Lecture 6 - Economics 101A (Lecture 6) Stefano DellaVigna...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 101A (Lecture 6) Stefano DellaVigna September 15, 2009
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Outline 1. Utility maximization 2. Utility maximization — Tricky Cases 3. Indirect Utility Function
Background image of page 2
1 Utility Maximization Nicholson, Ch. 4, pp. 114—124 (94—105, 9th) X = R 2 + (2 goods) Consumers: choose bundle x =( x 1 ,x 2 ) in X which yields highest utility. Constraint: income = M Price of good 1 = p 1 , price of good 2 = p 2 Bundle x is feasible if p 1 x 1 + p 2 x 2 M Consumer maximizes max x 1 ,x 2 u ( x 1 2 ) s.t. p 1 x 1 + p 2 x 2 M x 1 0 2 0
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Maximization subject to inequality. How do we solve that? Trick: u strictly increasing in at least one dimension. ( º strictly monotonic) Budget constraint always satis f ed with equality Ignore temporarily x 1 0 ,x 2 0 and check after- wards that they are satis f ed for x 1 and x 2 .
Background image of page 4
Problem becomes max x 1 ,x 2 u ( x 1 ,x 2 ) s.t. p 1 x 1 + p 2 x 2 M =0 L ( x 1 2 )= u ( x 1 2 ) λ ( p 1 x 1 + p 2 x 2 = M ) F.o.c.s: u 0 x i λp i for i =1 , 2 p 1 x 1 + p 2 x 2 M
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Moving the two terms across and dividing, we get: MRS = u 0 x 1 u 0 x 2 = p 1 p 2 Graphical interpretation.
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 17

Lecture 6 - Economics 101A (Lecture 6) Stefano DellaVigna...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online