...towards mastery in the practice of problem solving Assessments MODULE 4 Technology 1. You are the manager of 2 small stores with production functions q = K¼L¼ and a larger store with production function q = 2K¼L¼. You hire capital for $4, labour for $1. When you took over this role, your boss told you that Q = 24 was the profit maximizing output for this multi-plan firm: 24 = q1 + q2 + q3. Now, the price of labour rises to $4. Provide (i) Isoquant/Isocost diagrams, (ii) Total Cost and (iii) Marginal Cost diagrams. Illustrate the substitution effect (point a to b) and output effect (point b to c) on these diagrams. Explain why your firm uses less capital even when the price of labour increases. (September 2010) For the production function q = K2 + L2 (A) Demonstrate that the elasticity of substitution is negative. (B) Provide a labelled diagram showing the q = 100 isoquant (C) Briefly explain what a negative value means for σ 3. 4. A special production function is q = min( 80K, 4L1 + 2L2). Discuss the production process described by this function. Is this production function constant returns to scale? Five-year-old Jack has set up a hot chocolate stand outside his home. His customers like hot chocolate made in only one way, one unit of chocolate and 3 units of milk to go into each unit of hot chocolate. Jack’s mother, Naomi, provides him with heat, cups and cleaning free of charge. However, she charges him $0.25 for each unit of chocolate and $0.50 for each unit of milk. What...
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...Fuzzy Control Kevin M. Passino Department of Electrical Engineering The Ohio State University Stephen Yurkovich Department of Electrical Engineering The Ohio State University An Imprint of Addison-Wesley Longman, Inc. Menlo Park, California • Reading, Massachusetts Don Mills, Ontaria • Sydney • Bonn • Harlow, England • Berkeley, California • Amsterdam • Mexico City ii Assistant Editor: Laura Cheu Editorial Assistant: Royden Tonomura Senior Production Editor: Teri Hyde Marketing Manager: Rob Merino Manufacturing Supervisor: Janet Weaver Art and Design Manager: Kevin Berry Cover Design: Yvo Riezebos (technical drawing by K. Passino) Text Design: Peter Vacek Design Macro Writer: William Erik Baxter Copyeditor: Brian Jones Proofreader: Holly McLean-Aldis Copyright c 1998 Addison Wesley Longman, Inc. All rights reserved. No part of this publication may be reproduced, or stored in a database or retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. Printed simultaneously in Canada. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and AddisonWesley was aware of a trademark claim, the designations have been printed in initial caps or in all caps. MATLAB is a registered trademark of The MathWorks...
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...list of Frequently Used Symbols and Notation A text such as Intermediate Financial Theory is, by nature, relatively notation intensive. We have adopted a strategy to minimize the notational burden within each individual chapter at the cost of being, at times, inconsistent in our use of symbols across chapters. We list here a set of symbols regularly used with their specific meaning. At times, however, we have found it more practical to use some of the listed symbols to represent a different concept. In other instances, clarity required making the symbolic representation more precise (e.g., by being more specific as to the time dimension of an interest rate). Roman Alphabet a Amount invested in the risky asset; in Chapter 14, fraction of wealth invested in the risky asset or portfolio AT Transpose of the matrix (or vector)A c Consumption; in Chapter 14 only, consumption is represented by C, while c represents ln C ck Consumption of agent k in state of nature θ θ CE Certainty equivalent CA Price of an American call option CE Price of a European call option d Dividend rate or amount ∆ Number of shares in the replicating portfolio (Chapter xx E The expectations operator ek Endowment of agent k in state of nature θ θ f Futures position (Chapter 16); pf Price of a futures contract (Chapter 16) F, G Cumulative distribution functions associated with densities: f, g Probability density functions K The strike or exercise price of an option K(˜) Kurtosis of the random variable x x ˜ L A lottery...
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...PHYSIC AL CONSTANTS CONSTANT Speed of light Elementary charge Electron mass Proton mass Gravitational constant Permeability constant Permittivity constant Boltzmann’s constant Universal gas constant Stefan–Boltzmann constant Planck’s constant Avogadro’s number Bohr radius SYMBOL c e me mp G m0 P0 k R s h 15 2p"2 NA a0 THREE-FIGURE VALUE 3.003108 m/s 1.60310219 C 9.11310231 kg 1.67310227 kg 6.67310211 N # m2/kg 2 1.2631026 N/A2 1H/m2 8.85310212 C 2/N # m2 1F/m2 1.38310223 J/K 8.31 J/K # mol 5.6731028 W/m2 # K4 6.63310234 J # s 6.0231023 mol21 5.29310211 m BEST KNOWN VALUE* 299 792 458 m/s (exact) 1.602 176 4871402 310219 C 9.109 382 151452 310231 kg 1.672 621 6371832 310227 kg 6.674 281672 310211 N # m2/kg 2 4p31027 (exact) 1/m0c2 (exact) 1.380 65041242 310223 J/K 8.314 4721152 J/K # mol 5.670 4001402 31028 W/m2 # K4 6.626 068 961332 310234 J # s 6.022 141 791302 31023 mol21 5.291 772 08591362 310211 m *Parentheses indicate uncertainties in last decimal places. Source: U.S. National Institute of Standards and Technology, 2007 values SI PREFIXES POWER 1024 1021 1018 1015 1012 109 106 103 102 101 100 1021 1022 1023 1026 1029 10212 10215 10218 10221 10224 THE GREEK ALPHABET PREFIX yotta zetta exa peta tera giga mega kilo hecto deca — deci centi milli micro nano pico femto atto zepto yocto SYMBOL Y Z E P T G M k h da — d c m μ n p f a z y Alpha ...
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