Week12 - ECON 117 Mathematical Economics Spring 2008 Week...

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ECON 117 Spring 2008 Mathematical Economics Week 12 Q) Solve the following program 1, 2 12 max . . 1 xx st x x += Page 1 of 11
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ECON 117 Spring 2008 Mathematical Economics 2.2 Utility Maximization Ex) There are two goods 12 (, ) x x . The price of 1 x : 1 P The price of 2 x : 2 P Your income : I Your utility function Q) Define your utility maximization program and make the Lagrange program. Q) Find the first-order-conditions. Page 2 of 11
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ECON 117 Spring 2008 Mathematical Economics [Technical explanation of the F.O.C.s] Def) The set of vectors () { } ,0 | 0, n H ≡∈ ⋅= ∈ zxz x z \ n \ is called a basic hyperplane given . n z \ Q) . Find 2 1,1 =∈ z \ H z Q) Then, find a hyperplane ( ) { } 2 ,| , Ha a a x \\ Page 3 of 11
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ECON 117 Spring 2008 Mathematical Economics Q) . 1 2 1 p-vector 2 p p ⎛⎞ ⎛⎞ == ⎜⎟ ⎜⎟ ⎝⎠ 10 I = Draw a budget constraint. Q) . 1 2 3 1 p-vector 1 1 p p p ⎛⎞⎛ ⎜⎟⎜ ⎝⎠⎝ 10 I = Draw a budget constraint. Page 4 of 11
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ECON 117 Spring 2008 Mathematical Economics Def) () { } |, , : n fa a f ∈= xx \\ \ n \ is called a level set
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This note was uploaded on 09/15/2008 for the course ECON 324 taught by Professor Kim during the Spring '08 term at HKUST.

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Week12 - ECON 117 Mathematical Economics Spring 2008 Week...

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