Marginal Analysis Outline
|
|
- Maud Hunt
- 6 years ago
- Views:
Transcription
1 Marginal Analysis Outline 1. Definition and Assumptions 2. Optimality criteria Analysis Interpretation Application 3. Key concepts Expansion path Cost function Economies of scale 4. Summary Massachusetts Institute of Technology Marginal Analysis Slide 1 of 17 Marginal Analysis Basic form of optimization of design Combines: Production function - Technical efficiency Input cost function, c(x) Economic efficiency Massachusetts Institute of Technology Marginal Analysis Slide 2 of 17 Page 1
2 Assumptions of Marginal Analysis Feasible region is convex (over relevant portion) This is key. Why? To guarantee no other optimum missed No constraints on resources Models are analytic (needed for proof) Defines optimum by looking at the margins -- the derivatives Massachusetts Institute of Technology Marginal Analysis Slide 3 of 17 Optimality Conditions for Design, by Marginal Analysis The Problem: Min C(Y ) = c(x) s.t. g(x) = Y cost of inputs production function vector of resources Fixed level of output The Lagrangean: L = c(x) - λ [g(x) - Y ] Massachusetts Institute of Technology Marginal Analysis Slide 4 of 17 Page 2
3 Optimality Conditions for Design, by Marginal Analysis (2) Key Result: c(x) / X i = λ g(x) / X i marginal cost marginal product Optimality Conditions: MP i / MC i = MP j /MC j = 1 / λ MC j / MP j = MC i / MP i = λ = Shadow Price on Product A balanced design Each X i contributes same bang for buck Massachusetts Institute of Technology Marginal Analysis Slide 5 of 17 Graphical Interpretation of Optimality Conditions (A) Input Cost Function X 2 B/P 2 B = Budget c(x) = Σp i X i B P 2 P 1 Linear case: In general, non-linear (as in curved line) B/P 1 X 1 Massachusetts Institute of Technology Marginal Analysis Slide 6 of 17 Page 3
4 Graphical Interpretation of Optimality Conditions (2) (B) Conditions X 2 Slope = MRS ij = - MP 1 / MP 2 = - MC 1 / MC 2 Isoquant $ X 1 Massachusetts Institute of Technology Marginal Analysis Slide 7 of 17 Application of Optimality Conditions Problem: Y = a 0 X 1 a1 X 2 a2 c(x) = Σp i X i Note: Linearity of Input Cost Function - typically assumed by economists - in general, not valid! prices rise with demand! wholesale, volume discounts Solution: [a 1 / X 1 *] Y / p 1 = [a 2 / X 2 *] Y / p 2 ( * denotes an optimum value) Massachusetts Institute of Technology Marginal Analysis Slide 8 of 17 Page 4
5 Expansion Path Locus of all optimal designs X* Not a property of technical system alone Depends on local prices Optimal designs do not, in general, maintain constant ratios between optimal X i * e.g.: crew of 20,000 ton ship crew of 200,000 ton ship Massachusetts Institute of Technology Marginal Analysis Slide 9 of 17 Calculation of Expansion Path Assume: Y = 2X X (increasing RTS) c(x) = X 1 + X (increasing costs) Optimality Conditions: (0.48 / X 1 ) Y / 1 = (0.72 / X 2 ) Y / (1.5X ) = MP i / MC i => X 1 * = (X 2 *) 1.5 Graphically: Y X 2 Expansion Path Massachusetts Institute of Technology Marginal Analysis Slide 10 of 17 X 1 Page 5
6 Cost Functions Not same as input cost function It represents the optimal cost of Y Not the cost of any set of X C(Y) = C(X*) = f (Y) Massachusetts Institute of Technology Marginal Analysis Slide 11 of 17 Graphically: Cost Functions (2) C(Y) Feasible Economist s view Y Feasible Engineer s view Cost-Effectiveness Y C(Y) Great practical use: How much Y for budget? Y for B? Cost effectiveness, B / Y Massachusetts Institute of Technology Marginal Analysis Slide 12 of 17 Page 6
7 Calculation of Cost Function Cobb-Douglas Prod. Fcn: Y = a 0 πx ai i Linear input cost function: c(x) = Σp i X i Result C(Y) = A(πp i ai/ r )Y 1/r where r = Σa i Easy to estimate statistically => Solution for a i => Estimate of prod. fcn. Y = a 0 πx i ai Massachusetts Institute of Technology Marginal Analysis Slide 13 of 17 Calculation of Cost Function (2) Assume Again: Y = 2X X c(x) = X 1 + X Expansion Path: X 1 * = (X 2 *) 1.5 Thus: Y = 2(X 2 *) 1.44 c(x*) = 2(X 2 *) 1.5 => X 2 * = (Y/2) 0.7 c(y) = c(x*) = ( )Y 1.05 Massachusetts Institute of Technology Marginal Analysis Slide 14 of 17 Page 7
8 Economies of Scale A possible characteristic of cost function Concept similar to returns to scale, except ratio of X i not constant refers to costs (economies) not returns Economies of scale exist if costs increase slower than product Total cost = C(Y) = Y < 1.0 Massachusetts Institute of Technology Marginal Analysis Slide 15 of 17 Economies of Scale (2) Note: If Cobb-Douglas, linear input costs Increasing RTS => Economies of scale r = Σa i > 1.0 => C(Y) = fcn Y 1/r Not necessarily true in general See example!! c(y) = c(x*) = ( )Y 1.05 Massachusetts Institute of Technology Marginal Analysis Slide 16 of 17 Page 8
9 Marginal Analysis Summary Assumptions convex feasible region -- Unconstrained Optimality Criteria MC/MP same for all inputs Expansion path -- Locus of Optimal Design Cost function -- cost along Expansion Path Economies of scale (vs Returns to Scale) -- Exist if Cost/Unit decreases with volume Massachusetts Institute of Technology Marginal Analysis Slide 17 of 17 Page 9
Basic form of optimization of design Combines: Production function - Technical efficiency Input cost function, c(x) Economic efficiency
Marginal Analysis Outline 1. Definition 2. Assumptions 3. Optimality criteria Analysis Interpretation Application 4. Expansion path 5. Cost function 6. Economies of scale Massachusetts Institute of Technology
More informationMarginal Analysis. Marginal Analysis: Outline
Page 1 Marginal Analysis Purposes: 1. To present a basic application of constrained optimization 2. Apply to Production Function to get criteria and patterns of optimal system design Massachusetts Institute
More informationPRODUCTION COSTS. Econ 311 Microeconomics 1 Lecture Material Prepared by Dr. Emmanuel Codjoe
PRODUCTION COSTS In this section we introduce production costs into the analysis of the firm. So far, our emphasis has been on the production process without any consideration of costs. However, production
More informationUnderstand general-equilibrium relationships, such as the relationship between barriers to trade, and the domestic distribution of income.
Review of Production Theory: Chapter 2 1 Why? Understand the determinants of what goods and services a country produces efficiently and which inefficiently. Understand how the processes of a market economy
More informationCost Functions. PowerPoint Slides prepared by: Andreea CHIRITESCU Eastern Illinois University
Cost Functions PowerPoint Slides prepared by: Andreea CHIRITESCU Eastern Illinois University 1 Definitions of Costs It is important to differentiate between accounting cost and economic cost Accountants:
More informationChapter 4. Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization
Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization The Representative Consumer Preferences Goods: The Consumption Good and Leisure The Utility Function More Preferred
More informationChapter 11: Cost Minimisation and the Demand for Factors
Chapter 11: Cost Minimisation and the Demand for Factors 11.1: Introduction We assume a very simple objective for firms namely, that they want to maximise profits 1. We will explore the implications of
More informationIntro to Economic analysis
Intro to Economic analysis Alberto Bisin - NYU 1 The Consumer Problem Consider an agent choosing her consumption of goods 1 and 2 for a given budget. This is the workhorse of microeconomic theory. (Notice
More informationProblem Set 5 Answers. A grocery shop is owned by Mr. Moore and has the following statement of revenues and costs:
1. Ch 7, Problem 7.2 Problem Set 5 Answers A grocery shop is owned by Mr. Moore and has the following statement of revenues and costs: Revenues $250,000 Supplies $25,000 Electricity $6,000 Employee salaries
More informationConsider the production function f(x 1, x 2 ) = x 1/2. 1 x 3/4
In this chapter you work with production functions, relating output of a firm to the inputs it uses. This theory will look familiar to you, because it closely parallels the theory of utility functions.
More informationFirm s demand for the input. Supply of the input = price of the input.
Chapter 8 Costs Functions The economic cost of an input is the minimum payment required to keep the input in its present employment. It is the payment the input would receive in its best alternative employment.
More informationOutline 1 Technology 2 Cost minimization 3 Profit maximization 4 The firm supply Comparative statics 5 Multiproduct firms P. Piacquadio (p.g.piacquadi
Microeconomics 3200/4200: Part 1 P. Piacquadio p.g.piacquadio@econ.uio.no September 14, 2017 P. Piacquadio (p.g.piacquadio@econ.uio.no) Micro 3200/4200 September 14, 2017 1 / 41 Outline 1 Technology 2
More informationWe want to solve for the optimal bundle (a combination of goods) that a rational consumer will purchase.
Chapter 3 page1 Chapter 3 page2 The budget constraint and the Feasible set What causes changes in the Budget constraint? Consumer Preferences The utility function Lagrange Multipliers Indifference Curves
More informationChoice. A. Optimal choice 1. move along the budget line until preferred set doesn t cross the budget set. Figure 5.1.
Choice 34 Choice A. Optimal choice 1. move along the budget line until preferred set doesn t cross the budget set. Figure 5.1. Optimal choice x* 2 x* x 1 1 Figure 5.1 2. note that tangency occurs at optimal
More informationLecture 2: Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and
Lecture 2: Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization The marginal or derivative function and optimization-basic principles The average function
More informationR.E.Marks 1997 Recap 1. R.E.Marks 1997 Recap 2
R.E.Marks 1997 Recap 1 R.E.Marks 1997 Recap 2 Concepts Covered maximisation (& minimisation) prices, CPI, inflation, purchasing power demand & supply market equilibrium, gluts, excess demand elasticity
More informationChapter 8 COST FUNCTIONS. Copyright 2005 by South-western, a division of Thomson learning. All rights reserved.
Chapter 8 COST FUNCTIONS Copyright 2005 by South-western, a division of Thomson learning. All rights reserved. 1 Definitions of Costs It is important to differentiate between accounting cost and economic
More informationReview of whole course
Page 1 Review of whole course A thumbnail outline of major elements Intended as a study guide Emphasis on key points to be mastered Massachusetts Institute of Technology Review for Final Slide 1 of 24
More informationINTERMEDIATE MICROECONOMICS LECTURE 9 THE COSTS OF PRODUCTION
9-1 INTERMEDIATE MICROECONOMICS LECTURE 9 THE COSTS OF PRODUCTION The opportunity cost of an asset (or, more generally, of a choice) is the highest valued opportunity that must be passed up to allow current
More informationLecture 7. The consumer s problem(s) Randall Romero Aguilar, PhD I Semestre 2018 Last updated: April 28, 2018
Lecture 7 The consumer s problem(s) Randall Romero Aguilar, PhD I Semestre 2018 Last updated: April 28, 2018 Universidad de Costa Rica EC3201 - Teoría Macroeconómica 2 Table of contents 1. Introducing
More informationMacroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 1
Macroeconomics I, UPF Professor Antonio Ciccone SOLUTIONS PROBLEM SET 1 1.1 (from Romer Advanced Macroeconomics Chapter 1) Basic properties of growth rates which will be used over and over again. Use the
More informationProblem Set VI: Edgeworth Box
Problem Set VI: Edgeworth Box Paolo Crosetto paolo.crosetto@unimi.it DEAS - University of Milan Exercises solved in class on March 15th, 2010 Recap: pure exchange The simplest model of a general equilibrium
More information14.54 International Trade Lecture 3: Preferences and Demand
14.54 International Trade Lecture 3: Preferences and Demand 14.54 Week 2 Fall 2016 14.54 (Week 2) Preferences and Demand Fall 2016 1 / 29 Today s Plan 1 2 Utility maximization 1 2 3 4 Budget set Preferences
More informationElements of Economic Analysis II Lecture II: Production Function and Profit Maximization
Elements of Economic Analysis II Lecture II: Production Function and Profit Maximization Kai Hao Yang 09/26/2017 1 Production Function Just as consumer theory uses utility function a function that assign
More informationMicroeconomics. Lecture Outline. Claudia Vogel. Winter Term 2009/2010. Part II Producers, Consumers, and Competitive Markets
Microeconomics Claudia Vogel EUV Winter Term 2009/2010 Claudia Vogel (EUV) Microeconomics Winter Term 2009/2010 1 / 36 Lecture Outline Part II Producers, Consumers, and Competitive Markets 7 Measuring
More informationFirm s Problem. Simon Board. This Version: September 20, 2009 First Version: December, 2009.
Firm s Problem This Version: September 20, 2009 First Version: December, 2009. In these notes we address the firm s problem. questions. We can break the firm s problem into three 1. Which combinations
More informationFinal Exam Economic 210A, Fall 2009 Answer any 7 questions.
Final Exam Economic 10A, Fall 009 Answer any 7 questions For a person with income m, let us define the compensating variation of a price change from price vector p to price vector p to be the amount of
More informationThe Theory of the Firm
The Theory of the Firm I. Introduction: A Schematic Comparison of the Neoclassical Approaches to the Studies Between the Theories of the Consumer and the Firm A. The Theory of Consumer Choice: Consumer
More informationMath: Deriving supply and demand curves
Chapter 0 Math: Deriving supply and demand curves At a basic level, individual supply and demand curves come from individual optimization: if at price p an individual or firm is willing to buy or sell
More informationGraphs Details Math Examples Using data Tax example. Decision. Intermediate Micro. Lecture 5. Chapter 5 of Varian
Decision Intermediate Micro Lecture 5 Chapter 5 of Varian Decision-making Now have tools to model decision-making Set of options At-least-as-good sets Mathematical tools to calculate exact answer Problem
More informationManagerial Economics & Business Strategy Chapter 5. The Production Process and Costs
Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs I. Production Analysis Overview Total Product, Marginal Product, Average Product Isoquants Isocosts Cost Minimization
More informationMicroeconomics Pre-sessional September 2016
Microeconomics Pre-sessional September 2016 So7ris Georganas Economics Department City University ondon Organisa7on of the Microeconomics Pre-sessional Introduc7on 10:00-10:30 Demand and Supply 10:30-11:10
More informationECON Answers Homework #3
ECON 331 - Answers Homework #3 Exercise 1: (a) First, I calculate the derivative of y with respect to t. Then, to get the growth rate, I calculate the ratio of this derive and the function: (b) dy dt =
More informationChapter 4 Topics. Behavior of the representative consumer Behavior of the representative firm Pearson Education, Inc.
Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm 1-1 Representative Consumer Consumer s preferences over consumption and leisure as represented by indifference
More informationThe objectives of the producer
The objectives of the producer Laurent Simula October 19, 2017 Dr Laurent Simula (Institute) The objectives of the producer October 19, 2017 1 / 47 1 MINIMIZING COSTS Long-Run Cost Minimization Graphical
More informationHotelling Under Pressure. Soren Anderson (Michigan State) Ryan Kellogg (Michigan) Stephen Salant (Maryland)
Hotelling Under Pressure Soren Anderson (Michigan State) Ryan Kellogg (Michigan) Stephen Salant (Maryland) October 2015 Hotelling has conceptually underpinned most of the resource extraction literature
More informationEconomics 386-A1. Practice Assignment 3. S Landon Fall 2003
Economics 386-A1 Practice Assignment 3 S Landon Fall 003 This assignment will not be graded. Answers will be made available on the Economics 386 web page: http://www.arts.ualberta.ca/~econweb/landon/e38603.html.
More informationI. More Fundamental Concepts and Definitions from Mathematics
An Introduction to Optimization The core of modern economics is the notion that individuals optimize. That is to say, individuals use the resources available to them to advance their own personal objectives
More informationDemand Side: Community Indifference Curve (CIC) Shows various combinations of two goods with equivalent welfare
Basic Tools for General Equilibrium Analysis Demand Side: Community Indifference Curve (CIC) Shows various combinations of two goods with equivalent welfare Good Y Downward sloping And Convexity CI Since
More informationReview of General Economic Principles. Review Notes from AGB 212
Review of General Economic Principles Review Notes from AGB 212 1 Agenda Production Theory One input, one output Production Theory Two inputs, one output Production Theory One input, two outputs 2 The
More informationECON 310 Fall 2005 Final Exam - Version A. Multiple Choice: (circle the letter of the best response; 3 points each) and x
ECON 30 Fall 005 Final Exam - Version A Name: Multiple Choice: (circle the letter of the best response; 3 points each) Mo has monotonic preferences for x and x Which of the changes described below could
More informationReview of Production Theory: Chapter 2 1
Review of Production Theory: Chapter 2 1 Why? Trade is a residual (EX x = Q x -C x; IM y= C y- Q y) Understand the determinants of what goods and services a country produces efficiently and which inefficiently.
More informationManagerial Economics & Business Strategy Chapter 5. The Production Process and Costs
Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs I. Production Analysis Overview Total Product, Marginal Product, Average Product Isoquants Isocosts Cost Minimization
More information9 D/S of/for Labor. 9.1 Demand for Labor. Microeconomics I - Lecture #9, April 14, 2009
Microeconomics I - Lecture #9, April 14, 2009 9 D/S of/for Labor 9.1 Demand for Labor Demand for labor depends on the price of labor, price of output and production function. In optimum a firm employs
More informationLecture 1: The market and consumer theory. Intermediate microeconomics Jonas Vlachos Stockholms universitet
Lecture 1: The market and consumer theory Intermediate microeconomics Jonas Vlachos Stockholms universitet 1 The market Demand Supply Equilibrium Comparative statics Elasticities 2 Demand Demand function.
More informationConsumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization
Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 1 Discussion So far: How to measure variables of macroeconomic
More informationOverview Definitions Mathematical Properties Properties of Economic Functions Exam Tips. Midterm 1 Review. ECON 100A - Fall Vincent Leah-Martin
ECON 100A - Fall 2013 1 UCSD October 20, 2013 1 vleahmar@uscd.edu Preferences We started with a bundle of commodities: (x 1, x 2, x 3,...) (apples, bannanas, beer,...) Preferences We started with a bundle
More informationTHEORY OF COST. Cost: The sacrifice incurred whenever an exchange or transformation of resources takes place.
THEORY OF COST Glossary of New Terms Cost: The sacrifice incurred whenever an exchange or transformation of resources takes place. Sunk Cost: A cost incurred regardless of the alternative action chosen
More informationProduction. Economics II: Microeconomics. November Aslanyan (VŠE Praha) Production 11/09 1 / 25
Production Economics II: Microeconomics VŠE Praha November 2009 Aslanyan (VŠE Praha) Production 11/09 1 / 25 Microeconomics Consumers: Firms: People. Households. Internal Organisation. Industrial Organisation.
More informationMicroeconomics Pre-sessional September Sotiris Georganas Economics Department City University London
Microeconomics Pre-sessional September 2016 Sotiris Georganas Economics Department City University London Organisation of the Microeconomics Pre-sessional o Introduction 10:00-10:30 o Demand and Supply
More informationProduction. Any activity that creates present or future economic value (utility). The transformation of inputs into outputs
Production Any activity that creates present or future economic value (utility). The transformation of inputs into outputs Inputs can include categories such as: labour, capital, energy, land, entrepreneurship
More informationConsumers cannot afford all the goods and services they desire. Consumers are limited by their income and the prices of goods.
Budget Constraint: Review Consumers cannot afford all the goods and services they desire. Consumers are limited by their income and the prices of goods. Model Assumption: Consumers spend all their income
More informationProduction Theory. Lesson 7. Ryan Safner 1. Hood College. ECON Microeconomic Analysis Fall 2016
Production Theory Lesson 7 Ryan Safner 1 1 Department of Economics Hood College ECON 306 - Microeconomic Analysis Fall 2016 Ryan Safner (Hood College) ECON 306 - Lesson 7 Fall 2016 1 / 64 Lesson Plan 1
More informationA PRODUCER OPTIMUM. Lecture 7 Producer Behavior
Lecture 7 Producer Behavior A PRODUCER OPTIMUM The Digital Economist A producer optimum represents a solution to a problem facing all business firms -- maximizing the profits from the production and sales
More informationPublic Economics (ECON 131) Section #8: Public Goods
Public Economics (ECON 131) Section #8: Public Goods March 20 and 22, 2017 Contents 1 Key Concepts 1 2 Practise Problems 2 2.1 Gruber, Ch.7, Q.13...................................... 2 2.2 Gruber, Ch.7,
More informationAdvanced Microeconomics
Advanced Microeconomics Ivan Etzo University of Cagliari ietzo@unica.it Dottorato in Scienze Economiche e Aziendali, XXXIII ciclo Ivan Etzo (UNICA) Lecture 3: Cost Minimization 1 / 3 Overview 1 The Cost
More informationPractice Questions Chapters 9 to 11
Practice Questions Chapters 9 to 11 Producer Theory ECON 203 Kevin Hasker These questions are to help you prepare for the exams only. Do not turn them in. Note that not all questions can be completely
More informationMidterm 2 (Group A) U (x 1 ;x 2 )=3lnx 1 +3 ln x 2
Econ 301 Midterm 2 (Group A) You have 70 minutes to complete the exam. The midterm consists of 4 questions (25,30,25 and 20 points). Problem 1 (25p). (Uncertainty and insurance) You are an owner of a luxurious
More informationThis appendix discusses two extensions of the cost concepts developed in Chapter 10.
CHAPTER 10 APPENDIX MATHEMATICAL EXTENSIONS OF THE THEORY OF COSTS This appendix discusses two extensions of the cost concepts developed in Chapter 10. The Relationship Between Long-Run and Short-Run Cost
More informationU(x 1, x 2 ) = 2 ln x 1 + x 2
Solutions to Spring 014 ECON 301 Final Group A Problem 1. (Quasilinear income effect) (5 points) Mirabella consumes chocolate candy bars x 1 and fruits x. The prices of the two goods are = 4 and p = 4
More informationLecture 8: Producer Behavior
Lecture 8: Producer Behavior October 23, 2018 Overview Course Administration Basics of Production Production in the Short Run Production in the Long Run The Firm s Problem: Cost Minimization Returns to
More informationBudget Constrained Choice with Two Commodities
Budget Constrained Choice with Two Commodities Joseph Tao-yi Wang 2009/10/2 (Lecture 4, Micro Theory I) 1 The Consumer Problem We have some powerful tools: Constrained Maximization (Shadow Prices) Envelope
More informationTheoretical Tools of Public Finance. 131 Undergraduate Public Economics Emmanuel Saez UC Berkeley
Theoretical Tools of Public Finance 131 Undergraduate Public Economics Emmanuel Saez UC Berkeley 1 THEORETICAL AND EMPIRICAL TOOLS Theoretical tools: The set of tools designed to understand the mechanics
More informationUC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A)
UC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A) Production and the costs production (PR 7.1-7.2) Cost concepts and the relations among costs Lectures 3-4 Aug.
More informationUtility Maximization and Choice
Utility Maximization and Choice PowerPoint Slides prepared by: Andreea CHIRITESCU Eastern Illinois University 1 Utility Maximization and Choice Complaints about the Economic Approach Do individuals make
More informationEconomics 393 Test 2 Thursday 28 th June 2018
Economics 393 Test 2 Thursday 28 th June 2018 Please turn off all electronic devices computers, cell phones, calculators. Answer all questions. Each question is worth 10 marks. 1. Suppose the citizens
More informationECON 3020 Intermediate Macroeconomics
ECON 3020 Intermediate Macroeconomics Chapter 4 Consumer and Firm Behavior The Work-Leisure Decision and Profit Maximization 1 Instructor: Xiaohui Huang Department of Economics University of Virginia 1
More informationEconS 301 Review Session #6 Chapter 8: Cost Curves
EconS 01 Revie Session #6 Chapter 8: Cost Curves 8.1. Consider a production function ith to inputs, labor and capital, given by (. The marginal products associated ith this production function are as follos:
More informationECON Micro Foundations
ECON 302 - Micro Foundations Michael Bar September 13, 2016 Contents 1 Consumer s Choice 2 1.1 Preferences.................................... 2 1.2 Budget Constraint................................ 3
More informationExercise 1 Modelling and Convexity
TMA947 / MMG621 Nonlinear optimization Exercise 1 Modelling and Convexity Emil Gustavsson, Michael Patriksson, Adam Wojciechowski, Zuzana Šabartová September 16, 2014 E1.1 (easy) To produce a g. of cookies
More informationChapter 5 The Production Process and Costs
Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs McGraw-Hill/Irwin Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. I. Production Analysis Overview
More informationChapter 4. Consumer and Firm Behavior: The Work- Leisure Decision and Profit Maximization. Copyright 2014 Pearson Education, Inc.
Chapter 4 Consumer and Firm Behavior: The Work- Leisure Decision and Profit Maximization Copyright Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm 1-2 Representative
More informationChoice. A. Optimal choice 1. move along the budget line until preferred set doesn t cross the budget set. Figure 5.1.
Choice 2 Choice A. choice. move along the budget line until preferred set doesn t cross the budget set. Figure 5.. choice * 2 * Figure 5. 2. note that tangency occurs at optimal point necessary condition
More informationChapter 21. The Monetary Policy and Aggregate Demand Curves
Chapter 21 The Monetary Policy and Aggregate Demand Curves The Federal Reserve and Monetary Policy The Fed of the United States conducts monetary policy by setting the federal funds rate the interest rate
More informationTÁMOP /2/A/KMR
ABOR ECONOMICS ABOR ECONOMICS Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics, Faculty of Social Sciences, Eötvös oránd University Budapest (ETE)
More informationCONSUMER OPTIMISATION
Prerequisites Almost essential Firm: Optimisation Consumption: Basics CONSUMER OPTIMISATION MICROECONOMICS Principles and Analysis Frank Cowell Note: the detail in slides marked * can only be seen if you
More informationSummer 2016 ECN 303 Problem Set #1
Summer 2016 ECN 303 Problem Set #1 Due at the beginning of class on Monday, May 23. Give complete answers and show your work. The assignment will be graded on a credit/no credit basis. In order to receive
More informationThere are 9 questions on this exam. These 9 questions are independent of each other.
Economics 21: Microeconomics (Summer 2001) Midterm Exam 1 Professor Andreas Bentz instructions You can obtain a total of 100 points on this exam. Read each question carefully before answering it. Do not
More informationECON 3020 Intermediate Macroeconomics
ECON 3020 Intermediate Macroeconomics Chapter 5 A Closed-Economy One-Period Macroeconomic Model Instructor: Xiaohui Huang Department of Economics University of Virginia c Copyright 2014 Xiaohui Huang.
More informationBudget Constrained Choice with Two Commodities
1 Budget Constrained Choice with Two Commodities Joseph Tao-yi Wang 2013/9/25 (Lecture 5, Micro Theory I) The Consumer Problem 2 We have some powerful tools: Constrained Maximization (Shadow Prices) Envelope
More informationEconomic Dispatch. Quantitative Energy Economics. Anthony Papavasiliou 1 / 21
1 / 21 Economic Dispatch Quantitative Energy Economics Anthony Papavasiliou Economic Dispatch 2 / 21 1 Optimization Model of Economic Dispatch 2 Equilibrium Model of Economic Dispatch Outline 3 / 21 1
More informationThe Role of Physical Capital
San Francisco State University ECO 560 The Role of Physical Capital Michael Bar As we mentioned in the introduction, the most important macroeconomic observation in the world is the huge di erences in
More informationConsumer Budgets, Indifference Curves, and Utility Maximization 1 Instructional Primer 2
Consumer Budgets, Indifference Curves, and Utility Maximization 1 Instructional Primer 2 As rational, self-interested and utility maximizing economic agents, consumers seek to have the greatest level of
More informationChapter 3: Model of Consumer Behavior
CHAPTER 3 CONSUMER THEORY Chapter 3: Model of Consumer Behavior Premises of the model: 1.Individual tastes or preferences determine the amount of pleasure people derive from the goods and services they
More informationECON 311 Winter Quarter, 2010 NAME: KEY Prof. Hamilton
ECON 311 Winter Quarter, 2010 NAME: KEY Prof. Hamilton FINAL EXAM 200 points 1. (30 points). A firm produces rubber gaskets using labor, L, and capital, K, according to a production function Q = f(l,k).
More informationPORTFOLIO THEORY. Master in Finance INVESTMENTS. Szabolcs Sebestyén
PORTFOLIO THEORY Szabolcs Sebestyén szabolcs.sebestyen@iscte.pt Master in Finance INVESTMENTS Sebestyén (ISCTE-IUL) Portfolio Theory Investments 1 / 60 Outline 1 Modern Portfolio Theory Introduction Mean-Variance
More informationEC Intermediate Microeconomic Theory
EC 311 - Intermediate Microeconomic Theory Lecture: Cost of Production Cont. Bekah Selby rebekahs@uoregon.edu May 5, 2014 Selby EC 311 - Lectures May 5, 2014 1 / 23 Review A firm faces several types of
More informationUnit 1 : Principles of Optimizing Behavior
Unit 1 : Principles of Optimizing Behavior Prof. Antonio Rangel January 2, 2016 1 Introduction Most models in economics are based on the assumption that economic agents optimize some objective function.
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering.7 Water Resource Systems Lecture 5 Multiobjective Optimization and Utility Oct., 006 Multiobjective problems Benefits
More informationChapter 6. Production. Introduction. Production Decisions of a Firm. Production Decisions of a Firm
Chapter 6 Production Introduction Our study of consumer behavior was broken down into 3 steps Describing consumer preferences Consumers face budget constraints Consumers choose to maximize utility Production
More informationECONOMICS 100A: MICROECONOMICS
ECONOMICS 100A: MICROECONOMICS Summer Session II 2011 Tues, Thur 8:00-10:50am Center Hall 214 Professor Mark Machina Office: Econ Bldg 217 Office Hrs: Tu/Th 11:30-1:30 TA: Michael Futch Office: Sequoyah
More informationIntermediate microeconomics. Lecture 3: Production theory. Varian, chapters 19-24
Intermediate microeconomics Lecture 3: Production theory. Varian, chapters 19-24 Part 1: Profit maximization 1. Technology a) Production quantity and production function b) Marginal product and technical
More informationThe homework is due on Wednesday, September 7. Each questions is worth 0.8 points. No partial credits.
Homework : Econ500 Fall, 0 The homework is due on Wednesday, September 7. Each questions is worth 0. points. No partial credits. For the graphic arguments, use the graphing paper that is attached. Clearly
More information= 500 4q. Some Applications of Differentiation Single Variable Case
Some Applications of Differentiation Single Variable Case In economics the differential calculus has had many prolific applications. It is convenient at this stage to list some of the functional relationships
More informationChapter 7: Portfolio Theory
Chapter 7: Portfolio Theory 1. Introduction 2. Portfolio Basics 3. The Feasible Set 4. Portfolio Selection Rules 5. The Efficient Frontier 6. Indifference Curves 7. The Two-Asset Portfolio 8. Unrestriceted
More informationWhere does stuff come from?
Where does stuff come from? Factors of production Technology Factors of production: Thanks, Marx! The stuff we use to make other stuff Factors of production: Thanks, Marx! The stuff we use to make other
More information1 Economical Applications
WEEK 4 Reading [SB], 3.6, pp. 58-69 1 Economical Applications 1.1 Production Function A production function y f(q) assigns to amount q of input the corresponding output y. Usually f is - increasing, that
More informationChapter 4. Our Consumption Choices. What can we buy with this money? UTILITY MAXIMIZATION AND CHOICE
Chapter 4 UTILITY MAXIMIZATION AND CHOICE 1 Our Consumption Choices Suppose that each month we have a stipend of $1250. What can we buy with this money? 2 What can we buy with this money? Pay the rent,
More informationIntroductory to Microeconomic Theory [08/29/12] Karen Tsai
Introductory to Microeconomic Theory [08/29/12] Karen Tsai What is microeconomics? Study of: Choice behavior of individual agents Key assumption: agents have well-defined objectives and limited resources
More informationFalse_ The average revenue of a firm can be increasing in the firm s output.
LECTURE 12: SPECIAL COST FUNCTIONS AND PROFIT MAXIMIZATION ANSWERS AND SOLUTIONS True/False Questions False_ If the isoquants of a production function exhibit diminishing MRTS, then the input choice that
More information