Questions tagged [mathematical-economics]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
33 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 ...
4
votes
1answer
48 views

Interpolation of Gini Index?

Is there a conventional curve used to interpolate the Lorenz curves that model the distribution for calculating the Gini coefficient? Is it polynomial? But why? Which degree?
-1
votes
0answers
13 views

Why are NNP/GNP loosing there significance?

It is a well known fact that NNP and GNP are loosing their significance with time. I tried to find a solution to this issue and in a book I found the following statement: "NNP and GNP are ...
0
votes
1answer
26 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}}...
2
votes
1answer
48 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 ...
7
votes
1answer
133 views

Uniform bounds on rate of merging for Bayesian learners

Update. Cross posted at Cross Validated. In a well-known paper, Blackwell & Dubins (1962) show that the posterior probabilities of two Bayesian agents, whose priors agree on events of measure $0$,...
2
votes
1answer
84 views

If production function is concave, then demonstrate that profit function will also be concave

Show that concavity of firm's production function implies concavity of its profit function. (Hint: For a concave function, first order conditions gives the vector that maximizes the function) ...
0
votes
1answer
28 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 +\...
0
votes
0answers
27 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(...
1
vote
1answer
45 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+...
6
votes
1answer
155 views

Derivation of Surplus in Paul Romer's paper on “mathiness”

In this paper by P. Romer https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.p20151066 I'm wondering the Surplus $S$ was derived. By using the given condition I found that $$q_0=m^{-\tfrac{1}{a+b}}N^{-\...
15
votes
1answer
452 views

How accurate is duality?

In economic theory we know that with the use of some calculus, Hotellings Lemma and Sheppards lemma we can derive a given firms supply function and in term its Profit function. With data of a given ...
0
votes
0answers
50 views

Uses of simple interest

Recently I started to read again Brealey & Myers's "Principles of Corporate Finance" (an older edition I hold it since I attended to the university course on Economics and Corporate ...
1
vote
0answers
28 views

graph of dependent income

I would need help with the following problem about consumer theory. Let us say that $X$ is the amount of days at the sea and $Y$ is the amount of days on the cottage. We have some utility function $u(...
1
vote
0answers
15 views

Measure of urban-ness or city density

I have a dependent variable I want to examine in relation to a measure of city density. This means city population as well as geographical spread. Ideally, it would also include a measure of ...
0
votes
0answers
10 views

Uniform price auction as a mixed integer program

I am considering a uniform price auction between one seller and multiple buyers for one divisible good. My question is the following: How may I reformulate the auction (determination of the allocation ...
11
votes
1answer
601 views

Calculus and Indifference Curves in an Urban Economics Example

I am reading the paper 'The Structure of Urban Equilibria' by Jan Brueckner. It uses a monocentric city model, where all consumers earn income $y$ at the centre of the city. They buy $q$ housing for ...
3
votes
1answer
45 views

Set of consumption over all period is convex in $\mathbb{R}^T_+$?

Today in class, the professor said that the set of all consumption $c(S)$ is non-empty, compact and convex subset of $\mathbb{R}^T_+$. i.e. we know $\sum \limits_{t=1} ^T c_t = S$ where $c_t$ is ...
1
vote
1answer
52 views

How does explanatory variables in variance affect unconditional variance of GARCH(1,1)

I have a question about the unconditional variance of a GARCH process, where exogenous explanatory variables are included in the variance. The usual GARCH models the variance using: $$\sigma^2_t=\...
3
votes
4answers
87 views

Why should $dp_2=dm =0$ in this problem?

I am studying Essential Mathematics for Economic Analysis and in chapter 12 problem 10 there is a problem that I can solve but I do not understand why the solution works. The problem asks us to ...
1
vote
1answer
94 views

Mathematical framework for modelling the relationship between price and sales of a product

In my job as a data scientist, I am required to model the relationship between the price of a product and the sales or number of unit sold. I am trying to build a simplistic model, the assumptions of ...
3
votes
1answer
79 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 ...
1
vote
1answer
86 views

Generalizing demand for perfect substitutes utility function

I have the utility function: $U(x_1,...,x_n)=a_0+\sum_{i=1}^{n}a_ix_i\;\;\;\;\;\;\;\;\;a_j\in\mathbb{R}_+ \;\;\forall j=\{0,...,n\}$ (maybe $a_0$ could be zero) $\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...
0
votes
0answers
35 views

Deconvolution in economics

Here it says In mathematics, deconvolution is an algorithm-based process used to enhance signals from recorded data. Where the recorded data can be modeled as a pure signal that is distorted by a ...
0
votes
0answers
33 views

The Envelope Theorem, Some Workings/Substitution

I have an application of the envelope theorem below, and would love some feedback on the steps taken to get from (2) - (3) and (3) - (4) and (4) - (5) The overall question is: 'derive the marginal ...
4
votes
2answers
84 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 ...
1
vote
0answers
24 views

Can anyone help me derive saving from the OLG model? (Just check to see if my start is okay please)

Question assumptions: Consider the effect of a capital tax on the OLG model. The government imposes a capital tax rate at the rate $\tau\in[0,1)$ and pays all the tax revenues back to the old in a ...
2
votes
1answer
79 views

Existing metric for personal productivity hours needed per life hour?

With about 50 hours of productivity a week, including work, cooking, etc. I can complete the tasks and pay the expenses necessary to live about a week. Subtract maybe 5 hours of labor that goes into ...
0
votes
1answer
39 views

Competitive equilibrium with production

Consider an economy with four goods, two individuals and two firms. Firm 1 produces good $x$, firm 2 produces good $y$. Consumers' utilities are $u_1(x,y,z,w)=\min\{x,2y\}$ and $u_2(x,y,z,w)=\min\{2x,...
3
votes
1answer
84 views

What model did the MONIAC use?

Phillips designed a hydraulic computer to model the UK economy in 1949; 12-14 copies were built. What model did it compute with? How have modern models of the UK built on that work?
3
votes
1answer
64 views

homothetic functions in economics

Are there any results in economics that require function to be homothetic? The textbook I am using (Essential Mathematics for Economic Analysis) says that function is homothetic when " $f(x)=f(y)$...
0
votes
2answers
53 views

Can we model risk with only probability?

Sorry for the confusion! I am adding an example to see if it helps: For example, consider a gamble A, with payoffs {a,b,c,d}, whose probability of each payoff being realized is equal (so 25% each); ...
1
vote
1answer
31 views

Would some help me fill in missing steps from a textbook exercise left for the reader

Question: Suppose $C_t=(1-s)Y_t-\lambda G_t$ where $s>\sigma$ as in the basic Solow model. Out of the government expenditure , proportion $\phi$ is invested in public capital formation. Hence we ...
3
votes
1answer
27 views

Are there any analysis of what is the net benefit of NASA program to US economy?

I am looking for some study that tries to calculate whether the NASA program on a net basis benefits the US economy. The program is very expensive, but it generates lots of patents, research, jobs and ...
1
vote
1answer
31 views

Would someone be able to help me solve capital per capita in the steady state (check my work)

Question: Suppose $C_t=(1-s)Y_t$ where $s>\sigma$ as in the basic Solow model. Solve for capital per capita in the steady state. $Y_t=K^{\alpha}_tL^{1-\alpha}_t$ $Y_t=C_t+I_t+G_t$ $K_{t+1}=I_t+(1-\...
1
vote
1answer
37 views

How can I know whether a good is inferior or normal? I can't determine elasticity with this?

I just need to make sense out of elasticities and how to determine if a good is normal or inferior. I have determined by $X_1$ which is in the form $m/p_1 - p_1/p_2$, that I should just take the ...
1
vote
0answers
24 views

Can someone help me prove that the CES function is also a Cobb-Douglass function [duplicate]

I would like some assistance with a problem that I have showing a CES function is also a Cobb-Douglass utility function. Question: we have a CES function: $Y=A[\alpha K^{((1-\sigma)/\sigma))}+(1-\...
1
vote
2answers
77 views

How to find $\phi$, that denotes the correlation of signals among informed traders?

Since I do not have an answer on Quantitative Finance in my question I cross-post here the problem to tag some other categories The following assumptions are part of the paper of Back, Chao and ...
1
vote
1answer
33 views

What are the advantages of using demand systems estimation? How is this different from individual demand estimation for product?

I am unable to understand how is demand systems estimation is different from simple demand equation estimation. What's the best resource for getting a history line of demand systems?
2
votes
1answer
197 views

The Principle of Optimality and the Bellman Equation

I endeavour to prove that a Bellman equation exists for a dynamic optimisation problem: $\ max \Sigma\beta^s U(C_t)$ Subject to the following constraints. $C_t + K_{t+1}= F(K_F, E_F,S_t)$ $E_t = F_E(...
6
votes
0answers
90 views

Certainty equivalence when the utility is semi-continuous instead of continuous

Let $U:\mathbb R^2\to\mathbb R$ be a utility function. If $U$ is strictly increasing and continuous, then it is well known that for any $(x_1,x_2)$ there exists a certainty $(c,c)$ such that $$U(x_1,...
1
vote
1answer
38 views

Find equilibrium price using excess demand function

Consider an economy with two agents. There are two goods, x and y. Agents' preferences are Leontif ones as follows: $u_1(x,y)=\min(x,4y)$ and $u_2(x,y)=\min(x,y)$. Initial endowment for 1 is (2,4), ...
0
votes
0answers
26 views

What are the values of the Laffer curve for Argentina?

According to this article, (spanish only) Argentine companies pay 106% of taxes for their revenues Supposedly the Laffer curve is different from country to country. Which are the tax rate values at ...
0
votes
1answer
26 views

Slope vs elasticity of demand function - Is it the same thing?

Do the slope of a linear demand function and the elastisicy of demand coincide when we use specific preferences for pricing. As a paradigm, if we consider the case of CARA normal preferences, by ...
1
vote
0answers
50 views

What are the mathematical prerequisites to understand Whinston and Green's “Microeconomic Thoery”?

I've completed my under graduation in economics where I used micro books like Nicholson and Snyder's Microeconomic Theory and Hal Varian's Intermediate Microeconomics. I am comfortable with topics ...
0
votes
1answer
23 views

Economic and Statistical Significance Of Coefficient

I want to know If I am comprehending these terms correctly Summarizing the difference between economic and statistical significance of coefficients (Describing the terms, process of assessing each ...
2
votes
0answers
21 views

Why does the following approximation hold?

In Essential Mathematics for Economic Analysis, on page 426 there is a model on gains from search where profit function is given as: $$\pi (t) = [p^0 -p(t)]x^0 -wt$$ $t$ is time, $p$ price, $x$ ...
2
votes
0answers
47 views

Recursive Models of dynamic linear economics (Hansen / Sargent, 2014) - optimal linear regulator problem / solution of bellman equation p. 34 ff

The optimal linear regulator problem according to Hansen/Sargent, 2014, Recursive models of dynamic linear economies, on page 34 ff. is stated as follows: $-E\sum_{t=0}^{\infty}\beta^t[x_t' R x_t+u_t'...
3
votes
0answers
42 views

Why is my elasticity of substitution wrong?

I am calculating elasticity of substitution for the following production function: $$F(K,L) = A(aK^{-\gamma}+bL^{-\gamma})^{-\mu/\gamma}$$ where $A, a, b, \mu, \gamma$ are constants. $A, a, b, > 0$,...
1
vote
1answer
763 views

How to find the maximum profit in a graph?

We know the maximum profit will occur at the quantity where the gap of total revenue over total cost is largest. But how can we find such gap?

1
2 3 4 5
14