Coursenotes_ECON301

Coursenotes_ECON301 - UNIVERSITY OF WATERLOO DEPARTMENT OF...

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UNIVERSITY OF WATERLOO DEPARTMENT OF ECONOMICS ECONOMICS 301 MICROECONOMIC THEORY II C. H. VAN DE WAAL The learning materials contained in this booklet have been reproduced for the exclusive use of the students registered in the above course at the University of Waterloo. They may not be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopied, recorded or otherwise, either in whole or in part, without obtaining the written permission of the course author.
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i TABLE OF CONTENTS L E C T U R E 1 1 L E C T U R E 2 1 4 L E C T U R E 3 3 9 L E C T U R E 4 5 4 L E C T U R E 5 7 1 L E C T U R E 6 8 9 L E C T U R E 7 1 0 9 L E C T U R E 8 1 2 9 L E C T U R E 9 1 4 5 L E C T U R E 1 0 1 6 6 L E C T U R E 1 1 1 8 0 L E C T U R E 1 2 1 9 7 L E C T U R E 1 3 2 2 0 L E C T U R E 1 4 2 3 6 L E C T U R E 1 5 2 6 0 L E C T U R E 1 6 2 8 1 L E C T U R E 1 7 2 9 4 L E C T U R E 1 8 3 0 9 L E C T U R E 1 9 3 2 5
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1 ECON 301 – LECTURE #1 REVIEW: Consumer Equilibrium (Utility Maximization) The consumer desires to maximize their Total Utility subject to their budget constraint. Let’s consider the case where the consumer has the choice between 2 goods, X and Y. Max U(X,Y) subject to P X X + P Y Y = M X,Y Using ECON 201 logic, we know that for the consumer to reach an equilibrium he/she must have no further incentives to shift consumption among the two goods (in terms of Utility). This implies that the last unit purchased of X and the last unit purchased of Y must give the consumer the same “satisfaction”. Suppose, for example, that P X = 2 and P Y = 1. We should notice the relationship between P X and P Y is simply P X = 2P Y . Our ECON 201 logic is that if X costs twice as much as Y … to be worth paying double for X, its marginal utility (utility per additional unit) must be twice the marginal utility of Y in equilibrium. This implies that; MU X = 2MU Y Rearranging, MU X = MU Y 2 1 or simply, MU X = MU Y P X P Y Of course, this condition extends to the case of multiple (more than two) goods as follows: MU 1 = MU 2 = … = MU n P 1 P 2 P n ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ Now that we have taken ECON 211, we can arrive at this conclusion quantitatively. Using the Lagrangian technique learned in ECON 211, we can set up the consumer’s problem in general as:
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2 L: Max U(X,Y) + λ (M – P X X – P Y Y) X,Y Taking the First Order Conditions, we get: L / X = FOC X U X λ P X = 0 ( 1 ) L / Y = FOC Y U Y λ P Y = 0 ( 2 ) Where, U X = Marginal Utility of good X. U Y = Marginal Utility of good Y. Rearrange (1) and (2) to isolate λ on the LHS… λ = U X / P X from (1) (3) λ = U Y / P Y from (2) (4) Equate (3) and (4) to get, U X = U Y P X P Y or simply, MU X = MU Y P X P Y which is the consumer’s equilibrium condition that we arrived at above using our ECON 201 logic and intuition.
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Coursenotes_ECON301 - UNIVERSITY OF WATERLOO DEPARTMENT OF...

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