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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2answers
124 views

Third and average price auction

Third price auction: the winner is the highst bidder but this time instead of paying the second highst bid, he would pay the third highst bid. -assume there are at least 3 bidders. - Average price ...
1
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1answer
108 views

Conditional and unconditional variance in ARMA processes

How can I compute the conditional and unconditional variance of $x_t$ given its past if $\{x_t\}$ is an ARMA$(p,q)$ process. I'm literally struggling over that. Cheers
1
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1answer
234 views

Show that the least squares estimator of the slope is an unbiased estimator of the `true' slope in the model.

Under the assumptions of the classical simple linear regression model, show that the least squares estimator of the slope is an unbiased estimator of the `true' slope in the model. Anyone have any ...
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0answers
30 views

Properties of this set of functionals (mixed pairings)

(from the 4th page of http://www.math.toronto.edu/mccann/papers/econ.pdf) Let $X$ be a compact Hausdorff space, and let $\omega$ be a Borel probability measure on $X$. A Borel probability measure, ...
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1answer
87 views

Game Theory in relation to economics and sociology [closed]

I know some algebra and calculus, and have been reading about Linear Programming/Game Theory. How are the models in this field, even the infinite calculus models, usable in macro economics. Even ...
0
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1answer
147 views

Von Neumann–Morgenstern independence axiom vs. Savage independence theorm

Von Neumann–Morgenstern independence axiom: Savage independence theorem: What is the difference between the two? I'm think Von Neumann is talking about the prizes (outcomes) and Savage is talking ...
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1answer
29 views

Deriving Stochastic Euler Equation

If a consumer has utility function \begin{equation*} u(c_t) = ac_t - \cfrac{b}{2}c_t^2 \end{equation*} and present value budget constraint \begin{equation*} \sum_{j=0}^\infty E_t[\beta^jc_{t+j}] = ...
0
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1answer
108 views

OLS slope estimate of AR(1) with autocorrelation

I've stumbled upon this question in my econometric textbook and can't work out the right answer. The question: Consider $$Y_t = B_2Y_{t-1} + u_t\\ \\ u_t = pu_{t-1} + \epsilon_t\\ $$ where $ ...
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1answer
34 views

Solving optimisation problem with langrangian method

I have a a question regarding a constrained optimisation problem where there are three constraints. I was wondering if should include lagrangian multipliers for each of the constraints or whether the ...
0
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2answers
20 views

Variable with an exponent variable

I'm actually dealing with an economics problem, but it seems like the math is always what messes me up. Ignoring what the variables mean, I'm trying to understand how to get from step 1 to step 2. $$ ...
0
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1answer
39 views

Price and price elasticity problem in Economics

I cannot figure out this problem, if anyone can just point me in the right direction that would be great. The price is $\$20$ and the price elasticity changes from $-2$ to $-3.$ If $\$20$ was the ...
0
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1answer
8k 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: ...
2
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1answer
181 views

Euler Equation and Marginal Rate of Substitution

I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well ...
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1answer
32 views

Question about plotting indifference curves

So I am doing a last year paper on microeconomics I m asked to find pareto efficiencies , cores and so on within the edgeworth box. So what I wanna know is that whe they give me in this exercise the ...
0
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1answer
87 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 $A(Q)$ ...
3
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3answers
246 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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3answers
321 views

How practically relevant is game theory?

I usually don't care too much about the practical relevance of nice mathematics :-) But this time, as I am looking to find some areas where I can apply maths and possibly collaborate with ...
1
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0answers
23 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 ...
2
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1answer
55 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 ...
0
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1answer
69 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 ...
1
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0answers
34 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 ...
0
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2answers
33 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 ...
1
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1answer
78 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
71 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.
2
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3answers
274 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 ...
0
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1answer
402 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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1answer
79 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 ...
0
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0answers
32 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 ...
0
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0answers
41 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
250 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 ...
3
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1answer
83 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 ...
0
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0answers
106 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
39 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. ...
0
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2answers
52 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
70 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
12 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 ...
0
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2answers
56 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 ...
2
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2answers
1k 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 ...
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1answer
84 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
393 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
101 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 ...
0
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1answer
69 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 ...
8
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2answers
317 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 ...
0
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1answer
81 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 ...
0
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1answer
70 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 ...
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1answer
71 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
202 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
242 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
62 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
589 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 ...