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Chapter 4 Utility Functions

Chapter 4 Utility Functions. Utility. Ordinal Utility: The only property of a utility assignment is “how it orders the bundles of goods.” The size of the utility difference between two bundles does not matter.

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Chapter 4 Utility Functions

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  1. Chapter 4Utility Functions

  2. Utility • Ordinal Utility: The only property of a utility assignment is “how it orders the bundles of goods.” The size of the utility difference between two bundles does not matter. • Cardinal Utility: It attaches a significance to the magnitude of utility. The size of the utility difference between two bundles has some sort of significance.

  3. 04.01

  4. Panel A: A monotonic transformationPanel B: non-monotonic transformation since it sometime decreases.

  5. 04.02

  6. The utility function can be represented by a general function:u=f(x1, x2)

  7. 04.03

  8. Quasi-linear Utility Function: U=x1+v(x2)=x1+ln(x2)

  9. 04.04

  10. The Cobb-Douglas Utility Function U=(x1)^c (x2)^d where ^ represents the superscript Note: goods are imperfect substitutes

  11. 04.05

  12. Other Utility Functions: • Leontief Function: u=min[a*x1, b*x2] (perfect complements) • Linear Function: u=a*x1+b*x2 (perfect substitutes) • Lexicographic Preference: A is preferred to B if (I) x1(A) > x1(B) or (ii) x1(A)=x1(B) but x2(A)>x2(B).

  13. Leontief Function x2 Examples: (1) Left and right shoes (2) coffee and sugar x1

  14. Linear Function x2 Example: yellow and red pencils (assuming that colors are not your concern) x1

  15. Lexicographic Function x2 A is inferior to B Example: x1 (health) x2 (money) for a terminally ill patient . B . A x1

  16. Marginal Utility • Definition: Effect on utility with a little more of good 1 • Formally, MU1=dU/dx1=[u(x1+dx1, x2)- u(x1, x2)]/dx1

  17. MRS • The rate at which a consumer is just willing to substitute a small amount of good 2 for good 1. • Formally, MRS=MU1/MU2=[dU/dx1]/[dU/dx2], i.e., marginal utility ratio. • This is nothing but the slope of the indifference curve • Given strict convexity assumption, MRS diminishes as we move down along a indifference curve

  18. This concludes the Norton Media LibrarySlide Set for Chapter 4IntermediateMicroeconomics 6th EditionbyHal R. Varian W. W. Norton & CompanyIndependent and Employee-Owned

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