Lecture Notes: Budget Set and Budget Constraint

Introduction

• Topic: Understanding budget set and budget constraint.
• Objective: Derive the budget constraint and set graphically, and analyze changes with variations in prices and income.

Intuitive Example: Bill's Scenario

• Bill's Budget: $20
• Items:
  • Cookies: $2 each
  • Coffee Mugs: $4 each
• Objective: Determine affordable bundles of cookies and coffee mugs.

Bundles Considered

1. Basket 1:

   • 4 cookies, 4 mugs
   • Cost: $24 ($8 on cookies + $16 on mugs)
   • Conclusion: Not affordable

2. Basket 2:

   • 3 cookies, 3 mugs
   • Cost: $18 ($6 on cookies + $12 on mugs)
   • Conclusion: Affordable, within budget set (not all money spent)

3. Basket 3:

   • 2 cookies, 4 mugs
   • Cost: $20 ($4 on cookies + $16 on mugs)
   • Conclusion: On budget constraint (all money spent)

Definitions

• Budget Set: All affordable bundles, not requiring all money to be spent.
• Budget Constraint: Bundles that are just barely affordable (all money is spent).

Graphical Representation

• Budget Constraint Line: Shows combinations of goods that are just affordable.
• Budget Set: Area under the budget constraint line where bundles can be affordable without using all the budget.
• Non-Affordable Zone: Area outside budget constraint line.

Slope of the Budget Constraint

• Slope: Represents trade-off between goods.
• Example: Negative slope of -2/1 indicates giving up 1 coffee mug gains 2 cookies.
• Equation: ( P_M \times M + P_C \times C \leq 20 )
  • ( P_M ): Price of mugs, ( P_C ): Price of cookies

Effects of Price and Income Changes

• Increased Wealth to $24:

  • Basket 1 becomes affordable (on budget constraint)
  • Basket 2 and 3 remain in budget set
  • Basket 4 remains unaffordable

• Halving Price of Coffee Mugs:

  • New price: $2
  • Basket 1 enters budget set
  • Basket 4 moves to budget constraint

• Increasing Cookie Price to $4:

  • Basket 1, 2, 3, and 4 become unaffordable
  • Basket 5 enters budget constraint

Graphical Shifts

• Increased Wealth: Shifts budget constraint outward, parallel to the original.
• Price Changes:
  • Decreased Price of Coffee Mugs: Extends budget constraint outward, increasing affordable bundles.
  • Increased Price of Cookies: Budget constraint shifts inward, reducing affordable bundles.

Conclusion

• Implications: Changes in income and prices affect the budget constraint's position and slope, impacting affordable choices.
• Call to Action: Feedback and engagement encouraged for better understanding.