-2
votes
1answer
34 views
0
votes
1answer
48 views

Minimizing the cost of production by choosing between two options with different resource demands

Suppose that the firm has two possible activities to produce output. Activity $A$ uses $a_1$ units of good $1$ and $a_2$ units of good $2$ to produce $1$ unit of output. Activity $B$ uses $b_1$ units ...
1
vote
0answers
52 views

Application of a general “Weierstrass theorem”

http://books.google.at/books?id=9OSrV73a40gC&pg=PA45&lpg=PA45 gives a general Weierstrass theorem. Are there notable applications of this theorem, say in the calculus of variations? (I could ...
1
vote
0answers
20 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 ...
3
votes
1answer
57 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 ...
-1
votes
1answer
55 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
votes
2answers
116 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 ...
0
votes
1answer
82 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 ...
1
vote
1answer
24 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
votes
1answer
87 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
votes
0answers
58 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 ...
2
votes
1answer
68 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 ...
1
vote
0answers
848 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
86 views

Production function (economy)

A company produces one good using two factors of production factors. If $x$ and $y$ denotes the units of the factors used by the company, the technology function is given by $F(x; y) = xy^2$. In the ...
0
votes
0answers
36 views

Optimizing revenue clicks CPC

I am quite new to optimization procedure and would like to get some hints here: I am work for a small business that offers a service of niche selling items where subribers pay for every item they ...
1
vote
0answers
52 views

$\frac{\partial}{\partial\theta}\phi'\mu+\frac{\alpha\phi'\Sigma\phi}{2}=0$

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
0
votes
1answer
145 views

Mathematical Economics - Utility maximization

I am thankful to any hints: What I have: Simple log-utility form: $u = \log c_1 + \beta \log c_2$ Budget constraints: $c_1 + s \leq w$ $c_2 \leq R\; s$ Problem: For utility maximization: $s = ...
0
votes
2answers
366 views

Endowments & Utility Function to get Demand Function

We have two people, $A$ and $B$, A has $200$ units each of both good $X$ and $Y$ and $B$ has $100$ units each of both good $X$ and $Y$. $A$ has tastes providing a utility function such that $u(X,Y) = ...
0
votes
1answer
47 views

How to build (and maximize) this equation

I'm trying to solve an economics problem but I cannot figure out how to build the equation system, or how to find the maximum in a piecewise function. A simplified version of the function would be ...
0
votes
1answer
130 views

Minimizing total cost function

In today's test (question c) I had to minimize equation $(3)$ and solve for N*. I did it through deriving, setting to $0$ and solve for N (no doubts about that). My question is, in this image it ...
0
votes
1answer
147 views

Economic Analysis / Minimization Problem

I am studying and going through some old exams for a microeconomic analysis class. I am just looking for some clarification regarding one of the answers given. The question is as follows Suppose ...
0
votes
1answer
150 views

Finding competitve equilibrium(consumption rivalry)

Consider two agents (Pascal and Friedman) in a pure exchange economy with two goods and no free disposal. Pascal has a preference relation give by the utility function $$u^P(x_1^P,x_2^P)=a\ln ...
0
votes
1answer
108 views

Market optimization problem

Demand schedule: $Q_d=a_0-a_1P_d$Supply schedule: $Q_s=b_0+b_1P_s$$P_d$ and $P_s$ are prices faced by consumers and producers. $a_0,a_1,b_0,b_1$ are all positive constants, where $a_0>b_0$. The ...
0
votes
2answers
252 views

Portfolio Optimization Problem Without Correlation Info

I received this interesting problem from a friend today: Assume that you are a portfolio manager with $10 million to allocate to hedge funds. The due diligence team has identified the following ...
1
vote
1answer
203 views

Economic optimisation problem

Here is the question: Consider a car-owning consumer with utility function $$u (x) = x_1x_2 + x_3 (x_4)^2 ,$$ where $x_1$ denotes food consumed, $x_2$ denotes alcohol consumed, $x_3$ denotes kms of ...
3
votes
0answers
118 views

Optimal tax rate

Suppose you have two countries A and B, with a tax rate $T_A$ and $T_B$, respectively. The tax is redistributed to all people equally. Hence if you live in A and you make $I$ as income then you will ...
10
votes
1answer
371 views

A (mathematically) sound investment strategy

It is common wisdom in the investment community that a long-term investor saving for his future would do well to invest in high-risk/high-return assets when he is young, slowly switching his portfolio ...