E100LectureNotes4

E100LectureNotes4 - 1 Utility Maximization 2 Consumer’s...

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Unformatted text preview: 1/4/2008 1 Utility Maximization 1/4/2008 2 Consumer’s Problem max u(x 1 , x 2 ,... . x n ) x 1 ,x 2 ...,x n s.t. p 1 x 1 + ... + p n x n = I Simplify: max u(x 1 , x 2 ) x 1 ,x 2.. s.t. p 1 x 1 + p 2 x 2 = I Already talked about utility, the function to be maximized. Need to describe the constraint, which we call the budget constraint 1/4/2008 3 Budget Constraint Units p 1 x 1 +p 2 x 2 = I P 1 : ($/unit), P 2 : ($/unit) x 1 : (units/wk), x 2 : (units/wk) I: ($/wk) 1/4/2008 4 Budget Constraint – Graphical Representation p 1 x 1 +p 2 x 2 = I What is slope of budget line? A. p 2 B. p 1 C. p 2 /p 1 D. p 1 /p 2 E. I X 1 X 2 1/4/2008 5 Altering Budget Lines I ↓ I ↑ X 1 X 2 I/p 1 X 1 X 2 I/p 1 I/p 2 I/p 2 1/4/2008 6 Altering Budget Lines p 1 ↑ p 1 ↓ X 1 X 2 I/p 1 X 1 X 2 I/p 1 I/p 2 I/p 2 1/4/2008 7 Altering Budget Lines p 2 ↑ p 2 ↓ X 1 X 2 I/p 1 X 1 X 2 I/p 1 I/p 2 I/p 2 I/p 1 ’ 1/4/2008 8 Consumer’s Problem max u(x 1 , x 2 ) x 1 ,x 2.. s.t. p 1 x 1 + p 2 x 2 = I Utility - the function to be maximized: Budget constraint: Putting it all together: X 1 X 2 1/4/2008 9 Two conditions for solution Tangency condition (x 1 *, x 2 *) solves: slope indif curve = slope budget line This yields : Graphical Approach: X 1 X 2 1/4/2008 10 First-order conditions in constrained optimization problem: This yields Algebraically: X 1 X 2 X 1 * X 2 * c x x g x x x g x x x f x...
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This note was uploaded on 04/10/2008 for the course ECON 100A taught by Professor Babcock during the Spring '07 term at UCSB.

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E100LectureNotes4 - 1 Utility Maximization 2 Consumer’s...

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