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Composite Goods

Composite Goods. Apples and Bananas aren’t Everything. What happens if there are more than two goods?. Apples and Bananas aren’t Everything. What happens if there are more than two goods? Suppose we are making the choice among Apples Bananas Oranges Grapefruit. Extending the Model.

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Composite Goods

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  1. Composite Goods Lectures in Microeconomics-Charles W. Upton

  2. Apples and Bananas aren’t Everything • What happens if there are more than two goods? Composite Goods

  3. Apples and Bananas aren’t Everything • What happens if there are more than two goods? • Suppose we are making the choice among • Apples • Bananas • Oranges • Grapefruit Composite Goods

  4. Extending the Model • We could write U(A,B,O,G) paA +pbB + poO +pGG = Y Composite Goods

  5. Extending the Model • We could write U(A,B,O,G) paA +pbB + poO +pGG = Y • This is madness. The graphs get too complicated, even worse when we think about extending to many different goods Composite Goods

  6. The Composite Good • Let X be the amount we spend on all other goods. Composite Goods

  7. The Composite Good • Let X be the amount we spend on all other goods. • In this case, X = pbB + poO +pGG Composite Goods

  8. The Composite Good • Let X be the amount we spend on all other goods. • In this case, X = pbB + poO +pGG • Our Utility function is now U(X,A) Composite Goods

  9. The Composite Good • Let X be the amount we spend on all other goods. • In this case, X = pbB + poO +pGG • Our Utility function is now U(X,A) • Our budget constraint is now X + paA = Y Composite Goods

  10. An Indifference Curve Other Goods Apples I1 Composite Goods

  11. An Application • A Consumer has income of $100 a week. Peaches cost $1 each. Show graphically, how many peaches she will purchase. Composite Goods

  12. Peaches Other Goods Draw the Consumer’s Indifference Curves $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  13. Peaches Other Goods Draw the Consumer’s Indifference Curves Draw the Budget Line $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  14. Peaches Other Goods Along this budget line the MRT of peaches to other goods is 1 Draw the Consumer’s Indifference Curves Draw the Budget Line $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  15. Peaches Other Goods Draw the Consumer’s Indifference Curves Draw the Budget Line $100 Find the point of tangency $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  16. Peaches Other Goods At the point of tangency, the MRS between peaches and money spent on other goods is 1 Draw the Consumer’s Indifference Curves Draw the Budget Line $100 Find the point of tangency $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  17. She is now offered a chance to purchase peaches, from another vendor. The first 20 cost 50 cents each and others cost $1.50 each. Should she switch? A Peach of a Problem Composite Goods

  18. She is now offered a chance to purchase peaches, from another vendor. The first 20 cost 50¢ each and others cost $1.50 each. Should she switch? It is an all or nothing deal. A Peach of a Problem Composite Goods

  19. A Peach of a Problem • Some people argue that it makes no difference. Forty peaches cost $40. Composite Goods

  20. A Peach of a Problem • Some people argue that it makes no difference. Forty peaches cost $40. Nonsense! Composite Goods

  21. A Peach of a Problem • Some people argue that it makes no difference. Forty peaches cost $40. • At the old prices, MRS = MRT = $1. Composite Goods

  22. A Peach of a Problem • Some people argue that it makes no difference. Forty peaches cost $40. • But there is a difference. At the old prices, MRS = MRT = $1. • If the consumer purchases 40 peaches, the MRS is still 1. Composite Goods

  23. A Peach of a Problem • Some people argue that it makes no difference. Forty peaches cost $40. • But there is a difference. At the old prices, MRS = MRT = $1. • If the consumer purchases 40 peaches, the MRS is still 1. The MRT is now $1.50 Composite Goods

  24. A Peach of a Problem Other Goods The new and old budget lines $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  25. A Peach of a Problem Other Goods • If the consumer buys no peaches, money for other goods is the same. Ditto for buying 40 peaches. The new and old budget lines $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  26. A Peach of a Problem Other Goods • If she purchases fewer peaches she has more for other goods. • If she purchases more than 40, she has less for other goods The new and old budget lines $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  27. A Peach of a Problem Other Goods At 40 peaches, the MRS is still 1, but the MRT is now 1.50 $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  28. A Peach of a Problem Other Goods She will buy fewer peaches At 40 peaches, the MRS is still 1, but the MRT is now 1.50 $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  29. A Peach of a Problem Other Goods Remember why: when she was buying 40 peaches, she was indifferent between a peach and $1 to spend on other goods. $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  30. A Peach of a Problem Other Goods Remember why: when she was buying 40 peaches, she was indifferent between a peach and $1 to spend on other goods. Now, she can get $1.50 to spend on other goods so she is better off! $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  31. Suppose she had been offered another deal. The first twenty would cost $1.50 and the rest 50¢. Should she take that deal? A Twist on the Peach Problem Composite Goods

  32. Suppose she had been offered another deal. The first twenty would cost $1.50 and the rest 50¢. Should she take that deal? Again this is a take it or leave it deal. A Twist on the Peach Problem Composite Goods

  33. A Twist on the Peach Problem Other Goods The new and old budget lines $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  34. A Twist on the Peach Problem Other Goods • If the consumer buys no peaches, money for other goods is the same. Ditto for buying 40 peaches. The new and old budget lines $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  35. A Twist on the Peach Problem Other Goods • If she purchases fewer peaches she has more less for other goods. • If she purchases more than 40, she has less more for other goods. The new and old budget lines $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  36. A Twist on the Peach Problem Other Goods She will buy more and be better off. $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  37. The Simple Moral Other Goods As long as the MRT and MRS are unequal, it pays to change consumption. $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  38. The Simple Moral Other Goods Utility Maximization requires that the MRS = MRT (price) As long as the MRT and MRS are unequal, it pays to change consumption. $100 $80 $60 $40 $20 Peaches I1 Composite Goods 60 80 100 20 40

  39. End ©2004 Charles W. Upton Composite Goods

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