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
13 views

Average cost function and marginal cost function proof

I was wondering if someone could help me prove the following. Let $A(Q)$ be an average cost function and $M(Q)$ the corresponding marginal cost function. Show that if $M(Q)>A(Q)>0$ then $A(Q)$ ...
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0answers
22 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 ...
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0answers
17 views

Optimize profit given complete market information

Assume there are $N$ market participants (on the order of several hundred), and $M$ items (several thousand) being bought and sold on a market. For each participant/item pair, you know how many units ...
1
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1answer
21 views

Arrow's Impossibility Theorem Using Boolean Algebra

I am currently working on a research project which involves using Boolean matrices for the proof of Arrow's Impossibility Theorem and various other lemmas and results related to quasi ordered sets. In ...
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0answers
9 views

Use specific choices of coefficients and find numerical evidence that the prices can oscillate wildly if the condition is not satisfied.

We let $Q_k$ denote the supply of commodity, $D_k$ the demand for the commodity, and $p_k$ the price at $k$-th time. The demand depends on the current price, $D_k = a + b p_k$ and the supply depends ...
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1answer
33 views

Suppose that the sequence of prices{$p_k$} converges to a limiting price $\bar p$. What must $\bar p$ be?

We let $Q_k$ denote the supply of commodity, $D_k$ the demand for the commodity, and $p_k$ the price at $k$-th time. The demand depends on the current price, $D_k = a + b p_k$ and the supply depends ...
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0answers
12 views

Introductory book about economic models with deterministic chaos

I'm looking for introductory textbook about economic models (micro/macro/finance) which incorporate deterministic chaos. Models could be with or without random noise. By introductory I meant master ...
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2answers
20 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
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1answer
35 views

We are interested in price of a commodity, traded at regular intervals. Why it is reasonable to take $a$, $c$, and $d > 0$ and $b < 0$?

We are interested in the price of a commodity which is traded at regular intervals. We let $Q_k$ denote the supply of commodity, $D_k$ the demand for the commodity, and $p_k$ the price at $k$-th time. ...
1
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1answer
42 views

How to differentiate this expression with respect to t

I don't understand how to differentiate $f(tx_1,\cdots, tx_n)$ with respect to t.
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2answers
69 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
43 views

Sequence of learning mathematics from basic algebra to calculus.

What would be a step by step sequence of learning mathematics from basic algebra to basic calculus? I pose this question because I am in the process of self-learning mathematics as a preparation for a ...
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0answers
15 views

Equilibrium level of income question

Question: In the 2012 tax year, Consumption= (85% of income after tax) + (Autonomous Consumption) Taxation rate= 20% Autonomous consumption= 175 million Investment= 485 million Government ...
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0answers
13 views

Managerial economics/game theory

Hi, I would like to ask what is (i) What is the dominant strategy equilibrium above? (ii)Maximum Strategy. For dominant strategy equilibrium, Aero Golf has a dominant strategy but Super Bee does ...
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0answers
21 views

Inverse Supply Function

Efficient small firm with cost function $c(q) = qe^{0.5q}$ $0< q \leq 10$ where $q$ is the number of units produced. Determine the firm's inverse supply function.
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0answers
15 views

How to Build a Foresight System? [migrated]

For a research project, I'm asked to find ways to build an economic foresight system. For example, for the production of cheese. We will have data about the market indicators, like price, demand etc. ...
0
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0answers
18 views

2 competitive or cooperative products?

I found this question in a calculus book and I'm not sure how to go about solving it: What exactly am I supposed to do to answer this? Do I need to find the first and second derivatives of each ...
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0answers
22 views

Spence signalling model question

My thinking: The unconditional expected marginal product = $1p_1+2p_2+3p_3$. I'm finding it hard to understand where the $y^*$ would lie.
1
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2answers
46 views

Cobb Douglas production function problem

My question is related to the Cobb-Douglas production function: $Y= A \cdot L^\alpha \cdot K^\beta$ Assumptions: constant-returns to scale, meaning that when $L$ and $ K $ increase with a factor ...
2
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1answer
34 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I've asked the same question at the Quantitative Finance StackExchange. Consider the following example: "As a risk-averse consumer, you would want to choose a value of x so as to maximize expected ...
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0answers
25 views

Put-Call-Parity of Asian Options

I could need some help with deriving the put-call-parity for asian options. Let $S_t$ be the price of the underlying asset at time $t$ and set $Y_t = \int_0^t S_t dt$. Then the payoff of an asian ...
2
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1answer
28 views

Arbitrage opportunity for call price set on avarage

I have the following problem. Let C(K) be the market price of a Option Call with respect to the strike K. Let $C(100) = \frac{C(110)+C(90)}{2}$, then show that there exists an arbitrage opportunity. ...
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2answers
23 views

Point between left and right limits of a CDF

This is from the Chapter 15 text of Gourieroux and Monfort's Statistics and Econometric Models II: Set Up: Suppose that there are 2 possible parameter values $\theta_0$ and $\theta_1$ from which ...
0
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1answer
26 views

Welfare analysis after unit tax is imposed

image of welfare after tax This is what the lecturer drew in my class. $S_T$ is supply curve after a tax of $t$ dollars per unit is imposed .But I don't understand several things. 1. He said the tax ...
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0answers
9 views

Maximizing Revenue in Relation to Occupancy Cost

I'm working on an expansion strategy for a retail client and I want to develop the ideal size space to occupy. We have several stores worth of data to pull and we know revenue, square feet, occupancy ...
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0answers
40 views

Appendix question about $v_i = \frac{p_ix_i}{\sum_{j=1}^{n}p_jx_j}$

Can someone please explain to me how the authors (web.mit.edu/asuman/www/documents/aggregate-fluctuations.pdf‎) solve for $v_i = \frac{p_ix_i}{\sum_{j=1}^{n}p_jx_j}$? They are skipping a lot of steps ...
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0answers
90 views

mathematical economics (topology)

Let $I$ be a finite set of players and let $X=\{x_1,x_2,\ldots,x_n\}$ be the state space. let $A_i$ be player $i$'s action space and let $A = \prod_{i \in I} A_i$. suppose $s_0$ belonging to $X$ is ...
0
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2answers
48 views

Simple algebra, economics

Using some algebraic manipulation the expression $\displaystyle\frac{P-W_1P_x}{W_2}$ is made into $\displaystyle \frac{1-W_1 \frac{P_x}{P}}{W_2}$. It says it is simply multiplied by $\displaystyle ...
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0answers
22 views

What quantity should the firm produce if it wants to maximize its profit given short run marginal coast and short run total cost function

A bicycle repair shop charges the competitive market price of 10 dollars per bike repair. The firms short run total cost is given by STC(Q)=$\frac{Q^{2}}{2}$ and the associated marginal cost curve is ...
2
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2answers
82 views

Strictly Convex and Strictly Monotonic Preferences

On the assumptions for a well behaved preference, I read recently that a preference must be complete, transitive, continuous, strictly monotonous (if the vectors x≥y and x≠y, then x is strictly ...
-1
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1answer
41 views

Optimization: Finding line connecting non-pareto-optimal allocation in Edgeworth Box to PO allocation

Two people, A and B, with respective utility functions of: $$U_a(X_a,Y_a) = X_a^2 Y_a\\ U_b(X_b,Y_b) = X_b Y_b^2$$ Total $X$ (that is, $X_a+X_b$) is fixed at $36$. Total $Y$ ($Y_a+Y_b$) is fixed ...
2
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1answer
76 views

The implications of Completeness and the Continuity axiom for utility representation

Completenes means that every basket of goods in some set previously defined is comparable with the use of a complete preference. Now, with the additional assumption that the preferences are ...
2
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2answers
71 views

Understanding basic stochastic differential equations

This is from a physics course in economics, the literature provides a bare minimum of mathematical explanations. I am trying to understand how to work with stochastic differential equations given in ...
1
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1answer
40 views

utility and uncertainty of economics

United Petroleum is operating a deep water oil rig in the Gulf of Calexico. Management have been informed that the drilling riser may be susceptible to methane build up and hence at risk of an ...
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2answers
234 views

Existence of a utility function on the reals

Suppose I have $\preceq$, a total order on $\mathbb R^n$. I wish to show that there is a utility function $u:\mathbb R^n\to\mathbb R$ such that $x\preceq y \leftrightarrow u(x)\leq u(y)$. I came up ...
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0answers
30 views

Suppose two goods, $x_1(p, y)$ and $x_2(p, y)$, have equal income elasticity

Suppose two goods, $x_1(p, y)$ and $x_2(p, y)$, have equal income elasticity at $(p^0, y^0)$. Prove that $\partial x_1/\partial p_2 = \partial x_2/\partial p_1 $ at $(p^0, y^0)$. This is a question ...
0
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1answer
49 views

How do I provide an intuitive argument for this economics question?

In Syldavia the economists find that (annual) household consumption $c$ is related to (annual) income $y$ by the formula $c=\alpha +\beta y$, where $\alpha>0$ and $0<\beta<1$. Because of ...
0
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1answer
61 views

Finding the value of $p$

I need some help with this question: Consider an individual who possesses the Bernoulli utility function of $u(x)=\dfrac{x^{1-\gamma }}{1-\gamma }$ where $\gamma>0$, $\gamma \neq 1$. Who maintains ...
2
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1answer
135 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 ...
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0answers
71 views

Computing the certainty equivalent for the lottery of infinite expected value

How can I compute the certainty equivalent for the lottery for someone whose Bernoulli utility function is $u(x)=\frac{x^{1-\gamma }}{1-\gamma }$ where $0< \gamma < 1$? Also, how much would the ...
0
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1answer
39 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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1answer
66 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
31 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 ...
2
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1answer
71 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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0answers
90 views

Robinson Crusoe economy problem

Consider the Robinson-Crusoe one-consumer, one-producer economy. Compute the equilibrium prices, profits and consumption when the production function is $f(L)=\sqrt{L}$, the utility function is ...
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0answers
32 views

Deriving the lagrangian multiplier

Could someone kindly help me with: 1. a step by step method of deriving the lagrangian multiplier 2. what are the uses of the lagrangian multiplier. I'm really new to this and your help will be ...
2
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2answers
73 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
69 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
101 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 ...