In economics, an expansion path (also called a scale line) is a path connecting optimal input combinations as the scale of production expands. which is often represented as a curve in a graph with quantities of two inputs, typically physical capital and labor, plotted on the axes. A producer seeking to produce a given number of units of a product in the cheapest possible way chooses the point on the expansion path that is also on the isoquant associated with that output level. Economists Alfred Stonier and Douglas Hague defined “expansion path” as "that line which reflects the least–cost method of producing different levels of output, when factor prices remain constant." The points on an expansion path occur where the firm's isocost curves, each showing fixed total input cost, and its isoquants, each showing a particular level of output, are tangent; each tangency point determines the firm's conditional factor demands. As a producer's level of output increases, the firm moves from one of these tangency points to the next; the curve joining the tangency points is called the expansion path. If an expansion path forms a straight line from the origin, the production technology is considered homothetic (or homoethetic). In this case, the ratio of input usages is always the same regardless of the level of output, and the inputs can be expanded proportionately so as to maintain this optimal ratio as the level of output expands. A Cobb–Douglas production function is an example of a production function that has an expansion path which is a straight line through the origin. (Wikipedia).
Extended Fundamental Theorem of Calculus
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Extended Fundamental Theorem of Calculus. You can use this instead of the First Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus. - Formula - Proof sketch of the formula - Six Examples
From playlist Calculus
AWESOME physics experiments Ball expansion (science demonstrations)
In this video i demonstrate the effect of expansion! Enjoy.
From playlist physics
How to lead students to an activity from a book
A simple way of decreasing the scroll of death and making your activities more accessible.
From playlist How to add a book in your course
Timelapse of building of extension to my garage. Unfortunately I didn't think to do this until it was started...
From playlist Projects & Installations
If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.
From playlist Career Growth
Just a quick note on what we are going to cover.
From playlist Life Science Math: Limits in calculus
1A Introduction to this course on limits
A course on limits in calculus for healthcare and life sciences students.
From playlist Life Science Math: Limits in calculus
Linux Command Line Full course: Beginners to Experts. Bash Command Line Tutorials
Bash is a Unix shell and command language written by Brian Fox for the GNU Project as a free software replacement for the Bourne shell. First released in 1989, it has been used widely as the default login shell for most Linux distributions. In this course you will learn how use bash comman
From playlist Bash Command Tutorial
Lec 5 | MIT 5.60 Thermodynamics & Kinetics, Spring 2008
Lecture 05: Adiabatic changes. View the complete course at: http://ocw.mit.edu/5-60S08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.60 Thermodynamics & Kinetics, Spring 2008
Integration 4 The Definite Integral Part 3 Example 2
Working through another example of the definite integral.
From playlist Integration
CS224W: Machine Learning with Graphs | 2021 | Lecture 14.2 - Erdos Renyi Random Graphs
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3GzPg4L Jure Leskovec Computer Science, PhD We introduce the simplest model for graph generation, Erdös-Renyi graph (E-R graphs, Gnp graphs). The Gnp random graphs
From playlist Stanford CS224W: Machine Learning with Graphs
Cluster algebras from surfaces II: expansion formula (Lecture 1) by Jon Wilson
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
Unix terminals and shells - 4 of 5
Part of a series teaching programming. See codeschool.org
From playlist Unix terminals and shells
Paths and cycles in expanders - Michael Krivelevich
Computer Science/Discrete Mathematics Seminar I Topic: Paths and cycles in expanders Speaker: Michael Krivelevich Affiliation: Tel Aviv University Date: February 10, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Math 135 Complex Analysis Lecture 17 032615: Laurent Series
Laurent expansion of a function analytic in an annulus; uniqueness of the expansion; expansion of derivation of Laurent expansions (using algebra and uniqueness); evaluation of integrals, given Laurent expansion; isolated singularities: removable singularities, poles, essential singulariti
From playlist Course 8: Complex Analysis
Josef Teichmann: An elementary proof of the reconstruction theorem
CIRM VIRTUAL EVENT Recorded during the meeting "Pathwise Stochastic Analysis and Applications" the March 09, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Virtual Conference
Michael Lindsey - Many-body perturbation theory and Green's function methods - IPAM at UCLA
Recorded 10 March 2022. Michael Lindsey of New York University Mathematics presents "Many-body perturbation theory and Green's function methods" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Abstract: Beyond the single-particle picture of density function
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022
Epsilon delta limit (Example 3): Infinite limit at a point
This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!
From playlist Calculus
Perturbation Theory for Band Matrices - Sasha Sodin
Sasha Sodin Institute for Advanced Study November 19, 2010 ANALYSIS/MATHEMATICAL PHYSICS SEMINAR Band matrices are a class of random operators with rows and columns indexed by elements of the d-dimensional lattice, and random entries H(u, v) which are small when the distance between u and
From playlist Mathematics