Question 4: Robinson Crusoe Taxed Consider the Robinson Crusoe Economy with u(x,

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Question 4: Robinson Crusoe Taxed Consider the Robinson Crusoe Economy with u(x,T) -Vx+ vr, initial endowment of 24 hours of time, and production technology q-F(I) = I. Suppose now that government imposes a tax t 10% on labor income, so that, if Robinson earns wl from working he must pay twl to the government. Suppose the government returns all tax revenues r sum transfer S to individuals. Note that, from Robinsons perspective, the size of the government transfer he receives is not related to any choices he makes about consumption of goods and leisure. eceived in the form of a lump- Elements of Economic Analysis ECON 20100, Winter Quarter 2018 (a) What is the firm's supply for each price? (b) Write down the consumer's new budget constraint after the tax has been introduced (c) Determine the consumer's demand for consumption x and leisure r for any prices. (d) Solve for the equilibrium price and quantities (e) Does the new equilibrium allocation correspond to the solution to the planner's problem?

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5523.tp 7/1/04 5:21 PM Page 1 Economics with Calculus 5523.tp 7/1/04 5:21 PM Page 2 Economics with Calculus Michael C Lovell Wesleyan University, USA W World Scientific NEW JERSEY · LONDON · SINGAPORE · BEIJING · SHANGHAI · HONG KONG · TAIPED · CHENNAI This page intentionally left blank Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401–402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Economics with calculus / Michael C. Lovell. p. cm. Includes bibliographical references and index. ISBN 9812388257 (alk. paper) -- ISBN 9812388575 (pbk. : alk. paper) 1. Economics, Mathematical. 2. Calculus. I. Title. HB135 .L68 2004 330.01'515--dc22 2004052464 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Printed in Singapore. July 20, 2004 14:26 Economics with Calculus I dedicate this book to my family Adrienne Goolkasian Lovell Leslie and Kenneth Chausse: Nathaniel, Colleen, Laurel Stacie and Steve Markoski: Michael, Andrew, Alexander George Lovell and Carrie Cihak Martin Lovell and Sharon Hunter: Mica bk04-003/chap 0 This page intentionally left blank July 20, 2004 14:26 Economics with Calculus bk04-003/preface Preface How should one approach the study of economics? There is no one answer to this question because the appropriate learning style depends i

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