3 marks clara has utility function preferences ux y x

Info icon This preview shows page 4. Sign up to view the full content.

[3 marks] Clara has utility function preferences u(x, y) = x 1/2 + y 1/2 . She has income m = 48 and pays p X = 4, p Y = 2. Now p X falls to 2. Provide a labelled diagram that decomposes this price change using the Slutsky decomposition SE (A to B) and TE (B to C) and the Hicksian decomposition SE (A to H) and TE (H to C). Bundle A: MRS = (y/x) 1/2 = o-cost = 4/2 implies y = 4x and b-line 4x + 2y = 48 imply A(4, 16), u = 6 Slutsky cost 2 x 4 + 2 x 16 = 40 so CBL is 2x + 2y = 40, Slutsky compensation is 48 – 40 = 8 Bundle B: tan: y = x and b-line 2x + 2y = 40 imply B(10, 10) Bundle C: tan: y = x and b-line 2x + 2y = 48 imply C(12, 12) Bundle H: x 1/2 + y 1/2 = 6 and tan: x = y imply H(9, 9) costing 36 so CBL is 2x + 2y = 36 Hicksian compensation is 48 – 36 = 12 24 0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 12 14 16 18 20 22 X Axis Y Axis C A B 2x + 2y = 48 2x + xy = 40 2x + 2y = 36 Hicks CV = $12 Slutsky CV = $8 SE (H) SE (S)
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.
  • Summer '15
  • RobertBarber
  • Utility, Professor Stern, Professor Goodheart

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern