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

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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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25 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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Is delivery-capability (in economics) a probability?

A dealer with a large, but finite stock counts for 1 year a = the number of all purchase inquiries that reach him this year and b = the number of purchase inquiries that he can deliver on the ...
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192 views

Is Gaussian distribution the proper choice for step in financial time series? E.g. DJIA ROI suggests Laplace instead

Data compression uses Laplace distribution ($\rho=\exp(-|x-\mu|/b)/2b$) for probability distribution of differences, while I see it seems economy uses Gaussian distribution everywhere (?), e.g. in ...
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21 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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Calculating national equilibrium level of income

Please help me solve this. An economy has consumption function given as c=30+0.5y and investment and government expenditure is exogenously determined at 50 and 80 units respectively. Determine ...
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28 views

Is this way of modeling undisclosed debt correct?

I am woking with a model like the one in Alfaro and Kanczuk (2006), that is in turn based in Arellano (2008), where sovereign´s preferences are given by: that in case of not defaulting is subject to: ...
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11 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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25 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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88 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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21answers
9k 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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108 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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21 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) ...
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1answer
110 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
33 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
32 views

2. What is the relationship between a change in the size of a tax, and the change in the deadweight loss of the tax?

What is the relationship between a change in the size of a tax, and the change in the deadweight loss of the tax?
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2answers
48 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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45 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
52 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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85 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
73 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
175 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
79 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
138 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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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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56 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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130 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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276 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_{...
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1answer
71 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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160 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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53 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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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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41 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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63 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
218 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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applying envelope theorem to the first order condition

$\max u(c,s)$ subject to $y=c+P(s)$ is equal to $u(\bar{c}(y;P),\bar{s}(y;P))=v(y;P)$. Then, the first order condtion of $v(y;P)$ is $u_c(\bar{c}(y;P),\bar{s}(y;P))$, using the envelope condition....
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112 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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57 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 ...
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Textbook or website about intuition behind financial economics topics such as option pricing

I am currently taking a course in financial economics. I have to be able to interpret formulas in stochastic calculus (such as the Ito lemma), the Binomial option pricing tree as well as Black-Scholes ...
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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 ...
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4answers
81 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 ...
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1answer
35 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 ...
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1answer
38 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 ...
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44 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 ...
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28 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 $...
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45 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)=...
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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 ...
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1answer
57 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 $\...
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19 views

Why is it that without identical endowments the aggregate excess demand may not obey WARP?

Intuitively, I understand that this is more or less related to there being a representative agent - but I don't quite understand the requirement that the agents have to have identical endowments. I ...
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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 ...