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University of Hawai‘i at Mānoa Department of Economics

University of Hawai‘i at Mānoa Department of Economics. ECON 130 (003): Principles of Economics (Micro) http://www2.hawaii.edu/~lindoj Gerard Russo Lecture #12 Thursday, February 19, 2004. LECTURE 12. Ordinal and Cardinal Utility Utility Functions Indifference Curves

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University of Hawai‘i at Mānoa Department of Economics

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  1. University of Hawai‘i at MānoaDepartment of Economics ECON 130 (003): Principles of Economics (Micro) http://www2.hawaii.edu/~lindoj Gerard Russo Lecture #12 Thursday, February 19, 2004

  2. LECTURE 12 • Ordinal and Cardinal Utility • Utility Functions • Indifference Curves • Marginal Rate of Substitution • Consumer Optimization • Consumer Choice and Income Changes • Derivation of Consumer Demand • Application: Transfers in Cash vs. Transfers in Kind

  3. Utility Function • Consumer Utility is a function of the quantity of goods x and y consumed. • U=U(x,y) • One dependent variable, U, and two independent variables, x and y. • The function U(x,y) is three-dimensional.

  4. Example: Topographical Map Elevation 1000 meters Elevation 4000 meters Elevation 2000 meters

  5. I2 Quantity of Good y I1 Indifference Curve Map I0 Direction of Preference I2 I1 I0 0 Quantity of Good x

  6. U2 Quantity of Good y U1 U0 L• R• Z• A• U2 M• • B U1 U0 0 Quantity of Good x

  7. U2 Quantity of Good y e.g., Automobile Transportation U1 U0 Direction of Preference? U2 U1 U0 0 Quantity of Bad x e.g., Air Pollution

  8. Quantity of Bad y e.g., Garbage U0 Direction of Preference? U1 U2 U0 U1 U2 0 Quantity of Bad x e.g., Viral Disease

  9. Quantity of Bad y e.g., Poison Ivy Direction of Preference? U0 U1 U2 U0 U1 U2 0 Quantity of Good x e.g., Music CDs

  10. The Slope of an Indifference Curve = ∆y/∆x = -MUx/MUy = MRS = Marginal Rate of Substitution U0 Quantity of Good y ∆y ∆x U0 0 Quantity of Good x

  11. Quantity of Good y U2 U1 Slope of the indifference curve = -MUx/MUy. U0 U2 U1 U0 0 Quantity of Good x Slope of the budget line = -Px/Py

  12. OPTIMAL CONSUMER CHOICE • The Consumer maximizes utility subject to the budget constraint. • The optimum is characterized by the equality of the slopes of the budget line and the indifference curve. • -Px/Py = -MUx/MUy

  13. Quantity of Good y U2 U1 U0 The Optimal Choice is Consumption Bundle A. –Px/Py = -MUx/MUy. yA A• U2 U1 U0 0 xA Quantity of Good x

  14. The Optimal Condition • -Px/Py = -MUx/MUy • Px/Py = MUx/MUy • MUy/Py = MUx/Px

  15. Diminishing Marginal Utility • An increase (decrease) in the consumption of good x decreases (increases) the marginal utility of good x. • If x goes up, MUx goes down. If x goes down, MUx goes up. • An increase (decrease) in the consumption of good y decreases (increases) the marginal utility of good y. • If y goes up, MUy goes down. If y goes down, MUy goes up.

  16. Quantity of Good y U2 U1 Px/Py < MUx/MUy U0 Px/Py = MUx/MUy Z• A• U2 U1 L • U0 0 Px/Py > MUx/MUy Quantity of Good x

  17. Quantity of Good y U2 U1 Are goods x and y normal or inferior? U0 C• B• U2 A• U1 U0 0 Quantity of Good x

  18. Quantity of Good y U2 U1 Income-Consumption Path. U0 C• B• U2 A• U1 U0 0 Quantity of Good x

  19. Quantity of Good y U2 U1 U0 U2 U1 U0 0 Income-Consumption Path: Homothetic Preferences Quantity of Good x

  20. U2 Quantity of Good y Are goods x and y normal or inferior? U0 U1 C• U2 yB B• yA A• U1 U0 0 xA xB Quantity of Good x

  21. U2 Quantity of Good y Are goods x and y normal or inferior? U0 U1 C• yC U2 yB B• A• U1 U0 0 xC xB Quantity of Good x

  22. Quantity of Good y U2 U1 A decrease in the price of good x changes the optimum from point A to point B. U0 B• U2 A• U1 U0 0 Quantity of Good x

  23. Derivation of a Consumer Demand Curve y •C B• A• xA xB Px x xC PA •A' PB •B' Demand Curve PC •C' xA xB xC x

  24. Quantity of Alcoholic Beverage Application: Transfers in Cash versus Transfers in Kind. Budget Line After Transfer A• •B •C Quantity of Food Budget Line Before Transfer

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