Questions tagged [mathematical-economics]
The application of mathematical methods to represent theories and analyze problems in economics.
573
questions
0
votes
1answer
14 views
How to determine a corner solution? Growth Model
I'm working on a paper called "Fertility clubs and economic growth" of Ahituv and MOav (linked below) and arrived at this point:
The paper shows three optimal conditions respect to ...
0
votes
0answers
54 views
how to calculate Leontief demand functions from first order conditions of a CES function when sigma tends to 0?
This question is NOT about how to approximate a CES function to a leontief function.
Knowing that:
$i= good (\begin{array}{*{20}{c}}
{1}&{or}&{2}
\end{array})$
$j= firm (\begin{array}{*{20}{c}}...
1
vote
4answers
81 views
What are good advanced textbooks to learn mathematics for economist?
I am looking for books or other sources that focus on math that is above bachelor level (i.e. above just simple calculus). I am not looking for a specialized text for some field but just general ...
3
votes
0answers
49 views
Trying to find an optimization method
I'm working on a research about fertility choice and economic growth and I was trying to solve an Ahituv Moav paper where they develop a model of economic growth.
My main problem is when I'm trying to ...
0
votes
0answers
21 views
How to choose the autocorrelation type ? MA(q)^2 or AR(1)
I have heteroskedastic and serrialy correlated (autocorrelated) panel data. I want to test it with both dynamic and static models. For the dynamic test, I use GMM and the results of GMM is parallel to ...
-1
votes
0answers
13 views
Derivation for population growth rate formula? Given by r = 100 ln (P2 /P1)/(t2 -t1) [closed]
(a) Name: Population growth rate
(b) Brief Definition: The average annual rate of change of population size during a
specified period.
(c) Unit of Measurement: Usually expressed as a percentage.
The ...
1
vote
1answer
57 views
Interpretation of $x c '(x)$
Consider a cost function that is continuous, differentiable and (possibly) convex: $c(x):\mathbb{R}^+\to \mathbb{R}$. I was wondering if there is a "common" way to interpret the expression:
$...
0
votes
1answer
21 views
Expenditure function. Prove that this set is bounded
I need to prove that the following set is bounded in order to derive the expenditure function:
$e(p,v)=min_x px$
ST
$\{x \in R^n_+$ such that $U(x)\geq v\}$.
Knowing that $U(x):R^n \longrightarrow R$ ...
2
votes
2answers
61 views
Prove that budget constraint is Lower Hemi Continuos (LHC)
I need to prove that the following constraint is LHC.
$B=\{x \in R^n : px\leqslant pw)$
But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\...
-2
votes
0answers
36 views
Show that none of these critical points identifies a solution of the profit- maximization problem. Can you explain why this is the case?
Question: a firm produces a single output $y$ using three inputs $x_1,x_2,x_3$ in non-negative quantities through the relationship:
$y=g(x_1,x_2,x_3)=x_1(x_2+x_3)$
The unit price of $y$ is $p_y>0$...
2
votes
1answer
55 views
Can the weierstrass and the Kuhn-Tucker theorems be used to obtain and characterize a solution? Why or why not?
Question: An agent who consumes three commodities has a utility function given by:
$u(x_1,x_2,x_3)=x^{1/3}_1+\min\{ x_2,x_3\}$
Given an income $I$, and prices of $p_1,p_2,p_3$. Describe the consumerā...
3
votes
2answers
44 views
Convenient S-shaped production function (i.e. with IRS and DRS) to derive a discontinuous demand for labor
Let say that a firm produces a commodity using only one input (i.e. Labor if we suppose to be in the very short run). Then we have a general production function of the following form $y=f(L)$, for $Lā„...
1
vote
0answers
42 views
Private signals [closed]
Following the literature of information asymmetry (see in Kyle among others), we have seen that many papers introduce a private signal, that is
$$S=\tilde{v}+\tilde{e}$$
where, $(\tilde{v},\tilde{e})$...
2
votes
1answer
194 views
Why do we need the specific utility assumption?
In many microeconomic models, we read the assumption that agents have CARA normal utility preferences. We need the assumption of the utility to do pricing, but should someone do differently?
Namely, ...
0
votes
0answers
27 views
Auction Makrets and delearship markets
The largest difference is that the NYSE is an auction market and the Nasdaq is a dealer market. In the former, the highest bid for a stock is matched with the lowest asking price. In the latter, ...
3
votes
1answer
60 views
Certainty Equivalent
The certainty equivalent is a guaranteed return that someone would accept now, rather than taking a chance on a higher, but uncertain, return in the future. Otherwise, some definitions say that the ...
1
vote
1answer
69 views
Help with weierstrassā theorem
Question: Use the Weierstrass Theorem to show that a solution exists to the expenditure minimization problem of subsection 2.3.2, as long as the utility function II is continuous on $\mathbb{R}$ and ...
3
votes
1answer
32 views
Neutral technical progress
Recently I learnt that Cobb-Douglas production function has elasticity of substitution equal to 1, therefore it has neutral technical progress. Then Leontief production function has zero elasticity of ...
1
vote
0answers
16 views
Lerner Index Interpretation?
How do you interpret the Lerner Index?
I ask because at Uni. we have been told that, for monopoly, when the producer max. his profit, he sets the price such as the demand is elastic and the lerner ...
2
votes
1answer
38 views
What is the difference between the demand schedule and the demand curve?
What is the difference between the demand schedule and the demand curve that a monopolist or monopsonist has? Could someone provide details for both cases or even some paradigm or a graph. I can not ...
1
vote
0answers
19 views
SomersāD and Gini coefficient: differences
I would like to know what are the differences between somersād value and the Gini coefficient.
I have the following values for factors:
...
1
vote
1answer
54 views
Tadelis ātrading placesā Bayesian game
My question concerns the following problem: two players, $1$ and $2$, each owns a house. Each player $i$ values his own house at $v_{i}$. The value of player $i$'s house to the other player, i.e. to ...
11
votes
3answers
904 views
What is the point of all the models in an economics degree?
I am a student of Economics doing my masters degree and I have to say I am a bit tired of all the models.
On the one side, there is these models where I can see how they are derived, which always ...
0
votes
0answers
34 views
Characteristics of market liquidity
The characteristics of market liquidity, accoridng to Kyle, are tightness of the market, depth of the marekt and resiliency of prices. By referring to tightness, it descriebes the cost of turning ...
2
votes
2answers
41 views
Why should the cost of home ownership and home renting be equal in the long run?
According to the person in this video (at about 10:10) from the economist, the evidence shows that long run cost of owning and renting homes are approximately same.
The video itself tries to explain ...
2
votes
0answers
18 views
How are productions called that solve the pooling problem
A well known mathematical optimization problem is called the pooling problem (see here pooling problem)
It has many application for example in oil production, food, chemical processes. Basically you ...
0
votes
0answers
31 views
Empirical Bayes Estimation
I would be greatful if You can give some advise regarding the following problems:
As I reviewed some empirical papers, I learnt that most of them using relatively small number of observations for ...
1
vote
2answers
55 views
Compute yield to maturity for a bond with coupons when price is different from face value
Given the formula $P = \sum_{t=1}^n \frac{CF_t}{(1+i)^t} $
we can apply it to the case of a bond with constant coupons so that :
$\displaystyle P =\sum_{t=1}^n \frac{C}{(1+i)^t} + \frac{FV}{(1+i)^...
0
votes
0answers
17 views
Replicating a Fertility Choice Model
I'm working on the Ahtiuv&Moav work of fertility choice and economic growth.
When I want to maximice the main problem I can not do it because I dont know which mathematical tool I should use.
...
0
votes
0answers
14 views
Returns to Scale off a figure
This is the table given for levels of output for different levels of inputs.
\begin{pmatrix}
Q & K & L\\
100 & 3 & 6\\
200 & 5 & 10\\
300 & 7.5 & 15 \\
400 & 10 &...
0
votes
0answers
14 views
Elasticity of substitution of a general production function with labor-augmenting technological progress
I am following and trying to fully understand a famous and interesting work of Bentolila and Saint-paul (2003). They try to explain movements of the factor's share in terms of a relationship between ...
0
votes
1answer
29 views
converting sum of consumption basket to integral
In our lecture, first we had expenditure of consumption basket as $\sum_{i=1}^{n} p_{i}c_{i} $ but later my professor converted it to $\int_{0}^{1}p_{i}c_{i}di$. I want to understand how she did this? ...
0
votes
0answers
17 views
How to calculate effects of inflation over a period of time
I am interested in weather there is a standard way of calculating and predicting the distribution of the decreased value over time as caused by inflation (something like money friction)? For example ...
0
votes
2answers
53 views
What are the concepts in Linear Algebra that model the idea of Identification Strategy in Econometrics?
I just would like to know what concepts one should know before talking about identification strategies in econometrics. I see people studying such concepts but I'm not sure they realize (or even know) ...
2
votes
1answer
87 views
Derivation of the elasticity of substitution of a general production function with labor-augmenting technological progress
I am following and trying to fully understand a famous and interesting work of Bentolila and Saint-paul (2003). They try to explain movements of the factor's share in terms of a relationship between ...
0
votes
2answers
38 views
How do I confirm that the constraint set wL + rK < Q is convex
Suppose a firm produces Q units using labour (L) for which the wage, w>0 and the price of capital (K) is r>0. It cannot employ negative amounts of its factors: L $\geq 0$, K $\geq 0$.
The firm's ...
4
votes
1answer
39 views
What is the difference between a perfect foresight equilibrium and a rational expections equilibrium?
What is the difference between a perfect foresight equilibrium and a rational expections equilibrium?
Why is it the same in case of a non-stochastic model?
Can there be a perfect foresight ...
3
votes
0answers
31 views
Estimating probability of Central Bank's interest rate changes
Recently, I came across this article, which offers a simple model for estimating the probabilities of interest rate cut/hike from a central bank. This is done by using market data, especially normal ...
0
votes
1answer
94 views
Quasi-concavity of profit function
I'm doing a simple exercise from my textbook: suppose the revenue function is $R(p)=p^{1-\epsilon}$ with $\epsilon > 0$. Suppose the cost function is convex. Show that the profit function is quasi-...
1
vote
0answers
20 views
Existence of Bayes Nash equilibria in behavioural strategies
Follow up from this question: Perturbing distributional strategies on a measure zero set
In the context of a Bayesian game, $\Gamma = \left< (\Theta_i,\mu_i)_{i \in N}, (A_i)_{i \in N}, (u_i)_{i \...
3
votes
1answer
40 views
Concavity of Cobb-Douglass Utility Function on Non-Open set
My textbook argues that the Cobb-Douglass utility function $u=(x1)^a(x2)^b$ with $a,b>0$ and $a+b<1$ is concave on $R2+$ by computing the Hessian and showing it to be negative semidefinite for ...
2
votes
2answers
64 views
Clarification on amortization of constant payments
I have found this formula on wikipedia :
$$P=C_k(1+i)^ {(n-k+1)}$$
which describe the constant payment that has to be paid every year ($C_k$ is the part of the initial loan that is extinguished with ...
0
votes
0answers
20 views
Taking the partial derivative of the demand function
Define the demand function which maximizes x -> U(x) as:
$\sum_{i=1}^n$$p_i$$\zeta_i$(p, I) = I
According to my textbook if I differentiate this with respect to $p_j$ I will obtain,
$\zeta_j$(p, ...
0
votes
0answers
21 views
Ramsey Model Market Clearing Condition
I have a problem understanding the market clearing condition for aggregated equilibrium in the Ramsey model.
Market clearing implies that all resources are used up, hence: $Y_t=C_t+I_t$ , where $Y_t$ ...
1
vote
0answers
19 views
Time-dependent market-clearing equilibrium price
I'm working my way through Chiang and Wainwright's Fundamental Methods of Mathematical Economics (4th ed) while holed up at home. On p. 532, in exercise 16.4 2. (b), the authors ask you to find the ...
0
votes
1answer
42 views
Continuity of preferences
Let $\succsim$ be a transitive and reflexive relation on a metric space $X$ with closed upper and lower contour sets. If $\succsim$ is not complete, does it hold that: for all converging sequences ...
0
votes
0answers
30 views
Relationship between strictly convex preference and convex preference
Let X be a convex subset of linear topological space and let binary relation >=
be a complete preordering.
prove: If preference relation is strictly convex and continuous, then it is convex.
Since ...
0
votes
0answers
28 views
Is optimizing revenue and expense objectives simultaneously better than optimizing profit as composite objective?
In the profit maximization problem, I am curious if co-optimizing revenue and expense objectives simultaneously are better than optimizing profit (revenue - expense) as a single composite objective? I ...
0
votes
0answers
37 views
How to calculate the maximum willingness to pay? (Reservation price)
I have to solve the following exercise. I cant figure out what I have to do know. I hope i can get some help.
Suppose you have the following utility: $U (x_1, x_2) = 4x_1 ^ .5+2x_2 ^ .5$ and you have ...
0
votes
1answer
41 views
How to determine price per unit and quantity sold of product from financial statement
Situation
I hope I'm asking in the right place. I'm writing a paper on the application of quadratic functions in economics and intend to use the Total Revenue function as well as the Profit function ...
