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# Chapter 1

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### Chapter 1

1. 1. Chapter 1 Budget Constraint
2. 2. CONSUMER THEORY <ul><li>Consumer theory: consumers choose the best bundle of goods they can afford. </li></ul>
3. 3. CONSUMER THEORY <ul><li>Two parts to theory </li></ul><ul><li>1. “can afford”___ budget constraint </li></ul><ul><li>2. “best” ___ according to consumers’ preferences </li></ul>
4. 4. Budget Constraints <ul><li>consumption bundle : </li></ul><ul><li>(x 1 , x 2 , …,x n ) __ how much of each good is consumed </li></ul><ul><li>Commodity prices are p 1 , p 2 , … , p n . </li></ul><ul><li>m __ money the consumer has to spend </li></ul>
5. 5. Budget Constraints <ul><li>A bundle (x 1 , … , x n ) is affordable at prices p 1 , … , p n : </li></ul><ul><li>When p 1 x 1 + … + p n x n  m where m is the consumer’s (disposable) income. </li></ul>
6. 6. Budget Constraints <ul><li>The consumer’s budget set is the set of all affordable bundles </li></ul><ul><li>The bundles that are only just affordable form the consumer’s budget line . </li></ul>
7. 7. Budget Set and Constraint for Two Commodities x 2 x 1 p 1 x 1 + p 2 x 2 = m is x 2 = -(p 1 /p 2 )x 1 + m /p 2 so slope is -p 1 /p 2 . m /p 1 Budget Set m /p 2
8. 8. Budget Constraints <ul><li>For n = 2 and x 1 on the horizontal axis, the constraint’s slope is -p 1 /p 2 . What does it mean? </li></ul>
9. 9. Budget Sets & Constraints; Income and Price Changes <ul><li>The budget line and budget set depend upon prices and income. What happens as prices or income change? </li></ul>
10. 10. How do the budget set and budget constraint change as income m increases? Original budget set x 2 x 1
11. 11. Higher income gives more choice Original budget set New affordable consumption choices x 2 x 1 Original and new budget constraints are parallel (same slope).
12. 12. How do the budget set and budget constraint change as income m decreases? Original budget set x 2 x 1
13. 13. How do the budget set and budget constraint change as income m decreases? x 2 x 1 New, smaller budget set Consumption bundles that are no longer affordable. Old and new constraints are parallel.
14. 14. Budget Constraints - Price Changes <ul><li>What happens if just one price decreases? </li></ul><ul><li>Suppose p 1 decreases. </li></ul>
15. 15. How do the budget set and budget constraint change as p 1 decreases from p 1 ’ to p 1 ” ? Original budget set x 2 x 1 m/p 2 m/p 1 ’ m/p 1 ” -p 1 ’/p 2
16. 16. How do the budget set and budget constraint change as p 1 decreases from p 1 ’ to p 1 ” ? Original budget set x 2 x 1 m/p 2 m/p 1 ’ m/p 1 ” New affordable choices -p 1 ’/p 2
17. 17. How do the budget set and budget constraint change as p 1 decreases from p 1 ’ to p 1 ” ? Original budget set x 2 x 1 m/p 2 m/p 1 ’ m/p 1 ” New affordable choices Budget constraint pivots; slope flattens from -p 1 ’/p 2 to -p 1 ”/p 2 -p 1 ’/p 2 -p 1 ”/p 2
18. 18. Taxes, subsidies and rationing <ul><li>Quantity tax ___ tax levied on units bought : p 1 + t </li></ul><ul><li>Value tax ___ tax levied on rupees spent : p 1 + α p 1. Also known as ad valorem tax </li></ul><ul><li>3. Subsidies ___ opposite of a tax </li></ul><ul><li>a) p 1 - s </li></ul><ul><li>b) p 1 - µ p 1 </li></ul>
19. 19. Taxes, subsidies and rationing <ul><li>4. lump sum tax or subsidy __ amount of tax or subsidy independent of the consumer’s choices. Also called a head tax or a poll tax. </li></ul><ul><li>5. Rationing ___ can’t consume more than a certain amount of some good </li></ul>
20. 20. The Food Stamp Program <ul><li>Food stamps are coupons that can be legally exchanged only for food. </li></ul><ul><li>How does a commodity-specific gift such as a food stamp alter a family’s budget constraint? </li></ul>
21. 21. The Food Stamp Program <ul><li>Suppose m = \$100, p F = \$1 and the price of “other goods” is p G = \$1. </li></ul><ul><li>The budget constraint is then F + G =100. </li></ul>
22. 22. The Food Stamp Program G F 100 100 F + G = 100; before stamps.
23. 23. The Food Stamp Program G F 100 100 F + G = 100: before stamps.
24. 24. The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 40
25. 25. The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 The family’s budget set is enlarged. 40
26. 26. The Food Stamp Program <ul><li>What if food stamps can be traded on a black market for \$0.50 each? </li></ul>
27. 27. Shapes of Budget Constraints - Quantity Discounts <ul><li>Suppose p 2 is constant at \$1 but that p 1 =\$2 for 0  x 1  20 and p 1 =\$1 for x 1 >20. </li></ul>
28. 28. Shapes of Budget Constraints with a Quantity Discount m = \$100 50 100 20 80 x 2 x 1 Budget Set Budget Constraint
29. 29. Shapes of Budget Constraints with a Quantity Penalty x 2 x 1 Budget Set Budget Constraint
30. 30. Shapes of Budget Constraints - One Price Negative <ul><li>Commodity 1 is stinky garbage. You are paid \$2 per unit to accept it; i.e. p 1 = - \$2. p 2 = \$1. Income, other than from accepting commodity 1, is m = \$10. </li></ul><ul><li>constraint ? </li></ul>
31. 31. More General Choice Sets <ul><li>Choices are usually constrained by more than a budget; e.g. time constraints and other resources constraints. </li></ul><ul><li>A bundle is available only if it meets every constraint. </li></ul>
32. 32. More General Choice Sets Food Other Stuff 10 At least 10 units of food must be eaten to survive
33. 33. More General Choice Sets Food Other Stuff 10 Budget Set Choice is also budget constrained.
34. 34. More General Choice Sets Food Other Stuff 10 Choice is further restricted by a time constraint.
35. 35. More General Choice Sets So what is the choice set?
36. 36. More General Choice Sets Food Other Stuff 10
37. 37. More General Choice Sets Food Other Stuff 10
38. 38. More General Choice Sets Food Other Stuff 10 The choice set is the intersection of all of the constraint sets.