In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. That is, any combinations of two products indicated by the curve will provide the consumer with equal levels of utility, and the consumer has no preference for one combination or bundle of goods over a different combination on the same curve. One can also refer to each point on the indifference curve as rendering the same level of utility (satisfaction) for the consumer. In other words, an indifference curve is the locus of various points showing different combinations of two goods providing equal utility to the consumer. Utility is then a device to represent preferences rather than something from which preferences come. The main use of indifference curves is in the representation of potentially observable demand patterns for individual consumers over commodity bundles. There are infinitely many indifference curves: one passes through each combination. A collection of (selected) indifference curves, illustrated graphically, is referred to as an indifference map. The slope of an indifference curve is called the MRS (marginal rate of substitution), and it indicates how much of good y must be sacrificed to keep the utility constant if good x is increased by one unit. Given a utility function u(x,y), to calculate the MRS, we simply take the partial derivative of the function u with respect to good x and divide it by the partial derivative of the function u with respect to good y. If the marginal rate of substitution is diminishing along an indifference curve, that is the magnitude of the slope is decreasing or becoming less steep, then the preference is convex. (Wikipedia).
Episode 19: Indifference Curve Analysis
Using Indifference Curve Analysis to determine a consumer's buying choice given income, prices, and preferences. NOTE: The scenario results that I go through at the end of the video are ENTIRELY dependent on the shape of the preferences. You may find that you get slightly different results
From playlist Microeconomics modules
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Minimal Discriminants and Minimal Weiestrass Forms For Elliptic Curves
This goes over the basic invariants I'm going to need for Elliptic curves for Szpiro's Conjecture.
From playlist ABC Conjecture Introduction
Elliptic curves: point at infinity in the projective plane
This video depicts point addition and doubling on elliptic curve in simple Weierstrass form in the projective plane depicted using stereographic projection where the point at infinity can actually be seen. Explanation is in the accompanying article https://trustica.cz/2018/04/05/elliptic-
From playlist Elliptic Curves - Number Theory and Applications
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Elliptic Curves - Lecture 6a - Ramification (continued)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Finding rational curves by forgetful map - Runpu Zong
Runpu Zong Member, School of Mathematics October 1, 2014 More videos on http://video.ias.edu
From playlist Mathematics
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
What is the exterior sum theorem for polygons
👉 Learn about the interior and the exterior angles of a polygon. A polygon is a plane shape bounded by a finite chain of straight lines. The interior angle of a polygon is the angle between two sides of the polygon. The sum of the interior angles of a regular polygon is given by the formul
From playlist Interior and Exterior Angles of Polygons
2. Preferences and Utility Functions
MIT 14.01 Principles of Microeconomics, Fall 2018 Instructor: Prof. Jonathan Gruber View the complete course: https://ocw.mit.edu/14-01F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62oJSoqb4Rf-vZMGUBe59G- This video focuses on the demand curve, derived from how co
From playlist MIT 14.01 Principles of Microeconomics, Fall 2018
Lec 4 | MIT 14.01SC Principles of Microeconomics
Lecture 4: Preferences and Utility Instructor: Jon Gruber, 14.01 students View the complete course: http://ocw.mit.edu/14-01SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 14.01SC Principles of Microeconomics
Optimal point on budget line | Microeconomics | Khan Academy
Using indifference curves to think about the point on the budget line that maximizes total utility Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/choices-opp-cost-tutorial/marginal-utility-tutorial/v/types-of-indifference-curves?utm_source=YT&ut
From playlist Theory of consumer choice | AP Microeconomics | Khan Academy
MIT 14.04 Intermediate Microeconomic Theory, Fall 2020 Instructor: Prof. Robert Townsend View the complete course: https://ocw.mit.edu/courses/14-04-intermediate-microeconomic-theory-fall-2020/ YouTube Playlist: https://www.youtube.com/watch?v=XSTSfCs74bg&list=PLUl4u3cNGP63wnrKge9vllow3Y2
From playlist MIT 14.04 Intermediate Microeconomic Theory, Fall 2020
Types of indifference curves | Microeconomics | Khan Academy
Indifference curves for normal goods, substitutes and perfect complements Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/firm-economic-profit/economic-profit-tutorial/v/economic-profit-vs-accounting-profit?utm_source=YT&utm_medium=Desc&utm_campa
From playlist Theory of consumer choice | AP Microeconomics | Khan Academy
6. From Classical to Neoclassical Utilitarianism
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From playlist The Moral Foundations of Politics with Ian Shapiro
Mod-05 Lec-38 Backward Induction: Exercises
Game Theory and Economics by Dr. Debarshi Das, Department of Humanities and Social Sciences, IIT Guwahati. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist IIT Guwahati: Game Theory and Economics | CosmoLearning.org Economics
Lec 5 | MIT 14.01SC Principles of Microeconomics
Lecture 5: Budget Constraints Instructor: Jon Gruber, 14.01 students View the complete course: http://ocw.mit.edu/14-01SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 14.01SC Principles of Microeconomics
What is the difference between convex and concave
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From playlist Classify Polygons
3. Budget Constraints and Constrained Choice
MIT 14.01 Principles of Microeconomics, Fall 2018 Instructor: Prof. Jonathan Gruber View the complete course: https://ocw.mit.edu/14-01F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62oJSoqb4Rf-vZMGUBe59G- This lecture continues the discussion about consumer choice
From playlist MIT 14.01 Principles of Microeconomics, Fall 2018