PS4Answers

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

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

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
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 Right Arrow Icon
Ask a homework question - tutors are online