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
263 views

Would a risk averse agent ever accept gambles with negative expected value? [closed]

Consider a risk-averse agent (his utility for money is strictly concave) that maximizes expected utility. Would such agent ever a accept a gamble whose expected value is negative? (e.g. think of state ...
0
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1answer
140 views

Differentiate the utility function.

I've never differentiated utility functions. I'm struggling to understand how the differentiation of this problem results in the answer that it does. Could someone please show me (step by step) how ...
0
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2answers
2k views

Elasticity of demand given a quantity and a price function

I have a price function: $$ \frac{8,100,000}{q^2+8,100} $$ Where $q$ is quantity demanded. How can I find the price elasticity when $q = 30$? I know how to differentiate, but I'm just not sure what ...
0
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1answer
42 views

Show that there exist prices at which agents can engage in mutually beneficial trades.

Consider an exchange economy with $2$ goods and $2m$ identical Households, but in this case each household has utility function $u(x_1,x_2)=x_{1}^2+x_{2}^2$, and endowments $w_1=w_2$. Show that there ...
3
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1answer
805 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 ...
2
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2answers
239 views

Multivariable optimization books

I have some economic data in hand, and I would like to make forecasting out of it (e.g., consumer demand, price elasticity and so on). As far as I understand, these characteristics can be (to some ...
2
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1answer
197 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 ...
2
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1answer
316 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
41 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
179 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
128 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
49 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
25 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 ...
3
votes
1answer
2k 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
247 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 ...
1
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0answers
107 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
vote
1answer
33 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 ...
1
vote
1answer
181 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
135 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 ...
1
vote
1answer
87 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
91 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
508 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
77 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
votes
1answer
84 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
147 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}+ ...
0
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1answer
176 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
540 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
46 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
66 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
votes
1answer
76 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
votes
1answer
31 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
112 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
47 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
74 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
117 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
419 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
541 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 ...
-1
votes
1answer
149 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 ...
2
votes
2answers
60 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
191 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 ...
1
vote
0answers
3k 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
votes
1answer
411 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
237 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
votes
1answer
181 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
100 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
votes
1answer
135 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 ...
9
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1answer
428 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
68 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
168 views

Mistake in 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 ...
1
vote
2answers
62 views

How to derive duration of unemployment?

The average monthly flow out of unemployment pool of $7.0$ million people each month is $3.1$ million. Put another way, the proportion of unemployed leaving unemployment equals $\frac{3.1}{7.0}$ or ...