lecture4 - Professor Jay Bhattacharya Spring 2001 Two...

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Professor Jay Bhattacharya Spring 2001 Econ 11--Lecture 4 1 Spring 2001 Econ 11--Lecture 4 1 Two Example Problems and One Policy Application • Two solved example problems • One policy applications using budget constraints and indifference curves • It is only the 4th class, but we already know enough to tackle an important policy question. – Housing Subsides Spring 2001 Econ 11--Lecture 4 2 Problem #1 from Nicholson •“One young connoisseur has $300 to spend to build a small wine cellar. She enjoys two vintages: an ‘expensive’ 1981 French Bordeaux ( W f ) at $20 per bottle and a less expensive 1983 California wine ( W c ) at $4 per bottle. How many bottles of each wine should she buy if her utility function is given by: () 3 1 3 2 , c f c f W W W W U = Spring 2001 Econ 11--Lecture 4 3 Wine Connoisseur’s Budget Constraint where, I W P W P c c f f + , 20 $ = f P , 4 $ = c P 300 $ = I The connoisseur should spend her whole budget on wine! g, simplifyin after or 300 4 20 = + c f W W 0 75 5 = + c f W W Spring 2001 Econ 11--Lecture 4 4 Wine Connoisseur’s Problem 0 75 5 : subject to = + c f W W 3 1 3 2 , max c f c f W W W W 75 5 , , max : Lagrangian the up set 3 1 3 2 + = c f c f c f W W W W L W W Spring 2001 Econ 11--Lecture 4 5 First Order Conditions 0 5 3 2 3 1 = = λ f c f W W W L (1) 0 3 1 3 2 = = c f c W W W L (2) (3) 0 75 5 = + = c f W W L Spring 2001 Econ 11--Lecture 4 6 Solving the Problem 5 2 5 3 1 3 2 : (2) by (1) Divide 3 2 3 1 3 2 3 1 = = f c f c c f f c W W W W W W W W 5 2 f c W W =
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Professor Jay Bhattacharya Spring 2001 Econ 11--Lecture 4 2 Spring 2001 Econ 11--Lecture 4 7 Plug Into Budget Constraint 0 75 5 into 5 2 : Plug = + = c f f c W W W W 0 75 2 = + c c W W bottles 25 = c W bottles 10 = f W Spring 2001 Econ 11--Lecture 4 8 Check Second Order Conditions • In a linearly constrained optimization problem with two variables, the second order conditions are given by: • Here, 0 2 2 1 22 2 1 12 2 2 11 < + f f f f f f f () 3 1 3 2 , c f c f W W W W U f = = Spring 2001 Econ 11--Lecture 4 9 Second Order Conditions (II) 0 10 25 3 2 3 2 3 1 3 1 1 > = = = f c f W W W U f 0 25 10 3
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This note was uploaded on 02/11/2012 for the course ECON 51 taught by Professor Tendall,m during the Fall '07 term at Stanford.

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lecture4 - Professor Jay Bhattacharya Spring 2001 Two...

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