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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2
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1answer
70 views

Brouwer's fixed point theorem

Theorem: If $f:D^n\rightarrow D^n$ is continuous then there is $x \in D^n$ such that $f(x)=x$. To prove the theorem we assume that $f$ is cts but has no fixed point, that is $f(x)\neq x$ for all ...
3
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1answer
103 views

No theft model of corruption

Consider the model of corruption explored by Shleifer and Vishni’s where there is one government-produced good $X$. There is a demand for that good described by the inverse demand equation $$Q_d = 10 ...
0
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1answer
28 views

Short and long positions of call options

I am on part c), and I want to know: Since I am the seller of this call option, I sold it for 0.44, and the option is worth 1 dollar at expiration. Assuming the buyer wants to make profit he will ...
1
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2answers
70 views

Why should a GE fail to exist in non-convex sets?

In an exchange economy with $2$ goods and $m$ identical Households where each household has utility function $u(x_1, x_2)$, together with positive endowments. If preferences are not convex, then why a ...
0
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1answer
50 views

How do I optimize a function subject to a two-part constraint?

I would like to maximize the following function $$\max\; U= log(xT_o + (1-x)T_s) + log(Y)$$ by choosing levels of $T_o$, $T_s$, and $Y$, and where $x\in[0:1]$ subject to $$N = \binom{P_sT_s+Y ...
0
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1answer
27 views

Forward contracts

How do I do this one? I'm assuming it's not as simple as "the initial value is just $50 since thats what the stock sells at"
0
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1answer
15 views

Difference Between Generalized and Alternative Compounded Interest Equations

I am currently studying a chapter called "An Economic Interpretation of e" in my Economics class and we are finding amounts of compounded interest. I am not actually looking for help on the problems ...
1
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1answer
85 views

Why can we assume that the expected value of the error term is zero? [closed]

Why can we assume that the expected value of the error term in a linear regression model is zero? This is with regard to a simple linear regression.
2
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0answers
81 views

Engineering Economics Cash Flow Diagram

I have the following question and solution below. What I don't understand is why is the 100,000 seen as savings/revenue when clearly it is coming out of pocket? Additionally, the monthly loan payment ...
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0answers
38 views

Using data points and a best-fit to find a function for quantity with respect to price

So I'm taking an entrepreneurship class, and we're doing a simulation where we run a donut shop. My math is pretty strong (integral and differential calculus level), so I'm trying to use my math ...
1
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1answer
22 views

Constrained optimization when lending money between two periods

The question is: A consumer has utility function $u= x_{11}x_{12}+\beta x_{21}x_{22}$ where $x_{ti}$ is amount of good $i$ consumed in period $t$, $\beta$ is a positive parameter. We are asked to ...
0
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1answer
84 views

“Multivariate” Markov Chains

I am interested in estimating regime-switching VAR models to a regime setup I don't know the name of. I am hoping that someone can help me out with some references, or if there exists a name for it ...
1
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2answers
88 views

Which Nash equilibrium is this?

There are two stores, A and B with the following demand functions, The open circles indicate an open interval, the filled circle is a closed interval. Both firms wants to maximize profit, and ...
0
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0answers
26 views

Uncertainty and Strategy problem

Let $\delta _i$ denote the probability distribution (or lottery) that gives probability $1$ to obtaining the $i$th prize. In other words, $\delta _i$ is the $n$-element vector that has a $1$ in the ...
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0answers
20 views

Accounting for social costs in a CBA

I am writing a report regarding the cost-benefit analysis of installing a wind turbine. The report takes into account market (i.e.cost of purchasing the turbine) and non-market costs and benefits ...
1
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1answer
53 views

Implications of axioms of expected utility theory

Axioms for Expected Utility: Let $\succ $ be a binary relation on $X$. A1. $\succ $ is asymmetric and negatively transitive. A2. Independence of Irrelevant Alternatives: If $p,q,r \in X$ and if ...
0
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2answers
45 views

differentiating a cost function using chain rule

How to differentiate the function (cost function) $$C(x)=V\left(\frac{px-W}{q}\right)$$ where $W,p,q$ are constants,and $W$ representing the consumer's budget or wealth. $V$ is a function of $x$. ...
1
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2answers
123 views

Consumer optimization problem

A customer has to decide how many of products $x$ and $y$ to buy. The price of $x$ is $2x^{1/2}$ and the price of $y$ is $4y^{1/2}$. The cost of $x$ is 10 dollars and the cost of $y$ is 5 dollars. ...
1
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1answer
48 views

Math / Accounting problem

I have been stuck for over an hour with the following problem. In my textbook the following is written: "Suppose, for example, that Polany Manufacturing Company enters into a long-term lease July 1 ...
2
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1answer
46 views

Measuring how “connected” nodes are in a network

I am an undergraduate studying economics and mathematics. I've never studied graph theory formally (only briefly in my spare time) and as such I don't have formal terms for what I'm clumsily trying to ...
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0answers
65 views

Solving the General Equilibrium with $4$ equations and $4$ unknowns

I have to solve four equations to solve the equlilibrium prices for the two countries: $\frac{2p_1}{w_1} + \frac{p_1}{w_2}= \frac{48w_1^2 + 4p_1^2+p_2^2}{8p_1w_1}+ ...
1
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1answer
78 views

Maximize $ax + by + c$

Working on a problem of comparative advantage of the economist David Ricardo, I've gone into solving a more general case of that study in which I stumbled over this question : how do we maximize the ...
0
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2answers
145 views

why is this economics parabola sideways? switch x and y axis

Why is this "parabola" sideways? Normally, f(x)=y, would be that x is graphed horizontally, and you would write that "wage rate is a function of hours worked", which is how I would normally think ...
1
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1answer
38 views

Need recommendations for a function with certain properties

Not sure if this might be a strange way of posing a question, but anyway: I need a function $f(v,p,a)$ with the following properties: it is defined for $v \in [-\infty,\infty]$ it is defined for $p ...
0
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2answers
39 views

Confusion regarding an alleged hyperbola

While studying a chapter called price elasticity of demand in my economics course, I have been presented with something called a unit elasticity curve (some sort of a hyperbola), which has supposed ...
0
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1answer
56 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income ...
0
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0answers
53 views

How are relative maximum problems solved?

I found this problem in an economics mathematics book self test and I really do not know how a person goes about solving a problem like this: I think there is differentiation involved but I'm just ...
0
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1answer
15 views

Understanding a component of an equation of finite game repetition

I have the following equation: T = total times the game is repeated t = current period delta = discount rate u_i(a_i^t...) = the state payoff to player i I'm attempting to understand the ...
-1
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1answer
50 views

econometric transformation of variables

I would like to ask a question, which has been already asked, however I dind´t fully understand the answer and nobody replied to my edit question..maybe you can give me a arithmetic example for one ...
0
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1answer
37 views

econometric data

I have a quit straight forward question: I have a variable which is coal rents measured in 2009 US Dollar. I would like to set this variable in relation (ratio) to another variable which is PPP ...
2
votes
1answer
65 views

How are these maximization problems same?

This question is from Nicholson-Snyder's "Microeconomic Theory",page 200.(e-book here.) Compare$$V^*(p_1,\dots,p_n,I_1,\dots,I_m)= \max_{x_1,…,x_n} \left[U(x_1,…,x_n)\text{ such that}\sum_{i\in ...
0
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1answer
73 views

Leontief Models: Characterizing efficient net outputs

Given a Leontief model with $n \times n$ input-output matrix $B$, whose diagonal elements are positive and off-diagonal elements are non-positive. There is a single unit of labor available to this ...
0
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1answer
59 views

How CES function becomes MINIMUM function?

Let the CES utility function be $$U(x,y)=\frac{x^\delta}{\delta}+\frac{y^\delta}{\delta},$$where $\delta\leq1,\delta\neq0.$ For $\delta=-\infty$, the given function is equivalent to ...
1
vote
1answer
59 views

What is my unit of observation for this time series data set?

My professor gave us a data set to run a regression and I have a data set which lists years from 1959-2007, gross private investments (in billions of dollars), and gross private savings (in billions ...
0
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1answer
184 views

profit function to find diminishing returns

For the profit function $p=3s^3 +45s^2 −125s+250$ , find the amount spent on advertising (in thousands of dollars) that is the point of diminishing returns?
0
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3answers
53 views

For the profit function, find the amount spent on advertising that maximizes the profit

For the profit function $p=3s^3+45s^2-125s+250$, find the amount spent on advertising (in thousands of dollars) that maximizes the profit.? Please help :(
-1
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1answer
91 views

For a price and cost function, at what rate do the weekly sales change per week?

For a price function of $p=4000-25x$ and a cost function of $C=1800x+4500$, if the profit is increasing at a rate of $3000$ per week and the weekly sales are $x=32$ units, at what rate do the weekly ...
0
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0answers
89 views

Question involving theory of the firm

Any ideas on how to help me get started on this question? A firm's technology possesses all the usual properties. It produces output using three inputs, with conditional input demands ...
-2
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1answer
72 views

utility and demand function

A consumer has the utility function $$U(X,Y)=3XY$$ The marginal rate of substitution is $MRS=Y/X$. 1-find the demand function for good $X$. 2-Calculate the income elasticity of demand for good ...
2
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2answers
40 views

Differential equation non linear first order

Can you find the solution of that equation please? I don't know how to solve it. I use it to solve a dynamic system in macroeconomics for my homework. $$\frac{dy}{dt} = y^3 + 1$$
0
votes
1answer
104 views

Nash Equilibrium in Cournot Duopoly

If you have a demand function Q1= 20 + 3/4 p2 - p1 and Q2= 20 + 3/4 p1 - p2, how does one go about solving for the Nash equilibrium if you know there are no costs? I've tried solving for Q and then ...
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0answers
622 views

Profit Maximization Question of a Leontief (Perfect Complements) Production Function?

This is a question from my intermediate micro economics text book. Any help is very appreciated! Given Info: Company ST (a company which offers custom travel-planning services) is a ...
0
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1answer
148 views

Question related to the General equilibrium in exchange economies

I need some help in solving this question: Consider the following two-person, two-good economy. Persons $A$ and $B$ each consume two goods xylophones $(x)$ and yams $(y)$. Person $A$ enters the world ...
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1answer
117 views

Does risk aversion cause diminishing marginal utility, or vice versa?

Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
0
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1answer
36 views

distinguish homogenous and homothetic

I am not sure how to distinguish whether a function is homothetic. For example, Q1. $$ U(x,y) = a\log(x) + b\log(y), $$ Q2. $$ U(x,y) = \exp[(x^a+by^a)^3 +r] $$ I can understand that these two ...
0
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1answer
32 views

Math behind Keynesian Expenditure Multiplier

Take a look at this page: http://wiki.ubc.ca/Keynesian_Multiplier Why can you find out the sum of the geometric series just by dividing the mps by 1?
2
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1answer
77 views

Generalized Mechanism Design, Stanley Reiter diagram and Vickrey Auction

I am trying to learn this new topic, Mechanism Design and stumbled upon the "Stanley Reiter" diagram (see the top-right side on the page). I have also learned that the Second Price Sealed Bid ...
5
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1answer
206 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 ...
0
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1answer
48 views

ordinary least square regression

i have a question and i'm confused with the concepts. Pls aid Consider the estimation of the population mean in the model: $Y_i = \beta + U_i$ for $i = 1,2,3$. Assume that $E(U_1) = E(U_2) = E(U_3) = ...
3
votes
1answer
104 views

Mistake wikipedia article on St petersburg paradox?

I suspect that there is a mistake in the wikipedia article on the St petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...