Questions tagged [mathematical-economics]

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

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65 views

Alternative way to calculate the symmetric BNE of the game

My problem. Consider the following auction for a single object. There are $n \geq 2$ bidders. They submit their bids simultaneously. The object is allocated to the player who submits the largest bid. ...
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Deriving the VECM form of a VAR(1) model [closed]

Above is a question regarding volatility models and specifically deriving the VECM form from a VAR(1) model, unfortunately my lecturer hasn't provided an example of such a question prior so would love ...
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Volatility Models in Applied Econometrics [closed]

Below is a practice exam question on the topic of volatility models in advanced econometrics. Any and all help would be very appreciated. Thanks.
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1answer
50 views

Show that slope of MR (marginal revenue) is negative for monopolists

I want to show that the marginal revenue is negative for monopolists. We assume $P(Q)$ is homogenous of degree 1, so it is linear (affine, strictly speaking): $P(Q)=a-bQ$. As we know, $\frac{dP(Q)}{dQ}...
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1answer
29 views

Differentiation in a inflation tax calculation

everyone. I am studying Advanced Macroeconomics, by Derek Leslie, and I am having some troubles in understanding the result of a differentiation in the Chapter 1, section 5. This section approaches ...
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1answer
41 views

Why do we call certain linear (affine) demand curves “elastic” or “inelastic” even though PED varies along the slope of an affine function?

I get that PED varies along linear (strictly speaking, affine) demand curves in a way that for a demand function $Q(P)=\alpha - \beta P$: $$|\epsilon_D|=1 \iff \frac{\alpha}{2\beta}=P \land |\...
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1answer
74 views

Demand derivation in vertical differentiation with a bad characteristic

Today's question is about a variant of Tirole vertical differentiation framework. I am stuck thinking about the demand and profit function derivation where consumers can pick the level of $x$ at their ...
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1answer
135 views

GE with an intermediate good

intro I'm looking at a simple model with 1 consumer, 2 goods and 2 firms. I'm trying to get a price vector [p0, p1] that makes it work. By makes it work, I mean, ...
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1answer
66 views

How to get the condition of OLS mathematically?

From this discussion, I asked @tdm about the condition of OLS but I still cannot get it, and it is not easy to answer the mathematic equation in comment part so I want to ask here. One way to see this ...
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1answer
113 views

Why standard errors in country-level variables are higher than that in firm-level variables?

From this dicussion, the commentor said Lastly, firm fixed effects may absorb more variation and likely reduced the size of their standard errors. In practice, I also mainly see that the standard ...
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1answer
46 views

Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$

I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
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Why excluding intercept is dangerous if there is no literature back up in DID setting?

Recently, I run the regression for the generalised DID following this paper: $Y_{it}$ = $\alpha$ + $\beta$ $(Leniency Law)_{kt}$ + $\delta$$X_{ikt}$ + $\theta$$_t$ + $\gamma$$_i$ +$\epsilon$$_{it}$ (1)...
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Why the common trend assumption of subsample will be the same with the whole sample in DID?

When separating the sample into subsamples in this topic, this answer stated that I guess parallel trend assumption must hold within municipality size. DID with homogeneous effect typically assumes E[...
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1answer
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What does "dependent and independent variables only vary at the ($g,t$) level mean?

From de Chaisemartin and D'Haultfoeuille 2020, p.2969 I saw an equation $D_{g,t}$ $=$ $\alpha$ + $\gamma_g$ + $\delta_t$ + $\epsilon_{g,t}$ $D_{g,t}$ is the treatment in group $g$ at period $t$ They ...
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1answer
47 views

What does expectation of $\varepsilon_{c,t}$ conditional on $_c$ mean?

From a discussion, I recieve a mathematic answer, I understand until one point This decomposition can always be made by setting $\delta_c$ to be the expectation of $\varepsilon_{c,t}$ conditional on $...
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2answers
105 views

Learning Economics in Three Dimensions

I am trying to teach myself microeconomics via video series. I have a fairly good mathematics foundation, currently studying Partial Differential Equations and having gone through all the prereqs you ...
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1answer
49 views

Current valued VS Present Valued Hamiltonian Differing Euler equations

I have been having some difficulties with recovering the same euler equation from the following optimal control problem when comparing the present valued hamiltonian to the current valued hamiltonian. ...
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Demand function for substitutes

I have a problem where my answer does not seem to be right anywhere. For the following set up: Budget constraint: $400=40x+20y$ Utility function: $u(x,y)=3x+y$ the problems asks to derive the demand ...
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1answer
54 views

Comparative statics of a monopoly

Consider a profit maximising monopolist with linear demand Q(P*) and total production cost C(Q(P*)) who faces a per unit tax t. Suppose the slope of marginal cost is decreasing in some parameter, μ. ...
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1answer
49 views

Multivariate implicit differentiation (Samuelson, 1948)

I am studying "The Simple Mathematics of Income Determination", by Paul Samuelson (from book is called "Macroeconomia (artigos selecionados)", by APEC-CAEN. It is the 1st chapter ...
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1answer
67 views

Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation

Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$ $$ \frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \...
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1answer
176 views

Economic theory journals for a refinement theorem about utility function representation

I would like to ask which are the (mathematical) economics journals that publish papers about economic theory and that focus mainly on the mathematical aspects of it. Let me be more precise. If I have ...
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1answer
67 views

A differentiation step in a economic growth model

I started studying Olivier Blanchard and Stanley Fischer's Lectures on Macroeconomics, but I couldn't follow the reasoning behind a differentiation step (at least I think it is something involving ...
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1answer
22 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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1answer
68 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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1answer
46 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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37 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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1answer
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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
76 views

Approaches in demand analysis

What is the difference between Engel Curve and the system approach of demand analysis?
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2answers
437 views

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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1answer
132 views

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
59 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
39 views

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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2answers
82 views

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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2answers
70 views

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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2answers
83 views

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
27 views

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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1answer
286 views

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
39 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
80 views

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
72 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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1answer
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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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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0answers
75 views

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
90 views

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
60 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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2answers
237 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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