Question: A set S is a convex cone if and only if 1. S S for every 0 2. S + S

A set S is a convex cone if and only if
1. αS ⊆ S for every α ≥ 0
2. S + S ⊆ S
Convex cones arise naturally in economics, where quantities are required to be nonnegative. The set of nonnegative prices vectors is a convex cone Rn and the production possibility set is often assumed to be a convex cone (example 1.102).

Step by Step Solution

★★★★★

3.47 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Assume satisfies 1 for every 0 2 By 1 is a cone To show that it is convex ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (166).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

A subset S of a linear space is a convex cone if and only if x + y S for every x, y S and x, +

A natural assumption for TP-coalitional games is super additivity, which requires that coalitions cannot lose through cooperation. Specifically, a TP-coalitional game is super additive if for all...

If S is a convex set in a normed linear space, ext (S) (S). The converse is not true in general; not all boundary points are extreme points. However, boundary points and extreme points coincide when...

TACKLE ALL PARTSP5 Problem 1 The Airfare Problem1. You are trying to get the cheapest airfare that you can. You just called up and found that the ticket home will cost $400, and it cannot be refunded...

Read the article: Bolton, P., Brunnermeier, M. K., & Veldkamp, L. (2013). Leadership, Coordination, and Corporate Culture. Review Of Economic Studies, 80(2), 512-537. Based on the article findings,...

ECO670...... 1. "Deriving the Envelope Thoerem: Consider the more general problem M(o, ) = max, f(x, a, 8) subject to g(r, a, 8) = 0. Show that: dM(a, B) _ Of(x', a, b) ag(x*, a, b) da da da 2. For...

Discuss the following operations categories for this site in relation to company and operations strategy: capacity, facilities, technology, vertical integration, sourcing, work force, quality,...

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...

Solve these attachments marginal cost coincides across plants. Intuitively, this indicates that the monopolist does not have further incentives to move production from one plant to another. Exercise...

Explain the following attachment marginal cost coincides across plants. Intuitively, this indicates that the monopolist does not have further incentives to move production from one plant to another....

Below is the SWOT analysis I completed about The Walt DisneyCompany. I need help answering the questions in the analysissection. How would you match the organizations strengths to itsopportunities?...

Read the case study: Coleman Art Museum and respond to the following: Problem statement 2 sentences. swot analysis: strength, weakness} identify 4-5 each opportunities and threats} identify 4-5 each...

"Case Study: Playing the field: Competing bids for Anadarko Petroleum Corporation" 1 . Why does Anadarko ( APC ) CEO Al Walker keep rejecting Occidental s ( OXY ) $ 7 6 offer only to accept Chevron s...

The major difference between the project coordinator and project expeditor forms of organization is that a. Strong commitment to the project usually does not exist in the project expeditor form of...

Refer to the Flexible Insurance Coverage case. Design a spreadsheet that will allow an individual employee with estimated annual medical expenses of $400 to compare the total expenses under each...

Refer to the Snoey Software Company case. Design a spreadsheet that will determine the annual profit when the prices for the Educational, Large-Scale, and Professional versions are $100, $300, and...

The accompanying data le contains 20 observations for a binary response variable yalong with the predictor variables x1 and x2. Click here for the Excel Data File 3. Estimate the logistic regression...

Please help with the following question: 2. Graduate students applying for entrance to many universities must take a Miller Analo- gies Test. It is known that the test scores have a mean of 75 and a...

3) The marketing director of FireStone.com was concerned about the performance of their call center employees. He found that average call times were higher than industry average. The manager decides...