{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# indi_choice - 7 Individual choice Comparative statics Engel...

This preview shows pages 1–4. Sign up to view the full content.

7 Individual choice Comparative statics: Engel curves: Response of x to changes in m . O ff er curves: Response of x i to change in p i ( p j ). Example: Excise and Income taxes.

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

View Full Document
7.1 Slutsky equation Theorem: ∂x j ( p , m ) ∂p i = ∂h j ( p , v ( p , m )) ∂p i ∂x j ( p , m ) ∂m x i ( p , m ) . Proof: Let x ( p , m ) and u = u ( x ) be a solution to Umax, then h j ( p , u ) x j ( p , e ( p , u )) . Di ff erentiate w.p. to p i and evaluate at p , obtain ∂h j ( p , u ) ∂p i = ∂x j ( p , m ) ∂p i + ∂x j ( p , m ) ∂m ∂e ( p , u ) ∂p i | {z } . = x i ( p ,m ) 7.2 Hicks and Slutsky compensations Setup: Prices change = Consumption changes = Indirect utility changes. Idea of compensations: Quantify (\$) the changes. Hicks: m , such that original utility is a ff ordable. Corresponds to income e ff ect change. Slutsky: m , such that original consumption bundle is a ff ordable. Corresponds to the total e ff ect. Example: Excise and income taxes.
7.3 Duality in consumption Prices normalized to make m = 1. Indirect utility: v ( p ) = max x u ( x ) , s.t. px = 1 . Direct utility (dual problem): u ( x ) = min p v ( p ) , s.t. px = 1 . Example: Cobb-Douglas. 7.4 Revealed Preferences Observe: ( p t , x t ) for some t . Suppose p t x t p t x , then u ( x t

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}