Questions tagged [mathematical-economics]

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

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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 ...
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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}}...
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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 ...
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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 ...
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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 ...
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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 ...
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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: $...
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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 $U(x):R^n \longrightarrow R$ ...
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2answers
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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\...
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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 $p_y>0$...
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1answer
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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 consumer’...
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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 $L≥...
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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, $(\tilde{v},\tilde{e})$...
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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, ...
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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, ...
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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 ...
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1answer
69 views

Help with weierstrass’ 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 ...
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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 ...
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0answers
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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 ...
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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 ...
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19 views

Somers’D and Gini coefficient: differences

I would like to know what are the differences between somers’d value and the Gini coefficient. I have the following values for factors: ...
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1answer
54 views

Tadelis ‘trading places’ 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 ...
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3answers
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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)^...
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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. ...
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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 &...
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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 ...
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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? ...
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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 ...
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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) ...
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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
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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 ...
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1answer
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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 ...
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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 ...
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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-...
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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 \...
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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 ...
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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 ...
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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, ...
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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 $Y_t$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...

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