Questions tagged [mathematical-economics]
The application of mathematical methods to represent theories and analyze problems in economics.
713
questions
2
votes
1answer
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. ...
-2
votes
0answers
14 views
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 ...
-3
votes
0answers
16 views
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.
1
vote
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}...
1
vote
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 ...
1
vote
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 $Q(P)=\alpha - \beta P$:
$$|\epsilon_D|=1 \iff \frac{\alpha}{2\beta}=P \land |\...
2
votes
1answer
74 views
Demand derivation in vertical differentiation with a bad characteristic
Today's question is about a variant of Tirole vertical differentiation framework. I am stuck thinking about the demand and profit function derivation where consumers can pick the level of $x$ at their ...
6
votes
1answer
135 views
GE with an intermediate good
intro
I'm looking at a simple model with 1 consumer, 2 goods and 2 firms.
I'm trying to get a price vector [p0, p1] that makes it work.
By makes it work, I mean, ...
3
votes
1answer
66 views
How to get the condition of OLS mathematically?
From this discussion, I asked @tdm about the condition of OLS but I still cannot get it, and it is not easy to answer the mathematic equation in comment part so I want to ask here.
One way to see this ...
4
votes
1answer
113 views
Why standard errors in country-level variables are higher than that in firm-level variables?
From this dicussion, the commentor said
Lastly, firm fixed effects may absorb more variation and likely
reduced the size of their standard errors.
In practice, I also mainly see that the standard ...
0
votes
1answer
46 views
Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$
I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
4
votes
1answer
80 views
Why excluding intercept is dangerous if there is no literature back up in DID setting?
Recently, I run the regression for the generalised DID following this paper:
$Y_{it}$ = $\alpha$ + $\beta$ $(Leniency Law)_{kt}$ + $\delta$$X_{ikt}$ + $\theta$$_t$ + $\gamma$$_i$ +$\epsilon$$_{it}$ (1)...
2
votes
0answers
56 views
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[...
2
votes
1answer
23 views
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 ...
3
votes
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 $...
2
votes
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 ...
3
votes
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.
...
2
votes
0answers
38 views
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 ...
3
votes
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. ...
2
votes
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 ...
4
votes
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, \...
7
votes
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 ...
2
votes
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 ...
0
votes
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 ...
1
vote
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/...
0
votes
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 ...
1
vote
0answers
57 views
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 ...
0
votes
0answers
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:
$$ \max_{x,y} U(x,y) = \alpha \ln(x-a) + \beta \ln(y-b) \text{ s.t. } px+qy=m \tag{*} ...
1
vote
1answer
70 views
Trouble at differentiating a consumption function
everyone.
This is kind of a basic question, but I have a weak background on calculus and I already tried to figure this out by myself for a few hours without success. So, I am finally appealing on you ...
2
votes
0answers
12 views
Quote or price driven markets
Where can I find some details about quote driven markets? Can anybody show any notes or provide some paradigm about what the trader sees when he is about to trade in such a market? They say that he/...
2
votes
1answer
76 views
Approaches in demand analysis
What is the difference between Engel Curve and the system approach of demand analysis?
5
votes
2answers
437 views
Euler equation in Continuous time VS Discrete time
I have seen the euler equation in discrete time for the baseline neoclassical growth model written as:
$$\frac{U'(c_{t+1})}{U'(c_{t})}=\frac{1}{\beta(1+r)}$$
however I have also seen the euler ...
7
votes
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, ...
2
votes
1answer
59 views
Cross-section experiment with Differences-in-Diffrences estimation [closed]
I am trying to answer the following question related to econometrics:
...
2
votes
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 ...
4
votes
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 ...
1
vote
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 ...
6
votes
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 ...
1
vote
0answers
40 views
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 ...
1
vote
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\%$$ or could be defined in terms of the consumer price index CPI, but in this case I think the former is the one to consider....
7
votes
1answer
286 views
Topology on the space of measurable functions
The context is as follows:
Suppose we have a 2 period sequential game, with player $i$ in stage $i$, with action set $A_i$.
Give $A_i$ all the nice properties, as compact, separable metric spaces (I'd ...
0
votes
1answer
39 views
Inada Conditions in Plain English
I wondered if someone could potentially explain the Inada conditions in plain English, and the implications.
$$lim_{c_t\searrow0}\frac{\partial U}{\partial Ct}= +\infty$$
$$lim_{c_t\nearrow+\infty}\...
3
votes
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 ...
1
vote
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 ...
1
vote
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 ...
3
votes
0answers
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:
$$0=E_t\sum_{i=0}^\infty(\beta\theta_w)^{t+i}\left\{\psi_W\left[L_{t+i}\left(\frac{W_{...
6
votes
0answers
75 views
Proof monotonicity on Blackwell sufficient conditions
I need to prove monotonicity assumption on Blackwell’s sufficient conditions for a contraction, that is:
Given the operator T defined as
$(Tf)(x) = sup [F(x,y)+bf(y)]$
I need to show that $f\leq g\...
7
votes
1answer
90 views
How to get this Production Function in Growth Rates
I'm struggling to understand how Khan & Reinhart (1990) go from the next production function.
$$y=A f(K,L,Z)$$
Where $y$ is the production of the economy, $A$ is a variable which contains the ...
0
votes
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 ...
5
votes
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 $i \in [n]$. ...
