Questions tagged [mathematical-economics]

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

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Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country in relation to others countries?

In my country we are told often that the tax pressure over the companies and people is huge, making it unbearable and being a reason bankrupting the Economy, and one of the largests in the world. We ...
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28 views

Shortcuts for elasticity of substitution

How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
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29 views

Equations of “rational mechanics” and general equilibrium

Vilfredo Pareto, referring to the equations that determine equilibrium, wrote: These equations do not seem new to me, they are old friends. They are the equations of rational mechanics. This ...
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Annual Fraud Recovery Over Time: Should I adjust for inflation?

I have a dataset of the total amount the U.S. Department of Justice obtained annually in settlements/judgments of government fraud cases from fiscal years 1988-2019. There's a lot of variation, but ...
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For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves

The question in the title sounds like a trick question, due to the monotonicity property that indifference curves have, such that for two goods x and y, strong monotonicity implies y > x. Possible ...
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28 views

How are low/middle/high classes defined mathematicaly?

I am only looking for mathematical references. I think this belongs to econometrics but am not sure nor where to look at it specifically. I suspect the definition is given with some kind of weighted ...
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Linearization of the dynamic system (I did it, but I have a mistake that I cannot catch. Help me please)

I have the following dynamic system in discrete time For p is price, d is demand and s is supply. $$p_{t+1}-p_t= a(d_t-s_t)$$ $$s_{t+1}-s_t=bp_ts_t-ws_t$$ $$d_t= k-gp_t$$ I have to linearize this ...
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Determine lot size with extra constraints and EOQ formula

Given a fixed price of 250,00 dollars for the warehouse and the price of the product is 5,00 dollars per product. The order cost is 500,00 dollars but if more than 1000 products are ordered then it ...
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How do you calculate the intrinsic value or fair value of real estate?

How do you calculate the intrinsic value or fair value of real estate? I mean how do you determine that the house/commercial estate is undervalued or overvalued?
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NPV but adding last year net value?

I have found the following NPV (Net Present Value) formula: CF = unlevered cashflow i = interest rate (WACC) $$NPV = -I_0 + \frac {CF_{2019}}{(1+i)} + \frac {CF_{2020}}{(1+i)^{2}} +\frac {CF_{2021}}...
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Behavioral Dictator Game

I am doing a self study on behavioral economics and I am trying to solve behavioral version of the dictator game with following utilities for person 1 and 2. $$ u_1( \sigma_1, \sigma_2 ) = \...
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A question on the accuracy of economic forecasts

I apologise if thi's question appears dumb or boring, but I am asking it as a lay person. The context is that I am always arguing with friends that they should trust the economists view that Bexit (...
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67 views

How do we define an efficient tax in microeconomics?

I am currently working through problems to study for an upcoming exam. I am not seeking a solution per se. I am looking at the intertemporal choice model. I am looking at two periods where consumption ...
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2answers
28 views

Definition of covered market

I do Industrial Organization course, and I've seen the phrase "market is covered" several times in my lecture slides, however, I'm struggling to find the formal definition of "covered market" and the ...
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Interpretation of dummy variable : Random Effects Model

I am running a RE regression and I have export similarity index between two countries as the dependent variable and have a dummy variable such as share a border(=1 if countries share border, 0 ...
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29 views

Why decreasing co-state variable (over time) is Compulsory?

I have a short question. In the continuous time infinite horizon optimal control maximization problem Like $$\max \int^{\infty}_0 u(c_t)e^{-pt}dt$$ I use current hamiltonian function and I obtain ...
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What is the economic interpretation of the solution of this optimal control problem?

I have the following optimal control problem $$\max_{c_t} \int^{\infty}_0 e^{-p_it}\ln(c_t(i))dt$$ subject to $$\dot{w_t}(i)=rw_t(i) -n_ic_t(i)$$ $$w_0(i)=w_0>0$$ I have some wealthy and ...
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51 views

How to find mixed optimal strategies in this zero-sum game?

I'm trying to solve this problem from last year final exam in game theory: Consider the zero-sum game $G=(X, Y, g)$ where $X=Y=[0,1]$, and $$\forall (x,y) \in X \times Y: g(x, y)=\max \{x(1-2 y), y(...
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Is there some definition about risk sharing?

I was searching for a definition of risk sharing and I have found the following: $\underline{Definition:}$ Risk Sharing — also known as "risk distribution," risk sharing means that the premiums and ...
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What is wrong with the idea that resource depletion causes recessions? [closed]

How can you refute this theory, such that it never comes up again.
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1answer
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Dimensional analysis of GDP

The GDP is sometimes given by $$ GDP=P\cdot h\cdot e \cdot F $$ Where $P$ is the Productivity, $h$ is the number of hours worked, $e$ is the employment rate and $F$ is the size of the labor force. ...
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Interpretation of $\frac{\partial }{\partial p_1}Q_1(p_1, p_2)/\frac{\partial}{\partial p_2} Q_1(p_1, p_2)$

I am interested in an economic interpretation for the ratio of partial derivatives of a demand function $Q_1(p_1, p_2)$, which is \begin{equation} t=\frac{\frac{\partial}{\partial p_1}Q_1(p_1, p_2)}{\...
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Writing constraint

A firm accumulates useful knowledge $k$ by investing in R&D activities. Specifically, if the firm invests $r > 0$ dollars into R&D, the stock of useful knowledge grows by about $2\sqrt{r}$ ...
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60 views

Can we have a Non-Reflexive Preference Relation?

I've been thinking about preferences alot recently and have been specifically thinking about the reflexivity requirement. That is: $$x \succsim x$$ Though this is apparent and obvious, I have been ...
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Finding optimal path in continuous time

I have the following optimal control problem $$\max_{c_t,l_t} \int_0^{\infty} [ln(c_t)+\theta ln(1-l_t)]e^{-pt}dt$$ st. $$\dot{k_t}=k_t^{1/2}l_t^{1/2}-c_t-\beta l_t$$ $$k_0>0$$ I do big part of ...
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How to use an instrumental variable to estimate the parameter?

I have the following linear model of log wages (w) explained using years of schooling (S), years of experience and its square $(E,E^2)$ and 3 dummy variables indicating whether the individual was ...
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Bliss point hamiltonian function

I have the following utility function $$u(c_t)=g(c_t-b)^2$$ for constants $g,b>0$ Edited: in order to be bliss utility function, It must be g is negative. But in the question g is given to be ...
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1answer
36 views

Linear Probability Model Instead of Logit in Fixed Effects Regression

In our panel data analysis we estimated a fixed effects linear probability model (LPM) instead of a fixed effects logit regression because our sample size was quite small (600 individuals) and the ...
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1answer
74 views

Present value heuristics problem

No idea if this is the right stackexchange for this, feel free to point me elsewhere! I'm teaching business calculus and one of the problems the students have is to figure out the present value of a ...
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1answer
26 views

Consumption Set in Arrow-Debreu

I'm very inexperienced in mathematical economics, so when I came across the idea of the consumption set in Arrow-Debreu, I was a little confused. So for each element x in consumption set X, what does ...
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How to show that the estimator is consistent?

$Y_i=\beta_0+\beta_1X_i+U_i$ is my regression model for an I.I.D. sample with N=1000 observations. Suppose $U_i\sim I.I.D.(0,\sigma^2)$ and Xi are also I.I.D for i=1,2,3......1000. Xi is independent ...
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1answer
50 views

How to test if the effect of one regressor entirely comes from other regressors?

I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know ...
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88 views

Linear Utility?

Consider a preference relation $\succeq$ on $X\subseteq\mathbb R^2$. If $\succeq$ satisifies: $$ \begin{align} &1.\mbox{ }(a_1,a_2)\succeq (b_1,b_2)\implies(a_1+t,a_2+s)\succeq (b_1+t,b_2+s),\...
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1answer
97 views

Dynamic programming, optimal consumption-savings (finite horizon) problem

Let $w_t$ denote a consumer's wealth at time $t$ and $c_t$, the amount she chooses to consume, so her savings exiting this time period are $w_t-c_t$. Given this savings decision, her savings $w_{t+1}$ ...
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What is Economic Interpretation of three nonlinear equations?

I have the following nonlinear system $w$ is wealth $c$ is consumption $r(w)$ is gross return on wealth $a,b, d$ are parameters which are strictly positive and fixed. $$\dot{w} =r(w)w-c$$ $$\...
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1answer
36 views

The assumptions of Rational Expectations Models

What are the assumptions between rational expectations models and how restricted are there for the following results of economic theory? Where can I find them all gathered in some textbook or in the ...
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1answer
45 views

Regarding the Expenditure Function Underlying a Bliss Point

I've been looking at expenditure systems and have been really interested in the behaviour of the demand system that underlies bliss points: Consider the bliss point utility function of the following ...
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Software used for solving demands of different functions

I'm currently doing some research on demand systems and have been experimenting with different underlying utility functions which will generate different systems of demands. However I've been doing ...
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Two different definitions for a Complete Relation

Many sources show this definition for completeness of a relation $$ \forall a, b \in A, a \neq b, (aRb) \text{ or } (bRa) \tag{1} $$ Others show only $$ \forall a, b \in A, (aRb) \text{ or } (bRa) \...
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Is it possible to have a preference relation that is complete but not transitive?

I've been doing my own reading on non-rational preference relations. Im currently under the impression that transitivity follows as a direct result of completeness of preferences. However my (much ...
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Existence of symmetric trembling hand perfect equilibria

Consider symmetric and finite game. By Nash (1950), the game must have at least one symmetric equilibrium (proof). Also, it must have at least one trembling hand perfect equilibrium (proof). ...
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Optimal Production Input in Relation to Cost Minimization Problem

I was doing my homework and got really confused about how to approach the optimal levels of inputs when there are three variables. My current understanding is that the problem is to solve the ...
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1answer
56 views

Regular annual pension

I am supposed to solve the problem: A 24-year-old man decides to invest 200,000 euros at a 7% annual interest rate to bring him a regular annual pension from 31 to 50 years inclusive. What will be ...
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48 views

Short cuts to solve Cobb Douglas Utility function (minimization)

Say a Cobb Douglas like: $$\max_{X,Y\: s.t. X \cdot P_x+ Y \cdot P_y=I} U=X^\alpha Y^\beta$$ When it comes to maximization I would do the following way (for the fastest result): x: $\alpha/(\alpha +...
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Revenue maximization problem

There are $N>0$ Households in an economy. The government has aim to maximize a weighted average of income by imposing tax on the rich people and redistribute the tax revenue to the labor ones. ...
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The centralized shift from barter to currency economy

Suppose some ancient king of small bronze age city-state wants to introduce universal currency instead of barter that is currently in overwhelming practice in his kingdom. In order to smooth the shift,...
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Overlapping Generations Model Pension System Question

Part 1 Pension System OLG Model with pension system: Each individual lives up to two periods. The surviving probability at period 2 is p. At period 1, the young household consumes c1, saves s1, and ...
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113 views

Algebraic approach towards convexity

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.
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Central bank loss function (I did a solution, but it doesn’t totally make sense I guess)

I have question on central bank loss function. We know that the central bank loss function is $$L(\pi, \bar{Y})= (\pi- \pi^e)^2+\beta \bar {Y}^2$$ And we know that fisher equation is $$i=r+\pi^e$$...
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derive value function from utility function

We have the utility function. $$U_{t} = \ln{c_{t}} + E_{t}\sum_{s=1}^{\infty}(\beta^{s}\ln{c_{t+s}})$$ And I am trying to find the value function. $U$ is utility function. $c_t$ is consumption at ...