Lecturer : Muchdie, PhD in Economics  PhD in Economics, 1998, Dept. of Economics, The University of Queensland, Australia.  Post Graduate Diploma in.

Slides:



Advertisements
Similar presentations
DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.
Advertisements

1 Topic 6: Optimization I Maximisation and Minimisation Jacques (4th Edition): Chapter 4.6 & 4.7.
Lecturer : Muchdie, PhD in Economics  PhD in Economics, 1998, Dept. of Economics, The University of Queensland, Australia.  Post Graduate Diploma in.
Lecturer : Muchdie, PhD in Economics  PhD in Economics, 1998, Dept. of Economics, The University of Queensland, Australia.  Post Graduate Diploma in.
The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.
Rules for Differentiating Univariate Functions Given a univariate function that is both continuous and smooth throughout, it is possible to determine its.
Managerial Economics & Business Strategy Chapter 1 The Fundamentals of Managerial Economics.
Managerial Economics & Business Strategy Chapter 1 The Fundamentals of Managerial Economics.
Law of Demand A decrease in the price of a good, all other things held constant, will cause an increase in the quantity demanded of the good. An increase.
Chapter 6 Differential Calculus
Differentiation in Economics – Objectives 1 Understand that differentiation lets us identify marginal relationships in economics Measure the rate of change.
Section 2.5 – Implicit Differentiation
Optimization Techniques Lecture 2 (Appendix C). 1. Optimization is: a process by which the maximum or minimum values of decision variables are determined.
Econ 533 Econometrics and Quantitative Methods One Variable Calculus and Applications to Economics.
Optimization Techniques Methods for maximizing or minimizing an objective function Examples –Consumers maximize utility by purchasing an optimal combination.
Managerial Economics Managerial Economics = economic theory + mathematical eco + statistical analysis.
Material for Week 2: Optimization Techniques Problem 3: Interest rate (i) = 15%
Chap # 5 : Optimization Techniques Tahir Islam Assistant Professor in Economics Kardan Institute of Higher Education, Kabul.
INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2011 Pearson Education, Inc. Chapter 11 Differentiation.
Slide 1  2005 South-Western Publishing Appendix 2A Differential Calculus in Management A function with one decision variable, X, can be written as Y =
Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics in a Global Economy Chapter 2 Optimization Techniques and New Management.
Slide 3- 1 Rule 1 Derivative of a Constant Function.
3.3: Rules of Differentiation Objective: Students will be able to… Apply the Power Rule, Sum and Difference Rule, Quotient and Product Rule for differentiation.
Section 2.5 – Implicit Differentiation. Explicit Equations The functions that we have differentiated and handled so far can be described by expressing.
Derivatives of Parametric Equations
Department of Business Administration FALL Optimization Techniques by Asst. Prof. Sami Fethi.
3.3 Rules for Differentiation What you’ll learn about Positive integer powers, multiples, sums, and differences Products and Quotients Negative Integer.
Prepared by Robert F. Brooker, Ph.D. Copyright ©2004 by South-Western, a division of Thomson Learning. All rights reserved.Slide 1 Managerial Economics.
Differentiation By: Doug Robeson. What is differentiation for? Finding the slope of a tangent line Finding maximums and minimums Finding the shape of.
1.6 – Differentiation Techniques The Product and Quotient Rules.
Optimization Techniques Lecture Optimization is: a process by which the maximum or minimum values of decision variables are determined.  Examples.
PowerPoint Slides by Robert F. BrookerHarcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc. Managerial Economics in a Global Economy.
Slide 1  2002 South-Western Publishing Web Chapter A Optimization Techniques Overview Unconstrained & Constrained Optimization Calculus of one variable.
Managerial Economics Managerial Economics = economic theory + mathematical eco + statistical analysis.
Powerpoint Templates Page 1 Powerpoint Templates Review Calculus.
1 SM1.21 Managerial Economics Welcome to session 2 Optimization Techniques and New Management Tools.
Marginal Analysis. Rules Marginal cost is the rate at which the total cost is changing, so it is the gradient, or the differentiation. Total Cost, TC.
Department of Business Administration FALL Optimization Techniques by Assoc. Prof. Sami Fethi.
Calculus and Analytical Geometry Lecture # 8 MTH 104.
Managerial Economics Lecture: Optimization Technique Date:
1 Differentiation Mona Kapoor. 2 Differentiation is all about measuring change! Measuring change in a linear function: y = a + bx a = intercept b = constant.
CHAPTER 4 DIFFERENTIATION NHAA/IMK/UNIMAP. INTRODUCTION Differentiation – Process of finding the derivative of a function. Notation NHAA/IMK/UNIMAP.
C opyright  2007 by Oxford University Press, Inc. PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.Slide 1 1.
4-5 Exploring Polynomial Functions Locating Zeros.
3.5 – Implicit Differentiation
Managerial economics Lecturer : Muchdie, PhD in Economics  PhD in Economics, 1998, Dept. of Economics, The University of Queensland, Australia.  Post.
© 2010 Pearson Education Inc.Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 12e– Slide 1 of 33 Chapter 3 Techniques of Differentiation.
Semester-2 Academic Year 2010/2011 Wednesday Room : 209 Major : Management Lecturer : Muchdie, PhD in Economics  PhD in Economics, 1998, Dept.
PowerPoint Slides by Robert F. BrookerCopyright (c) 2001 by Harcourt, Inc. All rights reserved. Managerial Economics in a Global Economy Chapter 2 Optimization.
Chapter 2 Optimization Techniques and New Management Tools
Appendix 2A Differential Calculus in Management
Chapter 2 Optimization Techniques and New Management Tools
Chapter 3 Techniques of Differentiation
Principles and Worldwide Applications, 7th Edition
CHAPTER 4 DIFFERENTIATION.
DIFFERENTIATION & INTEGRATION
Bab 4 : Peramalan Permintaan
2-5 Absolute Value Functions and Graphs
Managerial Economics in a Global Economy
Chapter 3 Optimization Techniques and New Management Tools
Dr Huw Owens Room B44 Sackville Street Building Telephone Number 65891
Chapter 3 Derivatives.
Differentiation.
Chain Rule AP Calculus.
2.4 The Chain Rule.
A function f is increasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2, we have f(x1) < f(x2). A function f is decreasing.
Graphs and the Derivative
Continuity and Differentiation
(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7
Differentiation and the Derivative
Presentation transcript:

Lecturer : Muchdie, PhD in Economics  PhD in Economics, 1998, Dept. of Economics, The University of Queensland, Australia.  Post Graduate Diploma in Regional Dev.,1994, Dept. of Economics, The Univ. of Queensland, Australia.  MS in Rural & Regional Development Planning, 1986, Graduate School, Bogor Agricultural University, Bogor Chapter 2 Optimization Techniques and New Management Tools

Equations: TR = 100Q - 10Q 2 Tables: Graphs:

AC = TC/Q MC =  TC/  Q

The derivative of Y with respect to X is equal to the limit of the ratio  Y/  X as  X approaches zero.

Constant Function Rule: The derivative of a constant, Y = f(X) = a, is zero for all values of a (the constant).

Power Function Rule: The derivative of a power function, where a and b are constants, is defined as follows.

Sum-and-Differences Rule: The derivative of the sum or difference of two functions U and V, is defined as follows.

Product Rule: The derivative of the product of two functions U and V, is defined as follows.

Quotient Rule: The derivative of the ratio of two functions U and V, is defined as follows.

Chain Rule: The derivative of a function that is a function of X is defined as follows.

Find X such that dY/dX = 0 Second derivative rules: If d 2 Y/dX 2 > 0, then X is a minimum. If d 2 Y/dX 2 < 0, then X is a maximum.

 Benchmarking  Total Quality Management  Reengineering  The Learning Organization

 Broadbanding  Direct Business Model  Networking  Pricing Power  Small-World Model  Virtual Integration  Virtual Management