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Budget Set and Constraint for Two Commodities

Budget Set and Constraint for Two Commodities. x 2. Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 2. x 1. m /p 1. Budget Set and Constraint for Two Commodities. x 2. Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 2. the collection of all affordable bundles.

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Budget Set and Constraint for Two Commodities

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  1. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 x1 m /p1

  2. Budget Set and Constraint for Two Commodities x2 Budget constraint is p1x1 + p2x2 = m. m /p2 the collection of all affordable bundles. Budget Set x1 m /p1

  3. Budget Constraints x2 Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2. -p1/p2 +1 x1

  4. Budget Sets & Constraints; Income and Price Changes • The budget constraint and budget set depend upon prices and income. What happens as prices or income change?

  5. How do the budget set and budget constraint change as income m increases? x2 Original budget set x1

  6. Higher income gives more choice x2 New affordable consumptionchoices Original and new budget constraints are parallel (same slope). Original budget set x1

  7. Budget Constraints - Income Changes • Changes in income (holding prices constant) m shift the constraint in a parallel manner.

  8. Budget Constraints - Price Changes • What happens if just one price decreases? • Suppose p1 decreases.

  9. How do the budget set and budget constraint change as p1decreases from p1’ to p1”? x2 m/p2 New affordable choices -p1’/p2 Original budget set m/p1’ x1 m/p1”

  10. Budget Constraints - Price Changes • Reducing the price of one commodity pivots the constraint outward. No old choice is lost and new choices are added, so reducing one price cannot make the consumer worse off.

  11. Budget Constraints - Price Changes • Similarly, increasing one price pivots the constraint inwards, reduces choice and may (typically will) make the consumer worse off.

  12. The Food Stamp Program • 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?

  13. The Food Stamp Program • Suppose m = $100, pF = $1 and the price of “other goods” is pG = $1. • The budget constraint is then F + G =100.

  14. The Food Stamp Program G F + G = 100: before stamps. 100 F 100

  15. The Food Stamp Program G F + G = 100: before stamps. 100 Budget set after 40 foodstamps issued. The family’s budgetset is enlarged. F 40 100 140

  16. The Food Stamp Program • What if food stamps can be traded on a black market for $0.50 each?

  17. The Food Stamp Program G F + G = 100: before stamps. 120 Budget constraint after 40 food stamps issued. 100 Budget constraint with black market trading. F 40 100 140

  18. The Food Stamp Program G F + G = 100: before stamps. 120 Budget constraint after 40 food stamps issued. 100 Black market trading makes the budget set larger again. F 40 100 140

  19. Budget Constraints - Relative Prices • “Numeraire” means “unit of account”. • If prices and income are measured in cents, then p1=200, p2=300, m=1200 and the constraint is 200x1 + 300x2 = 1200,the same as 2x1 + 3x2 = 12.

  20. Budget Constraints - Relative Prices • Changing the numeraire changes neither the budget constraint nor the budget set. • Any commodity can be chosen as the numeraire without changing the budget set or the budget constraint.

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