Questions tagged [mathematical-economics]

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

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1answer
109 views

Can there be a sample such that SRF and PRF do not intersect?

I am confused if it is possible for to randomly select a sample such that SRF and PRF do not intersect. I have thought of the concept of parallel lines, which allows for such a case but I am unsure if ...
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1answer
105 views

Income effect $-\frac{\partial x_i}{\partial m} x_i$ or $\frac{\partial x_i}{\partial m}x_i$?

Recall that the slutsky equation is: $$\frac{\partial x_i}{\partial p_i}=\frac{\partial h_i}{\partial p_i}-\frac{\partial x_i}{\partial m}x_i$$ I know $\frac{\partial h_i}{\partial p_i}$ defined as ...
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1answer
202 views

What is the concept of ordinal utility?

I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used. If that is so, how can one define a mathematical function for utility which gives a ...
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0answers
42 views

Anscombe and Auman Expected Utility

I would like to hopefully get some insights on the Anscombe and Aumann Expected utility. I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers ...
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1answer
67 views

Proving the existence of Nash Equilibrium using alternate approaches

Most of the standard books/papers/reading materials prove/state the existence of a Nash Equilibrium by appealing to Sperner's Lemma, or to Brouwer's/Kakutani's FPT. However, I've recently come to know ...
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1answer
223 views

Deriving average productivity from a CES production function

Following the work of Raurich et al. (2012) I got stuck trying to derive the average productivity starting from the following CES production function: $$Y=A\left [ \alpha K^{\frac{\sigma -1}{\sigma }}...
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0answers
121 views

Applications of Pure Mathematics in Economics

Are there any applications of number theory and abstract algebra in economics? An economist had told me that number theory had an application to a theorem in economics, however he did not remember ...
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0answers
40 views

Mean Field/Differential Game and Measurability

Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ...
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1answer
336 views

Is this Cost function concave or convex?

Given the following cost function, where t is the quantity of some product. $$C(t) = 1/3t^3 - 7t^2 +11t + 50$$ here is a graph between $t= 0$ and $t = 25$ We are asked if this function is convex or ...
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1answer
80 views

How likely are the Sonnenschein-Mantel-Debreu results?

I have been reading about the SMD results and it's "damning" nature for GET. My understanding of the result is as follows: price changes not only cause a substitution effect but also change the wealth ...
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1answer
112 views

Help needed to understand proof in Myerson and Satterthwaite (1983)

The following image is an excerpt taken from Myerson and Satterthwaite's 1983 paper Efficient Mechanisms for Bilateral Trading: I know what the theorem is all about, all I need is some help with the ...
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0answers
47 views

Value of companies with circular ownership [duplicate]

Given two companies, total assets of $100 million each. Company 'A' owns \$50M of company 'B'. Company 'B' owns \$50M of company 'A'. If you look at the value of both companies do you ...
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43 views

How should I calculate bulk selling price for a small business?

Some friends of mine run a small business, in a small garage-like space, with a few employees, making and selling "plumbuses". The typical customer orders about 5 plumbuses at a time. When I heard ...
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1answer
39 views

Purpose of Semidefinite Integral

I want to know the meaning of Semidefinite Integral. I am used to read definite and indefinite integral but I want to know the meaning of such equation : $\pi(e)\left(1-F\left[-\frac{a}{\pi(e)}\...
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2answers
94 views

Simplest model of an economy exhibiting (hyper)inflation

I would like to find a minimal mathematical model for describing financial crises of the type that produces hyperinflation. Here's a naive attempt, just to give the idea of what I'm thinking of. ...
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0answers
74 views

Open Foundational Problems in Mathematical Economics

What are some open problems in mathematical economics which are treated as if they have been solved in economics papers? As an example, one of my teachers has previously pointed out to me that there ...
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1answer
709 views

Euler's Theorem

Can anyone give me connection and intuition behind each of the following euler's equation- Euler's equation in production function represents that total factor payment equals degree of homogeneity ...
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0answers
31 views

Including definite integrals inside definite integrals - Crossposted from MathSE

This question is cross-posted from MathSE: link I have the following differential equation from a journal article: $\dot{g}(t) - \delta(t)g(t) = -H(t) --- (1) $, which is integrated between t and T. ...
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2answers
59 views

How do I calculate the amount of money I get from an investor and the percentage I give him in return?

Let's say I owe a company. At the final state I want to be left with 1M cash for myself and 50 percent of the company. The investor is not willing to buy shares and give me the money but only invest ...
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1answer
24 views

Devising a model for inflation for a closed points system

I am working on a project that involves points. The idea is that users will earn points and redeem them for certain rewards. The means via which the users earn are fairly limited (They can attend a ...
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1answer
70 views

How does this demand function satisfy the Weak axiom if it doesnt satisfy the necessary and sufficient conditions?

Let $x_k = \frac{w}{\sum{p_l}}$ for $k = 1...L$ be the demand function. This demand function does satisfy the weak axiom and this can be shown simply. The slutsky matrix is an $L \times L$ matrix ...
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1answer
145 views

Did I calculate the expected value and the variance correctly?

I have the following assignment to solve but I'm not sure if I solved it correctly. Questions Let the stochastic process $(Y_t)_t$ be defined by $Y_t = \mu + Y_{t-1} + \varepsilon _t$ with $(\...
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22answers
12k views

Criticism of Math in Economics

I've been reading and speaking to a number of educated economists and economics PhDs who are against the use of intense mathematics and mathematical proof in economic theory. Specifically I've been ...
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0answers
242 views

How can I determine if a token economic is viable?

Given a system where you incentivize people to do actions in a system, we might have good and bad actors. I would like to know if there is a software or framework where I could put the different <...
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0answers
37 views

Deriving Single Good Demand Curve

came across a problem set that I had no clue how to tackle, but looks painfully simple. It's a market for electricity where households utility is represented by: U(E) = aE - 2mL2 (Household Utility) ...
2
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1answer
970 views

Prove all cost functions are concave in input prices and demand for inputs is downward

I've seen proofs that cost functions are concave of the form $C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$ although this neither feels convincing nor does it seem like a ...
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1answer
38 views

Simple Regression With Dummy Variable

Consider a simple linear model: $Y = \beta_1 + \beta_2 MALE + u$ where $MALE$ is a dummy variable. $MALE = 0$ if female, $MALE = 1$ if male. A model is fitted: $\hat{Y} = \hat{\beta_1} + \hat{\...
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2answers
246 views

Demand curve confusion

My economics textbook says that demand curves slope downward - but then goes on to say that when demand increases, prices go up! Does anyone else find this confusing? Edit: from the small number of ...
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1answer
89 views

Interpretation of the Cross Partials of the Cobb-Douglas

Consider a Cobb-Douglas Prod. Function $$Y=AL^{a}K^{1-\alpha}$$ This has the cross-partial: $$\frac{\partial^2 Y}{\partial K\partial L}=(1-\alpha)\alpha AL^{\alpha-1}K^{-\alpha}$$ Is the ...
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1answer
77 views

Proof of DCF model by mathematical induction

I am confident with the concept of DCF. However, I wanted to check the following proof given that if investors hold a share in $ t $, sell it at $t+1$, receive dividend $\ D_{t+1} $ and the price at $...
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0answers
187 views

Firm's profit max problem, in present value terms

So I am kinda stuck on this question. The question goes as follows: Consider a multiperiod firm, selling q1 units of a product in period t=1 at spot price P1 and q2 units in period t=2 at spot price ...
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2answers
114 views

General model of economics, economics as mathematical structure

Contrary to the common view, the physics is all about models, there are no such thing as law of nature, because every physical law has its applicability range and therefore all of laws as models. But ...
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2answers
257 views

Finding subgame perfect equilibrium

The main part of the question is as follows (if you cannot read this, I can immediately write it) My question is how to find the subgame perfect Nash equilibrium for the both cases $\bar{g_2}\ge \...
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1answer
196 views

Kuhn-Tucker and optimization (continue)

This is a question related to the question: Kuhn-Tucker optimization problem and game theory .The question is: Some cultures emphasize more social interaction more than others. Is there a role for ...
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1answer
267 views

Revenue maximization

We have two firms with identical cost structure compete in a market Demand function = $p=a-bq$ And $q=q_1+q_2$ They are identical in every way. However, firm 1 maximizes profit and firm 2 ...
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0answers
94 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 : $s_i$ = $t_i$ + ...
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1answer
119 views

Profit maximization question

Two firms are in a market together. They produce a product. Total revenue from sales is $y=K+L$ K is the amount of capital L is the amount of labor These two firms each specialized in supplying ...
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1answer
363 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 ...
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1answer
425 views

Optimization problem with Kuhn-Tucker conditions

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 consumption and $s_i$ is social interaction. $s_i$ is given by $s_i=t_i+t_{ij}\times t_{...
1
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1answer
134 views

Kuhn Tucker optimization problem

Assume that the player I select $x_i \ge 0$ at constant cost level $c>0$ The payoff function for player i is $$v(x_i,t)-cx_i$$ where $t$ is technology parameter. The function v(.)is twice ...
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1answer
272 views

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 ...
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1answer
96 views

Can we use hotelling's lemma as a rule of thumb when wage rate can vary?

Disclaimer: I've been doing some simulation with excel to see how Hotelling's Lemma behaves when allowing another parameter to vary. I did this by producing 150 randomly generated profit functions (...
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2answers
259 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 ...
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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 ...
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1answer
158 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 ...
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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}...
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2answers
235 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
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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
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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
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4answers
132 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 ...