# PS4Answers - UCLA Economics 11 Fall 2010 Professor Mazzocco...

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

1 UCLA Economics 11 – Fall 2010 Professor Mazzocco Problem Set 4 – Solutions 1) a) The Lagrangian is L = X 1/4 Y 3/4 + λ(I – P X .X – P Y .Y), and its FOCs are: (1/4)X -3/4 Y 3/4 – λ.P X = 0, and (3/4)X 1/4 Y -1/4 – λ.P y = 0. Now using the budget constraint, i.e., I = P X .X + P Y .Y, it follows that d x (P X ,P Y ,I) = (1/4).(I/P X ), whereas d y (P X ,P Y ,I) = (3/4).(I/P Y ). b) Now we should minimize P X .X + P Y .Y subject to X 1/4 Y 3/4 ≥ U for some U>0. Or equivalently, we can maximize –[P X .X + P Y .Y] subject to X 1/4 Y 3/4 ≥ U for some U>0. Hence, the Lagrangian for this problem may be written as L = -[ P X .X + P Y .Y] + λ[X 1/4 Y 3/4 – U]. The FOCs in this case are: -P x + λ (1/2) X -3/4 Y 3/4 = 0, and -P y + λ (1/2) X 1/4 Y -1/4 = 0. Finally, combing the FOCs with the fact that the constraint should hold with equality, i.e., X 1/4 Y 3/4 = U, we obtain the compensated demands. Specifically, after playing a bit with the algebra, h x (P X ,P Y ,U) = [P

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.

## This note was uploaded on 11/09/2011 for the course ECON 11 taught by Professor Cunningham during the Fall '08 term at UCLA.

### Page1 / 2

PS4Answers - UCLA Economics 11 Fall 2010 Professor Mazzocco...

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

View Full Document
Ask a homework question - tutors are online