life span?

So, for most of us Americans, our official retirement age is 66 and we get 100% of our retirement benefits. If we delay retirement, that benefit increases by 8% each year (up to age 70) and if we ...
2
votes
1answer
74 views

Contest game: second order condition satisfied, but negative profits?

The following is taken from Nti (1999) Consider a 2 player game in which each exerts effort in attempt to win a prize. Let $V_1$ be player $1$'s valuation of the prize and let $V_2$ be player $2$'s ...
3
votes
1answer
154 views

Math in Melitz and Ottaviano (2008)

I am reading Melitz and Ottaviano (2008), but I find it hard to understand some math in the model. The preference is given by : , which implies a demand function: Then the paper says the "inverse ...
3
votes
1answer
251 views

What are directional derivatives used for in economics?

In a basic mathematics for economists course one is exposed to the concept of directional derviative. Recall that a directional derivative is defined as: $$\nabla f \frac{\mathbb{v}}{\|\mathbb{v}\|}$$...
0
votes
2answers
779 views

Transformation of Cobb Douglas Utility

So, I need to determine whether or not $u=x^{0.5}y^{0.5}$ exhibits the same preferences as $u'= log(x) + log (y)$. Any tricks I can use here? I've done the logarithmic transformation so that I now ...
0
votes
0answers
65 views

Good book/article that goes into depth about transversality conditions?

I know how to derive the transversality condition in simple models like the Ramsey model. However, I am looking to develop a deeper understanding of transversality conditions in more complex models. ...
3
votes
3answers
469 views

Multivariable Utility functions

For a highschool economics/mathematics interdisciplinary essay I will use the Lagrange multipliers and deriving formulas that find the maximum. Could some one maybe suggest any (utility) functions ...
1
vote
0answers
59 views

Deviating from Cournot-Nash

Suppose player $1$ and $2$ are playing a simultaneous move game where with continuous strategies $x_1$ and $x_2$. The Cournot equilibrium is $x_1^*,x_2^*$. The following diagram purports to show that ...
13
votes
5answers
4k views

Applications of Trig functions in Economics?

Are there any applications of trig functions (ie $\sin(x)$, $\cos(x)$,$\tan(x)$) in economics?
4
votes
1answer
83 views

Subgame Perfect Equilibrium in Baye, Shin (1999)

The following is taken from Baye, Shin (1999) Consider a contest over a prize valued at 1 with symmetric players $1$ and $2$ who exert a level of effort $x_1$ and $x_2$ respectively. Effort cannot ...