{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture10-2010

# Lecture10-2010 - Expected Utility Lecture X Charles B Moss...

This preview shows pages 1–3. Sign up to view the full content.

Expected Utility: Lecture X Charles B. Moss September 10, 2010 I. Basic Utility A. A typical economic axiom is that economic agents (consumers, producers, etc.) behave in a way that maximizes their expected utility. The typical formulation is max x 1 ,x 2 U ( x 1 ,x 2 ) s . t .p 1 x 1 + p 2 x 2 Y (1) x 1 and x 2 are consumption goods and Y is monetary income. In decision making under risk, we are typically interested in the utility of income U ( Y ). How do these concepts relate? B. The linkage between these two concepts is the indirect utility function which posits optimizing behavior by the economic agent. SpeciFcally, assuming an Cobb-Douglas utility function the gen- eral utility maximization problem can be rewritten as max x 1 ,x 2 x α 1 x β 2 s . t .p 1 x 1 + p 2 x 2 Y (2) Due to the concavity of the utility function, the inequality can be replaced with an equality. The maximization problem can then be reformulated as a Lagrangian L = x α 1 x β 2 + λ ( Y p 1 x 1 p 2 x 2 )( 3 ) The Frst order conditions are then 1

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

View Full Document
AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture X Fall 2010 ∂L ∂x 1 = α x α 1 x β 2 x 1 λp 1 =0 2 = β x α 1 x β 2 x 2 λp 2 ∂λ = Y p 1 x 1 p 2 x 2 (4) Taking the ratio of the ±rst two ±rst order conditions yields x 2 = β α x 1 p 1 p 2 (5) Substituting this result into the third ±rst order condition yields the demand for x 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

Lecture10-2010 - Expected Utility Lecture X Charles B Moss...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online