In microeconomics, the contract curve or Pareto set is the set of points representing final allocations of two goods between two people that could occur as a result of mutually beneficial trading between those people given their initial allocations of the goods. All the points on this locus are Pareto efficient allocations, meaning that from any one of these points there is no reallocation that could make one of the people more satisfied with his or her allocation without making the other person less satisfied. The contract curve is the subset of the Pareto efficient points that could be reached by trading from the people's initial holdings of the two goods. It is drawn in the Edgeworth box diagram shown here, in which each person's allocation is measured vertically for one good and horizontally for the other good from that person's origin (point of zero allocation of both goods); one person's origin is the lower left corner of the Edgeworth box, and the other person's origin is the upper right corner of the box. The people's initial endowments (starting allocations of the two goods) are represented by a point in the diagram; the two people will trade goods with each other until no further mutually beneficial trades are possible. The set of points that it is conceptually possible for them to stop at are the points on the contract curve. However, most authors identify the contract curve as the entire Pareto efficient locus from one origin to the other. Any Walrasian equilibrium lies on the contract curve. As with all points that are Pareto efficient, each point on the contract curve is a point of tangency between an indifference curve of one person and an indifference curve of the other person. Thus, on the contract curve the marginal rate of substitution is the same for both people. (Wikipedia).
Algebraic geometry 44: Survey of curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.
From playlist Algebraic geometry I: Varieties
11_6_1 Contours and Tangents to Contours Part 1
A contour is simply the intersection of the curve of a function and a plane or hyperplane at a specific level. The gradient of the original function is a vector perpendicular to the tangent of the contour at a point on the contour.
From playlist Advanced Calculus / Multivariable Calculus
Lecture 11: Discrete Curves (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
What are parallel lines and a transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
8: Tangent and Normal Vectors - Valuable Vector Calculus
Derivative of dot product: https://youtu.be/vykDXI9OjDM The tangent, normal, and binormal vectors of a space curve. We can use this to determine which direction a curve is turning, even in 3D space! Full Valuable Vector Calculus playlist: Valuable Vector Calculus: https://www.youtube.com
From playlist Valuable Vector Calculus
Geometrical Interpertation of Differentiation
#CalculusMadeEasy Calculus Made Easy, Chapter 10 (download: bit.ly/EasyCalculus). Two points of a function. Why does one have a derivative and the other point does not?
From playlist Calculus Made Easy
From playlist B. Differential Calculus
Hyperbola 3D Animation | Objective conic hyperbola | Digital Learning
Hyperbola 3D Animation In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other an
From playlist Maths Topics
Proving Parallel Lines with Angle Relationships
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Ekaterina Amerik: Rational curves and contraction loci on holomorphic symplectic manifolds
VIRTUAL LECTURE RECORDED DURING SOCIAL DISTANCING Recording during the meeting "Varieties with Trivial Canonical Class " the April 06, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by
From playlist Virtual Conference
What is General Relativity? Lesson 14: The covariant derivative of a covector
We start by demonstrating that contraction commutes with directional covariant derivative and then derive the CFREE and COMP expressions for the covariant derivative of a covector.
From playlist What is General Relativity?
Casagrande: Special rational fibrations in Fano 4-folds
Recording during the meeting "The Geometry of Algebraic Varieties" the October 03, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathe
From playlist Algebraic and Complex Geometry
Geometry of 2-dimensional Riemannian disks and spheres - Regina Rotman
Members' Seminar Topic: Geometry of 2-dimensional Riemannian disks and spheres. Speaker: Regina Rotman Affiliation: University of Toronto; Member, School of Mathematics Date: March 11, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Cécile Gachet : Positivity of higher exterior powers of the tangent bundle
CONFERENCE Recording during the thematic meeting : "Algebraic Geometry and Complex Geometry " the December1, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIRM's
From playlist Algebraic and Complex Geometry
Regina Rotman (5/28/22): Curvature bounds and the length of the shortest closed geodesic
I will discuss upper bounds for the length of the shortest periodic geodesic on closed Riemannian manifolds with various curvature bounds. In particular, I will present an upper bound for the length of the shortest closed geodesic on Riemannian manifolds with a positive Ricci curvature as
From playlist Vietoris-Rips Seminar
[my xls is here https://trtl.bz/2Nto24q] Three features of a commodity forward curve in CONTANGO (i.e., upward-sloping): 1. riskfree rate is greater than lease rate; 2. Negative roll yield for the long position; 3. Consistent with "normal backwardation". Discuss this video here in our FRM
From playlist Financial Markets and Products: Intro to Derivatives (FRM Topic 3, Hull Ch 1-7)
Tony Yue Yu - 3/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Notes: https://nextcloud.ihes.fr/index.php/s/pSQnsgx72a4S5zj 3/4 - Naive counts, tail conditions and deformation invariance. --- We show that the naive counts of rational curves in an affine log Calabi-Yau variety U, containing an open algebraic torus, determine in a surprisingly simple w
From playlist Tony Yue Yu - The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Geometric and algebraic aspects of space curves | Differential Geometry 20 | NJ Wildberger
A space curve has associated to it various interesting lines and planes at each point on it. The tangent vector determines a line, normal to that is the normal plane, while the span of adjacent normals (or equivalently the velocity and acceleration) is the osculating plane. In this lectur
From playlist Differential Geometry