Questions tagged [mathematical-economics]

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

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14 views

How do I determine PED from price consumption curve with slope of zero?

Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1. By ...
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50 views

Without knowing the Slutsky equation and income/substitution effect, how can I show a certain good is inferior or Giffen?

Say I've got a function $x_1(p_1,p_2,m)$ where $p_1, p_2$ are the prices for good 1, good 2 respectively and m is the income. Now, I haven't heard of the Slutsky equation yet nor the income/...
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What is the meaning of the definition of RBI from its preamble? [closed]

Please explain the meaning of this statement, "generally to operate the currency and credit system of the country to its advantage".
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Solving a maximization problem [closed]

As stated in the image above, I want to solve the maximization problem for the control, state and co-state variables.
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42 views

Calculating elasticity for $y^2e^{x+\frac{1}{y}}=3$

I want to calculate elasticity of y with respect to x for $$y^2e^{x+\frac{1}{y}}=3$$ My attempt: I calculate $y'$ using: $$y'= -\frac{f_1'(x,y)}{f_2'(x,y)} = - \frac{y}{2-y}$$ I calculated this using ...
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Importance of Combinatorics

I would like to know how important combinatorics is. I am an undergraduate student looking to take more math courses and I saw and intro to combinatorics as an option. The reason I am asking is ...
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33 views

How to derive consumer expenditures in EMEA 14.2.5

I am working on a problem 14.2.5 from EMEA by Sydsaeter, Hammond and Strom. Consider the consumer demand problem: $$ \max_{x,y} U(x,y) = \alpha \ln(x-a) + \beta \ln(y-b) \text{ s.t. } px+qy=m \tag{*} ...
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29 views

Microeconomics - Risk Aversion and Gambling [closed]

I'm really not sure how to answer this question - part (a) in particular has me stumped, because I don't understand how to write up a slope of a budget constraint linking Wa and Wb. Substituting the ...
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1answer
69 views

Trouble at differentiating a consumption function

everyone. This is kind of a basic question, but I have a weak background on calculus and I already tried to figure this out by myself for a few hours without success. So, I am finally appealing on you ...
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Quote or price driven markets

Where can I find some details about quote driven markets? Can anybody show any notes or provide some paradigm about what the trader sees when he is about to trade in such a market? They say that he/...
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1answer
71 views

Approaches in demand analysis

What is the difference between Engel Curve and the system approach of demand analysis?
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Euler equation in Continuous time VS Discrete time

I have seen the euler equation in discrete time for the baseline neoclassical growth model written as: $$\frac{U'(c_{t+1})}{U'(c_{t})}=\frac{1}{\beta(1+r)}$$ however I have also seen the euler ...
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Intuition behind Euler Lagrange equation in economics

When being exposed to the concept of the Euler Lagrange equation as a mathematical concept, many ideas from the physical sciences are used to explain its relevance in terms of choice of shortest path, ...
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1answer
58 views

Cross-section experiment with Differences-in-Diffrences estimation [closed]

I am trying to answer the following question related to econometrics: ...
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1answer
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Total differentiation in a IS curve context

everyone. I'm having a hard time trying to figure out how the total differentiation occurs in this exercise. In this excerpt, from Inflação e Crises", by Affonso Celso Pastore, the author ...
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Auction Theory: Proving that the found equilibrium is indeed optimal

I have been looking at auction theory and in the book Auction Theory by Krishna, there is one (seemingly simple) inequality that I just cannot follow. Context: given a private valuation $x$, the ...
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Multi dimensional Auction in economics

I am following this paper . They have different suppliers and one buyer and They are using auction to select best suppliers Suppliers will submit. suppliers offer a multidimensional bidding on quality ...
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Ordinally Separable Utility Representation

Let $X_i$ be a separable, compact, Banach space. Definition: A weak order $\succeq$ on $X=\prod_{i=1}^NX_i$ has an ordinally separable representation if there exists $u_i: X\rightarrow \mathbb{R}$ and ...
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Is this formula correct (monthly payments for a loan over time charging compounded interest while decreasing principal)?

I'm trying to derive a formula that I can use to optimize payments for my student loans. I'm not sure if Economics.SE is the best place for this because it is pretty math based, but the problem I have ...
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1answer
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From the aggregate supply equation to the definition of inflation rate

By definition the inflation rate is $$\pi=\dfrac{P-P_{-1}}{P_{-1}}\cdot100\%$$ or could be defined in terms of the consumer price index CPI, but in this case I think the former is the one to consider....
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Topology on the space of measurable functions

The context is as follows: Suppose we have a 2 period sequential game, with player $i$ in stage $i$, with action set $A_i$. Give $A_i$ all the nice properties, as compact, separable metric spaces (I'd ...
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1answer
35 views

Inada Conditions in Plain English

I wondered if someone could potentially explain the Inada conditions in plain English, and the implications. $$lim_{c_t\searrow0}\frac{\partial U}{\partial Ct}= +\infty$$ $$lim_{c_t\nearrow+\infty}\...
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1answer
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Multidimensional product differentiation and density functions

I’m having trouble with a model (link) I’m working on for a review. The author uses a two firms hotelling model with a multidimensional product space (x,y)with orthogonal characteristics, which are ...
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1answer
71 views

Comparative statics of a maximum

Suppose that $f(x,a)=\max[g(x,a),h(x,a)]$ and $x^{∗}=\arg\max_{x}f(x,a)$. Also, let $x_1(a)=\arg\max_{x}g(x,a)$ and $x_2(a)=\arg\max_{x}h(x,a)$. If both $x'_1(a)$ and $x'_2(a)$ are nonnegative, under ...
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87 views

Actions in economics

Mirowski 1989 argues economics and physics have frequently informed each other's theoretical development, and neoclassical economics has the same Lagrangian and Hamiltonian formalism frequently seen ...
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25 views

Derive optimal wage in New Keynesian-Calvo wage stickiness

Following Costa, 2016 in page 96, developing the labor variety optimal wage decided by the household, the FOC is: $$0=E_t\sum_{i=0}^\infty(\beta\theta_w)^{t+i}\left\{\psi_W\left[L_{t+i}\left(\frac{W_{...
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Proof monotonicity on Blackwell sufficient conditions

I need to prove monotonicity assumption on Blackwell’s sufficient conditions for a contraction, that is: Given the operator T defined as $(Tf)(x) = sup [F(x,y)+bf(y)]$ I need to show that $f\leq g\...
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1answer
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How to get this Production Function in Growth Rates

I'm struggling to understand how Khan & Reinhart (1990) go from the next production function. $$y=A f(K,L,Z)$$ Where $y$ is the production of the economy, $A$ is a variable which contains the ...
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1answer
55 views

Is there a book or notes that explain all about inflation? [closed]

Is there a book or notes or papers (but for easy understanding please) that explain all about inflation? Not at a research level but student level. From what is previously needed to define and ...
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233 views

Arrow-Debreu Theorem of Existence: Non satiation

Let $n$ be the number of consumers and $m$ be the number of commodities. The Arrow-Debreu theorem requires closed and convex consumption sets $X_i \subset \mathbb{R}^m$ for all buyers $i \in [n]$. ...
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1answer
50 views

Calculate average annual inflation

The price index in the year 1993 is 60. The base at 2012 is 100. The annual nominal interest rate between 1993 and 2012 is 66% on average. What is the average annual inflation between 1993 and 2012? I ...
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23 views

Economics behind reverse auctions with occasional non-profiting suppliers

I was curious about the theory behind a reverse auction system where some suppliers act in a non-profit manner, namely, that their consideration of extra-auctions benefits of providing their service ...
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1answer
77 views

Proof of Concavity of Cobb-Douglas Function

Given the function $F(\mathbf{x})=x^{a_1}_1x^{a_2}_2 \ldots x^{a_n}_n$ defined on the set $S=\{\mathbf{x}=(x_1, \ldots, x_n) \in \mathbb{R}^n: x_1>0, \ldots ,x_n>0\}$ with $a_1,a_2,\ldots,a_n &...
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2answers
272 views

Under what condition is a cost function strictly concave in prices?

Define the unit cost function as $$ c(w) = \min_{z\geq 0} w\cdot z $$ subject to $f(z)\geq 1$. Where $w$ is a vector of input prices, $z$ is the vector of inputs and $f$ is a production function. We ...
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39 views

Mathematical question in macroeconomic task

I am currently working on a project where I want to explore how changes in a couple of currencies affects the income for my countrys exported fish. My country (Norway) sells it fish in 4 different ...
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20 views

Market clearing price and dual variables in auctions

Suppose the allocation of an auction (or a market) is defined by the solution of a linear program. Then it is known that the associated clearing price is given by the dual variable associated to the ...
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1answer
44 views

Blackwell's Sufficiency Conditions for a Contraction:

I wondered if anyone could throw some intuition on Blackwell's sufficiency conditions: (1) Monotononicty; (2) Discounting; Would be genuinely appreciated to hear both terms expressed in plain English.
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2answers
63 views

Nested/Recursive Dynastic Utility Functions

I want to find a way of representing a dynastic utility function in which not only the head of the dynasty's utility is dependent on its descendants' utility, but all members of the family tree gain ...
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1answer
46 views

Finding optimum market value of vintage car

I am trying to find first and second order conditions for the following problem: $$P(t) = V(t)e^{-rt}- \int^t_0 me^{-r\tau}d \tau $$ I managed to find the first order condition: $$P'(t) = V'(t)e^{-rt} ...
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1answer
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Is $(\mathbb{R}^m)^n$ the real coordinate space of dimension $m\cdot n$?

Very simple question here: say that there are n individuals and each individual $i\leq n$ has a consumption bundle $x_i\in \mathbb{R}^m$ (i.e. there are $m$ types of goods). Suppose that social ...
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Probability transition matrix as a function of the variance in Matlab?

I am working on Probability transition Matrix on Matlab. I Have say 5 points (states) of discretized productivity grid. I would like to have two matrix of probability transition subject to the ...
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1answer
50 views

Integration by parts with CDF

I am told that the following equality follows from integration by parts: $$\int_{R-k}^{1}(\theta-R)dG(\theta)-G(R-k)k=\int_{R-k}^{1}(1-G(\theta))d\theta-k$$ Where $R>k>0$ and $G$ is the CDF of $\...
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1answer
25 views

Stationarity, ADF/KPSS, Autocorrelation and Heteroscedastiy

i have a time series which is not stationary due to ADF/KPSS test, but is is in its first difference. So ADF and KPSS tell me it is starionary so it has a constant mean/variance/autocorrelation. But i ...
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108 views

Comparing 2 equilibrium values (competitive vs centralized): can I compare only 1st derivative of objective function?

I have a rather complex model where analytical solutions do not seem achievable (I also tried symbolic solving in Matlab and Python and could not find any) so that I cannot get an explicit expression ...
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1answer
51 views

How can difference equations with an infinite summation be represented in matrix form?

I have derived the microeconomic foundations of a dsge model and I've obtained the IS and NKPC. I would like to represent them in matrix form to study the system. However the problem is that both ...
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1answer
31 views

Labor demand and supply curves in terms of elasticities

I would like to ask for your help to derive some expressions. Let the labor demand curve be described by: $N^D = N^D(W/P, \bar{K}), \quad N^D_{W/P}= \frac{1}{F_{NN}}< 0, \quad N^D_K = -\frac{F_{NK}}...
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1answer
51 views

Economic interpretation: IS curve contra GDP in equilibrium

I have in a problem shown that for the IS curve (Y) contra the GDP in equilibrium ($Y^*$) it applies that: $\frac{\partial Y}{\partial G}>\frac{\partial Y^*}{\partial G}$. Where G is public ...
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1answer
34 views

Variance in the Context of a AR (1) Model

I wondered if someone could help me in terms of the required algebraic steps from expressions (3) - (4), for the the moving average representation of the AR (1) below? Would be appreciated. $$y_t=a +\...
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1answer
66 views

Recursive Substitution in Time Series

Would appreciate some guidance on a matter of recursive substitution, where we have the AR model: $$y_t = \alpha +\theta_1y_{t-1}+ u_t$$ And $$E(y_t)= \mu_t$$ Where: $$\mu_t = (1+\theta_1 + \theta_1^2+...
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28 views

Interpretation of market condition given by relation between elasticities

The total market demand is given by the sum of the two destinations ($e$ and $f$) given to the product. Given these conditions: Demand: $d(p) = e(p) + f(p)$ where: $d(p) > 0$, $d'(p) \leq 0$; $e(...

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