# Questions tagged [optimization]

Mathematical techniques for the selection of a best element (with respect to some criteria) from the set of available alternatives.

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### Budget Constraint in Utility Maximisation Problem with Lagrange Multipliers

Lets say we have a utility function $U: \mathbb{R}^{2} \to \mathbb{R}$ given by $U(x,y)$ and a binding budget constraint $p_{x} x + p_{y} y = m$, where $p_{x}, p_{y}$ are prices of goods $x,y$ and $m$ ...
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### What does the elasticity say about the fraction of total cost used on input 1?

A firm have the following production function $$y=x_{1}^{\alpha} x_{2}^{1-\alpha}, \quad 0< \alpha < 1$$ $w_1>0$ is the cost of input 1 and $w_2 > 0$ is the cost of input 2. (1.1) ...
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### What is the economic interpretation of the solution of this optimal control problem?

I have the following optimal control problem $$\max_{c_t} \int^{\infty}_0 e^{-p_it}\ln(c_t(i))dt$$ subject to $$\dot{w_t}(i)=rw_t(i) -n_ic_t(i)$$ $$w_0(i)=w_0>0$$ I have some wealthy and ...
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198 views

### A question about Lagrange multiplier(when $\lambda=0$)

I need help in a maximization problem(finding the optimal investment portfolio). where $R_s$ and $\Phi$ are $n$ by $1$, with other variables being scalars. $C^s$ is consumption (or wealth) of an ...
375 views

### Is this Cost function concave or convex?

Given the following cost function, where t is the quantity of some product. $$C(t) = 1/3t^3 - 7t^2 +11t + 50$$ here is a graph between $t= 0$ and $t = 25$ We are asked if this function is convex or ...
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### Weierstrass Theorem in Optimization

Weierstrass Theorem states that any bounded sequence has a convergent subsequence. I did that in my maths course and understood it completely. But when I was learning optimization techniques in ...
106 views

### General Equilibrium with Linear Production

I don't think I understand how optimization problems with a linear function work as of now. If you have a production economy with two agents, two goods and Cobb-Douglas utility representation, and you ...
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### Finding savings in an Overlapping Generations model

I have not seen this question asked anywhere, so I'm posing it here in case anybody else (hopefully) can help me get to the answer. In a nutshell, my question is: how do we arrive at the saving ...
I am having troubles in solving correctly the following problem: A company wants to minimize its total costs, on the condition that the income obtained from the sale of the quantities $x_1, x_2$ of ...