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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26 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
29 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
45 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. ...
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1answer
59 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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3answers
173 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
188 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
54 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
29 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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33 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.
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2answers
143 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 ...
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1answer
68 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
59 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 ...
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1answer
35 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
40 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 ...
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1answer
50 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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11 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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2answers
51 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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2answers
465 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
60 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 ...
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1answer
148 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 ...
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2answers
90 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 ...
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1answer
62 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
271 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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1answer
76 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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1answer
60 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
69 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 ...
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1answer
169 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
158 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 ...
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1answer
55 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 ...
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1answer
289 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 ...
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1answer
33 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 ...
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1answer
223 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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115 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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36 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 ...
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2answers
135 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 ...
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1answer
111 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 ...
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1answer
118 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 ...
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1answer
34 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 ...
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2answers
86 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 ...
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1answer
85 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 ...
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1answer
32 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"
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1answer
19 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 ...
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1answer
427 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.
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0answers
121 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
65 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 ...
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1answer
25 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 ...
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1answer
110 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 ...
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2answers
104 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 ...
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32 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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21 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 ...