# 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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### Designing the payment function in Mechanism Design problems

Suppose we have a network in which agents request access to its resources. Thus we have a resource allocation problem. Ideally, we want to incentivize agents to send social-welfare supporting ...
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### Calculate optimal discount for product bundling

So recently I made some rules with my transaction data. Based on it I can determine which products are profitable to bundle it together. But even though I know e.g. product A→ product B, are there ...
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### Can I Upload my Preprint on Arxiv Before Submitting it to JPE

I wrote a paper relating the optimal deterrence strategy for crime to concepts on statistical physics, and I am considering submitting the paper to the Journal of Political Economy. I'm wondering if ...
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### Can $u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$ be solved by Kuhn–Tucker conditions?

Consider $\max_{x_1, x_2, x_3, x_4} u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$ s.t. $\; p_1x_1 + p_2x_2 + p_3x_3 + p_4x_4 \le w$ I know we can solve the max problem through separately considering ...
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### Cobb Douglas, Budget Line, Demand function question

use the general form of the Cobb Douglas utility function $U(x,y)= (x^a)(y^b)$ and the budget constraint in the form $B=p_{x}X + p_{y}Y$ to find the demand functions for good x and good y. Is this ...
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### Optimal point and MRS

I read that the tangency condition is not sufficient for optimality, and that one other condition is that the MRS must equal the slope of the budget line at an interior optimum. My confusion is that ...
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### How to find the optimal consumption basket? [closed]

A consumer has the following utility function and income. 𝑈(𝑥, 𝑦) =1/2 * ln 𝑥 + 1/2 * ln y Price of 𝑥 = Price of 𝑦 = 100. Income = 1000 Suppose that the consumer gets 2 redeemable coupons for ...
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### Constrained Optimization using Lagrangian method

The stationary points that we derive by solving the first order conditions of the Lagrangian are those points global optimum points or local optimum points?
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### Why do we have to normalize the income of consumers when working with an Edgeworth Box in a simple trade model with Pareto optima?

I was studying microeconomics and I confess I am not the brightest person for maths and sorry if this is very dumb but I get that we CAN normalize the income and I get where it comes from and how it ...
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### Utility Function Implies Consumption of Not All Goods

Suppose we have a utility function with three inputs, $j, k,$ and $s$ described by $$u(j,k,s) = A\ln(k^\alpha + \beta j^\alpha) + B\ln(s).$$ The price of $j, k,s$ are $p_j, p_k, p_s$, respectively, ...
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### Concave utility functions corner solution explanation

I seem to not be getting this. Could someone explain me the mathematical way to show a concave utility function [like (ax^2+by^2)] subject to a budget constraint has a corner solution. I get the ...
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### Karush-Kuhn-Tucker in infinite dimension

Does the Karush-Kuhn-Tucker theorem on sufficient conditions for optimality of a convex program apply in countable dimension? For precisions, see Definition 4.1.1 and Theorem 4.1.4 of this course. ...
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### 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 ...