For questions regarding the mathematical analysis of economic models and problems. This includes questions about the formulation or solution of models from microeconomics or macroeconomics.

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1answer
133 views

Impatience and interest rate

I'm having difficulties solving the following problem in economics. I come from a mathematical background, and it's hard for me to get some of the terms: Consider a two-period economy with a ...
-2
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0answers
35 views

Financial Economics. Uncertainty and Spot Market [closed]

Uncertainty and spot financial markets Consider an exchange economy with two periods (t = 0, 1), L goods and S states in the second period. An endowment is ωi ∈ R L(S+1) and preferences are ...
8
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1answer
269 views

Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest ...
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1answer
34 views

Lagranges multiplier to minimize function of two variables with two constraints

I have a Cobb Douglas type production function with $K$ and $L$ as inputs; $\alpha$ and $1-\alpha$ as output elasticities and $C$ as efficiency parameter. Now I have to minimize cost $=wL+rK$ w.r.t ...
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1answer
158 views

How to derive demand function from a utility function without any knowledge of Lagrange Multipliers?

How do I derive the demand function for a utility function of, say, $U(x,y)=\sqrt{11x+11y}$ for goods X and Y in terms of $P_x$, $P_y$, and income $I$, with basic mathematics (basic calculus, but no ...
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1answer
27 views

Utility function, plotting indifference curves

I know how to plot indifference curves; simply take the utility function and plot some level curves in $2D$. But how to plot a specific indifference curve, so all bundles on it are indifferent to a ...
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2answers
49 views

Cost per item. Diminishing marginal discount, if you will. (Bigger discount for first few items) Optimal number of units to buy?

The graph above shows price per unit. Say they are cupcakes. When you buy a higher quantity, you get a lower price per unit. Say it levels off like this graph. Obviously, buying 2 nets a nice ...
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5answers
166 views

A mathematical approach to economics

Are there books or papers where economics is formalized and studied very rigorously? I am very interested in this topic. I would preferably like free online books and/or papers, but that is not ...
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0answers
13 views

Finding the competitive equilibrium in an economy with two consumers and two commodities

I am unable to solve the following problem in general equilibrium. Consider an economy with two consumers and two commodities X and Y. $X_i$ and $Y_i$ are the amounts of commodities present with ...
0
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1answer
24 views

Utility function and preferences?

This might be more of an economical question, but perhaps some of you might've come across it before as math is involved; A person P prefers bundle (x1,x2) over (y1,y2) if (x1*x2) > (y1*y2). What is ...
0
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1answer
29 views

Utility Max Problem

I have a utility function $U(x,y)=\frac{xy}{x+y}$ and a budget of $200=2x+2y, P_x=P_y=2$. But for the first 50 units of product 1 sell for 2 dollars but for "$x>50$" the price of product 1 ...
2
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2answers
168 views

The 10.4 Problem on Benassy's *Macroeconomic Theory*

This a repost. In my first try at the problem here I was not very clear with my question and I was also troubled by my lack of knowledge of MathJax. And I probably lost the attention of you guys while ...
3
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1answer
166 views

Curvature and the Arrow Pratt Absolute Risk Coefficient

So I'm in my first year of grad school, and I'm taking a decision analysis course. One of the topics we're covering is risk aversion, and with that comes discussion of the Arrow Pratt Absolute Risk ...
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1answer
1k views

Microeconomics: Calculating Tax Revenue and Tax incidence

Australian Government has imposed a tax on Beer. Assume that the tax on Beer is $20 per unit (a unit is a carton of drinks) Assume the demand and supply functions for cartons of Beers per week are: ...
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0answers
54 views

Follow-up on solution to Markov process equation

I asked a question here about solving a system related to an absorbing Markov chain. I now have a variation where there are $m$ types (of student, job seeker, etc) each of which applies to ...
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0answers
12 views

Infinite Horizon Representative Agent

Consider an infinite horizon representative agent with utility function u(c(t)), where u'>0 and u"<0. Suppose that c(t), w(t), and x(t) be the consumer’s consumption, wage, and assets at time t, ...
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2answers
41 views

income distribution from N, min,max and mediansalary, and total compensation

My goal is to obtain a reasonable approximation of the Gini index of a company (UBS). I need to obtain an estimate of the salaries distribution from publicly available data: Nuber of employees=60205 ...
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2answers
320 views

What can I deduce from the graph of marginal value?

Homework problem: We have a graph of value: x coordinate number of widgets made. y coordinate value in $. For the first 5 widgets the value greatly increases to $100 and then after 5 ...
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2answers
90 views

Revenue cost profit [closed]

A company that makes and sell memory chips establishes the followings : Revenue function, $R(x) = x (75 – 3x)$ Cost function, $C(x) = 125 + 16x$ Where $x$ is in millions of chips, and $R(x)$ and ...
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0answers
35 views

Economics, Statistics

Now suppose I am trying to forecast using historical data and using random walk method, In the formula $ y_t = y_{t-1} + u_t $, how can I find the $u_t$ form the model ?
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0answers
16 views

Profit Maximization without an explicit functional form for f(x1, x2) - Need to infer the signs of derivatives

Consider the following 2 input, 1 output profit maximization problem: $$ \max_{y,x1,x2} \{py-w_1x_1-w_2x_2 : y=f(x_1,x_2)\} $$ where f is the producers production function, w_i>0 is the price of ...
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0answers
19 views

Project Management - PERT completion time question

The following represents a project with known activity times. All times are in weeks. Activity--Predecessor--Time A ……………………………..….4 B………………………………....3 C………………….A..…………..2 D………………….B…………...7 ...
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3answers
57 views

Capitalization of interest

I've got quiet a strange problem but a simple one I guess. So I have a starting sum of 10 and I would like to know how many years need to pass to achieve 30000 with 32% interest applied every 2 years. ...
0
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2answers
57 views

Simple differentiation / economics marginal cost question

This seems like a very simple question, so I'm sure I'm doing something stupid here, but I'm not quite getting my head around the following question: I have a total cost function: $C = 5x^2 +15x + ...
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0answers
19 views

How to characterize $F(x \mid Y = y)$ satisfies $\exists ! G(\cdot)( G(x) = \int F( x \mid Y = y) dG(y))$?

$F(x \mid Y = y)$ is the conditional distibution function $P(X \leq x \mid Y =y)$. $G(x)$,$G(y)$ represent $P(X \leq x)$ and $P(Y \leq y)$. Is there a charaterization of $F(x \mid Y = y)$ such that ...
0
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1answer
44 views

Calculating the chance of something happening over and over again

I'm trying to calculate the probability, and potential cost on society, of people returning to homelessness after going through the system one, two, or several more times. Let's say that someone who ...
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1answer
61 views

Economic Applications of Game Theory

I'm currently looking at this course in economic game theory. However, when attempting this example: In this question you are asked to price a simplified version of mortgage-backed securities. ...
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1answer
2k views

Computing the break-even point

Problem The Lake Shore Inn is trying to determine its break-even point. The inn has 50 rooms that are rented at $60 per night. Operating costs are as follows, in dollars ...
0
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1answer
26 views

Break Even Point

Suppose that x thousand units of a product will be sold when the price is p(x) = 50 - 1.25x dollars per unit and the cost of producing x thousand units is C(x) = 20x + 100 thousand dollars. a) What ...
0
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0answers
184 views

Understanding a Proof in Probability Theory

My question is pretty simple: I have two equations which are supposedly true (from a published paper) but I have no idea how to arrive at the solution myself. So it would be great if someone could a) ...
0
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0answers
45 views

How they're doing this calculation?

Consider this paper by Laura Alfaro, Sebnem Kalemli-Ozcan, and Vadym Volosovych: http://econ.sciences-po.fr/sites/default/files/file/pmartin/secondyear/restat.pdf In page 355, (actually page 9 in ...
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1answer
47 views

How to find the short run and long run cost functions, given the production function?

The production function of car is given by $f(x_1,x_2,x_3) = \sqrt{x_1}+\sqrt{x_2}+\sqrt{x_3}$ (assume competitive input and output markets). Find the short run cost function (let input 3 ...
2
votes
3answers
150 views

Precise definition of a “game of incomplete information” (Game Theory)

Question: In game theory, what is the precise definition of a "game of incomplete information"? What I've found so far: In the standard first year graduate economics textbook on microeconomics ...
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1answer
30 views

Variance of OLS estimator

Iam trying to understand how the variance of the OLS estimator is calculated. here is what i have: $E[\hat{ \beta} \mid X] = \beta$ and $V(\hat{\beta} \mid X) = \sigma^2(X^TX)^{-1}$ where ...
0
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1answer
51 views

Minimizing the cost of production by choosing between two options with different resource demands

Suppose that the firm has two possible activities to produce output. Activity $A$ uses $a_1$ units of good $1$ and $a_2$ units of good $2$ to produce $1$ unit of output. Activity $B$ uses $b_1$ units ...
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0answers
38 views

Cost functions in economics

A firm has two plants. One plant produces out- put according to the production function $x_1^ax_2^{1-a}$ . The other plant has a production function $x_1^bx_2^{1-b}$ . What is the cost function for ...
2
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1answer
50 views

Need help explaining how the elasticity was derived [closed]

We had a lecture on calculating elasticity in microeconomics and I need help understanding how the answer was derived. I didn't quite get how we came up with the answer. My classmate said to just ...
0
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2answers
40 views

Problem understanding an implicit differentiation

Here is a general budget constraint: $p{_1}x{_1}+p_{2}x_{2}=M\Leftrightarrow \frac{p_1}{p_2}x_1+x_2=\frac{M}{p_2}\Leftrightarrow {p_{1}}'x_1+x_2=M{}'$. The main idea is that since prices are given, ...
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1answer
42 views

In Courty and Li (2000) “Sequential Screening”, what justifies the last equation in Lemma 3.2?

Regarding the article "Sequential Screening," in Review of Economic Studies, 2000 by Courty and Li: In Lemma 3.2, the last equality states that ...
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0answers
15 views

variance-covariance matrix of 2sls in homoskedasticity and heteroskedasticity

How the variance-covariance matrix of two stage least square estimate in homoskedasticity or heteroskedasticity? The answer in homoskedasticity is $\sigma^2(E[xz'](E[zz'])^{-1}E[zx'])^{-1}$ and in ...
0
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1answer
75 views

Monotonicity of consumer preferences

I'm learning about monotonicity and I can't seem to figure out what larger $x$ is and what is smaller $x$. If I strictly prefer larger x when until $x<10$, what does that mean? Context The ...
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2answers
26 views

Rounding a real number w.r.t. a given amount of steps

Let $x$ be a real number, $x \in [0,1]$. Suppose a system can only provide a noisy signal about the value of $x$, given the granularity allowed by the system, $N \in \mathbb{N}^*$. I'm looking for an ...
0
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1answer
26 views

Microeconomics : Total revenue for unit elasticity

I recently read in my microeconomics book that when elasticity = 1, total revenue remains the same. However, I am unable to follow this. I have two questions on this concept: Question#1- ...
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0answers
52 views

Application of a general “Weierstrass theorem”

http://books.google.at/books?id=9OSrV73a40gC&pg=PA45&lpg=PA45 gives a general Weierstrass theorem. Are there notable applications of this theorem, say in the calculus of variations? (I could ...
4
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0answers
52 views

How to solve a non-homogeneous second-order linear difference equation with both a forward and a backward difference?

Quite a long title for this: I'm looking for the general solution of the following difference equation: $$ax_{t+1} -bx_t + x_{t-1} = c + u_t$$ where $a,b,c$ are real constants and $u_t$ is a bounded ...
13
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2answers
503 views

Pure mathematics in our society

Is there some book or essay which deals with the sociological and economical justification of doing and funding pure mathematics? I'm looking for a modern version of Hardy's A Mathematician's Apology, ...
0
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1answer
53 views

Profit Model from Ellison Glaeser 1997

Can someone help me understand the following profit maximization problem (from Ellison Glaeser 1997)? Manufacturing plants choose where to locate each of $N$ plants in one of $M$ locations. The ...
3
votes
1answer
122 views

The Historical Importance of Keynes' A Treatise on Probability

A visiting speaker in Economics recently happened to mention that John Maynard Keynes' A Treatise on Probability revolutionized probability theory. I have not heard any such claim before and it struck ...
4
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1answer
52 views

Expected revenue obtained by the Vickery auction with reserve price $1/2$

I would like to prove that the expected revenue of the Vickery auction with reserve price $1/2$ is $5/12$ when there are one item and two bidders the distribution of valuations are uniformly between ...