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- 1. Chapter 1 Budget Constraint
- 2. CONSUMER THEORY <ul><li>Consumer theory: consumers choose the best bundle of goods they can afford. </li></ul>
- 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. 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. 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. 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. 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. 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. 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. How do the budget set and budget constraint change as income m increases? Original budget set x 2 x 1
- 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. How do the budget set and budget constraint change as income m decreases? Original budget set x 2 x 1
- 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. Budget Constraints - Price Changes <ul><li>What happens if just one price decreases? </li></ul><ul><li>Suppose p 1 decreases. </li></ul>
- 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. 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. 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. 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. 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. 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. 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. The Food Stamp Program G F 100 100 F + G = 100; before stamps.
- 23. The Food Stamp Program G F 100 100 F + G = 100: before stamps.
- 24. The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 40
- 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. The Food Stamp Program <ul><li>What if food stamps can be traded on a black market for $0.50 each? </li></ul>
- 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. Shapes of Budget Constraints with a Quantity Discount m = $100 50 100 20 80 x 2 x 1 Budget Set Budget Constraint
- 29. Shapes of Budget Constraints with a Quantity Penalty x 2 x 1 Budget Set Budget Constraint
- 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. 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. More General Choice Sets Food Other Stuff 10 At least 10 units of food must be eaten to survive
- 33. More General Choice Sets Food Other Stuff 10 Budget Set Choice is also budget constrained.
- 34. More General Choice Sets Food Other Stuff 10 Choice is further restricted by a time constraint.
- 35. More General Choice Sets So what is the choice set?
- 36. More General Choice Sets Food Other Stuff 10
- 37. More General Choice Sets Food Other Stuff 10
- 38. More General Choice Sets Food Other Stuff 10 The choice set is the intersection of all of the constraint sets.
- 39. Thank You For Feed Back [email_address] [email_address]

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