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Modeling Tradeoffs

Modeling Tradeoffs. x 2. x 2 =Income (Things). Lots of stuff. —. What else do we need in order to build a theory that is useful for analyzing decisions such as these?. ?. —. (An “Endowment”). —. x 1 =Time (Leisure). 24 hrs. Budget Constraints. x 2. Budget Line (efficient

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Modeling Tradeoffs

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  1. Modeling Tradeoffs x2 x2=Income (Things) Lots of stuff — What else do we need in order to build a theory that is useful for analyzing decisions such as these? ? — (An “Endowment”) — x1 =Time (Leisure) 24 hrs.

  2. Budget Constraints x2 Budget Line (efficient consumption) Feasible consumption set x1

  3. Budget Constraints Price Changes Income Changes

  4. Modeling Preferences • Fundamental axioms: 1. Completeness Necessary for rank ordering and functional representation. 2. Transitivity 3. Continuity • Supplemental axioms: 4. Monotonicity Defines “well-behaved preferences. 5. Convexity

  5. Indifference Curves, Preferences, and Rational Ordering — — — —

  6. Indifference Curves, Preferences, and Rational Ordering — — — —

  7. Indifference Curves and Utility 16 U = 16 8 4 U = 8 U = 4 U = 2 16 4 8

  8. Bentham and Utilitarianism “By utility is meant that property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness (all this in the present case comes to the same thing) or (what comes again to the same thing) to prevent the happening of mischief, pain, evil, or unhappiness to the party whose interest is considered … “The interest of the community then is what? -- the sum of the interests of the several members who compose it. “An action then may be said to be conformable to the principle of utility* … when the tendency it has to augment the happiness of the community is greater than any it has to diminish it.” An Introduction to the Principles of Morals and Legislation, 1780 *Elsewhere, the greatest happiness principle. Jeremy Bentham 1748 – 1832

  9. Individual Demand D

  10. Substitution & Income Effects: Normal Good The Slutsky Approach – “Pivot and Shift” Price Decrease for x1 (p1↓) A B A’ SE IE

  11. Substitution & Income Effects: Normal Goods The Slutsky Approach – “Pivot and Shift” x1 (p1, p2, m) = 10 + m/10p1 p10 = 3 p11 = 2 m0 = 120 Original Demand (A): {x10, x20} = {14, 78} Compensated Income, m’ = 106 Compensated Demand (A’): {x1’, x2’} = {15.3, 75.4} B New Demand (B): {x11, x21} = {16, 88} 88 A SE 78 A’ 75.4 IE 14 16 15.3 1.3 = SE IE = 0.7

  12. Substitution & Income Effects: x1,Normal Good; x2, Inferior Good The Slutsky Approach – “Pivot and Shift” SE A A’ IE B SE IE

  13. Substitution & Income Effects: Inferior Good The Slutsky Approach – “Pivot and Shift” Price Decrease for x1 (p1↓) B A A’ SE IE

  14. Substitution & Income Effects: Giffen Good Slutsky Approach – “Pivot and Shift” Price Decrease for x1 (p1↓) B A A’ SE IE

  15. Substitution & Income Effects: Normal Good The Hicksian Approach – “Rotate and Shift” Price Decrease for x1 (p1↓) A B A’ SE IE

  16. Buying & Selling Initial Endowment Net Demander of good Initial Endowment Net Supplier of good Net Demander of good Net Supplier of good

  17. Buying and Selling: Consumer Choice Theory with Endowments Decomposition of effects of a price change into substitution, ordinary income and endowment income effects: Price decrease of a good currently being demanded. The value of the agent’s endowment is dependent upon the price of x1; thus, when its price falls, the agent’s purchasing power goes down – the endowment income effect is negative. The agent is a net demander of x1; thus, when its price falls, the agent’s purchasing power goes up – the ordinary income effect is positive. • • • • • SE OIE EIE

  18. Buying and Selling: Consumer Choice Theory with Endowments Decomposition of effects of a price change into substitution, ordinary income and endowment income effects: Price increase of a good currently being demanded. The value of the agent’s endowment is dependent upon the price of x1; thus, when its price increases, the agent’s purchasing power goes up – the endowment income effect is positive. The agent is a net demander of x1; thus, when its price increases, the agent’s purchasing power goes down – the ordinary income effect is negative. • • • • • SE OIE EIE

  19. Buying and Selling: Consumer Choice Theory with Endowments Decomposition of effects of a price change into substitution, ordinary income and endowment income effects: Price decrease of a good currently being supplied. • • • • • SE OIE EIE

  20. Buying and Selling: Consumer Choice Theory with Endowments Decomposition of effects of a price change into substitution, ordinary income and endowment income effects: Price increase of a good currently being supplied. • • • • • SE OIE EIE

  21. Buying and Selling: Consumer Choice Theory with Endowments Decomposition of effects of a price change into substitution, ordinary income and endowment income effects: Price increase of a good currently being supplied. An outcome illustrating perfectly inelastic demand for x1 … • • • • • SE OIE EIE

  22. Labor-leisure tradeoffs and labor supply = consumption, c C0 + (w/p)L0 A • c0 E • C0 = leisure, l l0 L0 Leisure Labor

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