prelims_Micro Prelim Sept 2004

# prelims_Micro Prelim Sept 2004 - University of California...

This preview shows pages 1–2. Sign up to view the full content.

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.

Unformatted text preview: University of California, Davis Date: September 2, 2004 Department of Economics Time: 4 hours Microeconomics Reading Time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE PLEASE ANSWER FOUR QUESTIONS (OUT OF FIVE) Question 1. In this question we consider utility functions of the additively separable form ) ( ) ,..., ( 1 1 j L j j L x u x x u ∑ = = , (1.1) where L j x u j j ,..., 1 , ) ( ' = > . Throughout this question, we assume that the UMAX[ p , w ] problems (where the price vector p and the wealth level w are strictly positive) have unique, interior solutions, and that all functions are (twice continuously) differentiable. Except for part 1(a), we consider a single consumer. 1(a) Suppose that all consumers have preferences representable by the same utility function, of form (1.1). Can we be sure that a positive representative consumer exists for an unrestricted domain of wealth vectors? If YES, justify your claim. If NO, provide a counterexample. 1(b) Write the L +1 first order equalities of the UMAX[ p , w ] problem, denoting its solution by )) , ( ~ ),..., , ( ~ ( ) , ( ~ 1 w p x w p x w p x L = and its (positive) Lagrange multiplier by ) , ( w p λ . 1(c) By differentiating the just obtained first-order equalities with respect to the parameters, obtain ( L +1) 2 equalities involving the partial derivatives of the Walrasian demand function. 1(d) Show that ) , ( ) , ( w p w w p v λ = ∂ ∂ , where ) , ( w p v is the indirect utility function, and interpret in words....
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

prelims_Micro Prelim Sept 2004 - University of California...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online