INTERMIC_LPPT_Ch2_Student.Businesssº12324

Business

1. CHAPTER 2 Budget Constraint Copyright © 2019 Hal R. Varian

2. Consumption Choice Sets A is the collection of all consumption choices available to the consumer. What constrains consumption choice? , , and other limitations. Copyright © 2019 Hal R. Varian

3. Budget Constraints – 1 A containing x 1 units of commodity 1, x 2 units of commodity 2, and so on up to x n units of commodity n is denoted by the vector ( x 1 , x 2 , . . . , x n ). For two goods, the consumption bundle is . Commodity prices are denoted by the vector ( p 1 , p 2 , . . . , p n ). For two goods, the price vector is . Copyright © 2019 Hal R. Varian

4. Budget Constraints – 2 When is a bundle ( x 1 , . . . , x n ) affordable at prices ( p 1 , . . . , p n )? When where m is the consumer’ s (disposable) . For 2 goods, ` Copyright © 2019 Hal R. Varian

5. Budget Constraints – 3 The bundles that are only just affordable form the consumer’ s . This is the set and Copyright © 2019 Hal R. Varian

6. Budget Constraints – 4 The consumer’ s is the set of all affordable bundles; and The budget constraint is the upper boundary of the budget set. Copyright © 2019 Hal R. Varian

7. Budget Set and Constraint for Two Commodities – 1 Copyright © 2019 Hal R. Varian

8. Budget Set and Constraint for Two Commodities – 2 Copyright © 2019 Hal R. Varian

9. Budget Set and Constraint for Two Commodities – 3 Copyright © 2019 Hal R. Varian

10. Budget Constraints – 5 If there are THREE goods, what do the budget constraint and the budget set look like? Copyright © 2019 Hal R. Varian

11. Budget Constraint for Three Commodities Copyright © 2019 Hal R. Varian

12. Budget Set for Three Commodities Copyright © 2019 Hal R. Varian

13. Budget Constraints – 6 For n = 2 and x 1 on the horizontal axis, the constraint’ s slope is – p 1 / p 2 . What does it mean? Increasing x 1 by 1 must reduce x 2 by . The opportunity cost of an extra unit of commodity 1 is . Copyright © 2019 Hal R. Varian

14. Budget Constraints – 7 Copyright © 2019 Hal R. Varian

15. Budget Sets & Constraints: Income and Price Changes The budget constraint and budget set depend upon . What happens as prices or income change? Copyright © 2019 Hal R. Varian

16. How Do the Budget Set & Constraint Change as Income m Changes? Copyright © 2019 Hal R. Varian

17. Higher Income Gives More Choice Copyright © 2019 Hal R. Varian

18. Lower Income Shrinks the Budget Set Copyright © 2019 Hal R. Varian

19. Budget Constraints: Income Changes – 1 Increases in income m the constraint in a manner, thereby the budget set and choice. Decreases in income m the constraint in a manner, thereby the budget set and choice. Copyright © 2019 Hal R. Varian

20. Budget Constraints: Income Changes – 2 No original choice is lost and new choices are added when income increases, so higher income cannot make a consumer . An income may (typically will) make the consumer worse off. Copyright © 2019 Hal R. Varian

21. Budget Constraints: Price Changes – 1 What happens if just one price decreases? Suppose p 1 decreases. Copyright © 2019 Hal R. Varian

22. How Do the Budget Set & Constraint Change as p 1 D ecreases from p 1 ʹ to p 1 ʺ ? – 1 Copyright © 2019 Hal R. Varian

23. How Do the Budget Set & Constraint Change as p 1 D ecreases from p 1 ʹ to p 1 ʺ ? – 2 Copyright © 2019 Hal R. Varian

24. Budget Constraints: Price Changes – 2 Reducing the price of one commodity the constraint . No old choice is lost and new choices are added, so reducing one price cannot make the consumer . Similarly, increasing one price the constraint , choice and may (typically will) make the consumer . Copyright © 2019 Hal R. Varian

25. Uniform Ad Valorem Sales Taxes – 1 An ad valorem sales tax levied at a rate of 5% increases all prices by 5%, from p to ( 1 + . 05) p = 1 . 05 p . An ad valorem sales tax levied at a rate of t increases all prices by tp from p to . A uniform sales tax is applied uniformly to all commodities. Copyright © 2019 Hal R. Varian

26. Uniform Ad Valorem Sales Taxes – 2 A uniform sales tax levied at rate t changes the constraint from to . Or equivalently, = . Copyright © 2019 Hal R. Varian

27. Uniform Ad Valorem Sales Taxes – 3 Copyright © 2019 Hal R. Varian

28. Uniform Ad Valorem Sales Taxes – 4 Copyright © 2019 Hal R. Varian

29. The Food Stamp Program – 1 Food stamps are coupons that can be legally exchanged only for food. How does a commodity-specific gift such as a food stamp alter a family’ s budget constraint? Copyright © 2019 Hal R. Varian

30. The Food Stamp Program – 2 Suppose and the price of “ other goods ” is The budget constraint is then . Copyright © 2019 Hal R. Varian

31. The Food Stamp Program – 3 Copyright © 2019 Hal R. Varian

32. The Food Stamp Program – 4 Copyright © 2019 Hal R. Varian

33. Budget Constraints: Relative Prices – 1 “ Numeraire ” means “ .” Suppose prices and income are measured in dollars. Say Then the constraint is: . Copyright © 2019 Hal R. Varian

34. Budget Constraints: Relative Prices – 2 If prices and income are measured in cents, then and the constraint is , the same as Changing the numeraire changes . Copyright © 2019 Hal R. Varian

35. Budget Constraints: Relative Prices – 3 The constraint for p 1 = 2, p 2 = 3, m = 12 is also the constraint for p 1 = 1 , p 2 = , m = . Setting p 1 = 1 makes commodity 1 the numeraire and defines all prices relative to p 1 . E.g., 3 /2 is the price of commodity 2 relative to the price of commodity 1. Copyright © 2019 Hal R. Varian

36. Budget Constraints: Relative Prices – 4 Any commodity can be chosen as the numeraire without changing the budget set or the budget constraint. Copyright © 2019 Hal R. Varian

37. Budget Constraints: Relative Prices – 5 Suppose p 1 = 2, p 2 = 3, and p 3 = 6. Price of commodity 2 relative to commodity 1 is , price of commodity 3 relative to commodity 1 is . Relative prices are the of commodities 2 and 3 for units of commodity 1. Copyright © 2019 Hal R. Varian

38. Shapes of Budget Constraints – 1 What makes a budget constraint a straight line? A straight line has a constant slope and the constraint is So, if prices are constants then a constraint is a . Copyright © 2019 Hal R. Varian

39. Shapes of Budget Constraints – 2 But what if prices are not constants? For example, bulk buying discounts, or price penalties for buying “ too much. ” Then constraints will be . Copyright © 2019 Hal R. Varian

40. Shapes of Budget Constraints: Quantity Discounts Suppose p 2 is constant at $1 but that p 1 = $2 for £ x 1 £ 20 and p 1 = $1 for x 1 > 20. Then the constraint’ s slope is: = , for and = , for Copyright © 2019 Hal R. Varian

41. Shapes of Budget Constraints with a Quantity Discount – 1 Copyright © 2019 Hal R. Varian

42. Shapes of Budget Constraints with a Quantity Discount – 2 Copyright © 2019 Hal R. Varian

43. Shapes of Budget Constraints with a Quantity Penalty Copyright © 2019 Hal R. Varian

44. Shapes of Budget Constraints: One Price Negative – 1 Commodity 1 is stinky garbage. You are paid $2 per unit to accept it; i.e., Income, other than from accepting commodity 1 ,is Then the constraint is or Copyright © 2019 Hal R. Varian

45. Shapes of Budget Constraints: One Price Negative – 2 Copyright © 2019 Hal R. Varian

46. Shapes of Budget Constraints: One Price Negative – 3 Copyright © 2019 Hal R. Varian

47. More General Choice Sets Choices are usually constrained by more than a budget; e.g., time constraints and other resources constraints. A bundle is available only if it meets constraint. Copyright © 2019 Hal R. Varian

48. Credits This concludes the Lecture PowerPoint presentation for Chapter 2 of Intermediate Microeconomics, 9e. For more resources, please visit http://digital.wwnorton.com/intermicro9media . Copyright © 2019 Hal R. Varian