1. Chapter 2 Budgets Intermediate Microeconomics: © 2016 Samiran Banerjee
A Tool-Building Approach
Routledge, UK
© 2016 Samiran Banerjee

2. Commodity Space • Two goods case: good 1 and good 2
• Quantities are denoted by x1 and x2
• Generally assume goods are divisible
A = (4, 3) is a commodity bundle
The commodity space is the entire non-negative quadrant

3. Competitive Budgets • Main feature: Price per unit is always constant
• Per unit prices are denoted by p1 and p2
• Income is denoted by m
• Budget constraint: p1x1 + p2x2 ≤ m
Expenditure on good 1
Expenditure on good 2
• Budget line: p1x1 + p2x2 = m
Rewriting,
Absolute value of the slope of the budget
x2 = m p2 – p1 x1
Vertical intercept
|Slope of budget| = ratio of prices

4. Competitive budget example 1
• p1 = $2 per unit
• p2 = $1 per unit
• m = $10
Budget line
Vertical intercept
Budget set
Horizontal intercept

5. Competitive budget example 2
• 3 goods
• p1 = p2 = p3 = $2 per unit
• m = $20
Budget “line”
(surface)
Intercept for good 3
Intercept for good 1
Intercept for good 2
(The tetrahedron defined by the space between the budget surface and the origin is the budget set.)

6. Competitive budget: Change in p1
• p2 = $1 per unit
• p1old = $2 per unit, falls to p1new = $1.25
New budget
Old budget

7. Competitive budget: Change in p2
• p1 = $2 per unit
• p2old = $1 per unit, rises to p2new = $2
Old budget
New budget

8. Competitive budget: Change in m
• p1 = $2 per unit
• p2 = $1 per unit
• mold = $10, falls to mnew = $6
Old budget
New budget

9. Endowment budget • Person i’s endowment: ωi = (4, 3)
“omega”
• Person i’s endowment: ωi = (4, 3)
• pa = $1 per unit
• pb = $2 per unit
The value of this endowment at these prices is $10:
($1 x 4) + ($2 x 3) = $10

10. Endowment budget: price change
• Person i’s endowment: ωi = (4, 3)
• pa = $1 per unit
• pb falls from $2 per unit to $1
The value of this endowment at these prices is $7:
($1 x 4) + ($1 x 3) = $7
Old budget
New budget
Budget line pivots about the endowment point!

11. Non-Competitive Budgets
• Main feature: Price per unit is NOT always constant
• Some examples:
– price discounts on incremental purchases
– price discounts with bulk purchases
– buying and selling at different prices
– food stamps
– coupons
• Assume goods are divisible!

12. Incremental price discounts
• p1 = $10 per unit up to 6 units
• p2 = $6 per unit
• m = $120
• p1 = $6 per unit beyond 6 units
• p2 = $6 per unit
• m = $120
Trade off is 5 units of good 2 for 3 units of good 1
Trade off is 1 unit of good 2 for 1 unit of good 1

13. Buy price ≠ Sell price
• ωk = (10, 10): Ms. k’s endowment of Euros and US dollars
• p$ = €0.80 per $ (a dollar can be bought for €0.80)
• p€ = $1.25 per € (a Euro can be bought for $1.25)
Starting from ωk, one Euro can be sold for $1.25. All 10 Euros can be sold for $8.
Starting from ωk, one dollar can be sold for €0.80. All 10 dollars can be sold for €8.

14. Food stamps • Price of food: p1 = $5 per unit
• Price of clothing: p2 = $5 per unit
• m = $100
• Government provides 4 stamps (divisible): 1 stamp = 1 unit of food
Budget line without food stamps
Shaded budget set with food stamps

15. BOGO* coupons • p1 = p2 = $1 per unit • m = $10
• Buy one whole unit of good 2 and get one free
Budget line after using coupon
Cannot redeem coupon since
x2 < 1 in this range
*Buy one get one