A ToolBuilding Approach Routledge UK 2016 Samiran Banerjee Commodity Space The commodity space is the entire nonnegative quadrant Two goods case good 1 and good 2 Q ID: 801797
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Slide1
Chapter 2Budgets
Intermediate Microeconomics:
A Tool-Building Approach
Routledge
, UK
© 2016
Samiran
Banerjee
Slide2Commodity Space
The
commodity space
is the entire non-negative quadrant
• 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
Slide3Competitive 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: p1
x1 + p2x2 ≤ m
Expenditure on good 1
Expenditure on good 2
•
Budget
line
:
p
1
x1 + p2x2 = m Rewriting,
x
2
=
m
p
2
–
p
1
p
2
x1
Vertical intercept
|Slope of budget| = ratio of prices
Absolute value of the slope of the budget
Slide4Competitive budget example 1
•
p
1
= $2 per unit • p2 = $1 per unit • m = $10
Vertical intercept
Horizontal intercept
Budget line
Budget set
Slide5Competitive budget example 2
• 3 goods
• p
1
= p2 = p3 = $2 per unit • m = $20
Intercept for good 1
Intercept for good 2
Intercept for good 3
Budget “line”
(surface)
(The tetrahedron defined by the space between the budget surface and the origin is the budget set.)
Slide6Competitive budget: Change in p1
•
m
= $
10• p2 = $1 per unit • p1old
= $2 per
unit, falls to p1new = $1.25
Old budget
New budget
Slide7Competitive budget: Change in p2
•
m
= $
10• p1 = $2 per unit • p2old
= $1
per unit, rises to p2new = $2
New budget
Old budget
Slide8Competitive budget: Change in m
•
p
1
= $2 per unit• p2 = $1 per unit • mold
= $10, falls to m
new = $6
New budget
Old budget
Slide9Endowment budget
• Person
i
’s endowment:
ωi = (4, 3)• pa = $1 per unit • pb
= $2 per unit
“omega”
The value of this endowment at these prices is $10:
($1 x 4) + ($2 x 3) = $10
Slide10Endowment budget: price change
• Person
i
’s endowment:
ωi = (4, 3)• pa = $1 per unit • p
b falls from $2 per
unit to $1The value of this endowment at these prices is $7:($1 x 4) + ($1 x 3) = $7
New budget
Old budget
Budget line pivots about the endowment point!
Slide11Non-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!
Slide12Incremental price discounts
•
p
1
= $10 per unit up to 6 units• p2 = $6 per unit • m = $120
• p
1 = $6 per unit beyond 6 units• p2 = $6 per unit • m = $120
Trade off is 5 units of good 2 for 3 units of good 1
Trade off is 1 unit of good 2 for 1 unit of good 1
Slide13Buy price ≠ Sell price
•
ω
k
= (10, 10): Ms. k’s endowment of Euros and US dollars• p$ = €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
ω
k
, one dollar can be sold for €0.80. All 10 dollars can be sold for €8.
Slide14Food stamps
• Price of food:
p
1
= $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
Slide15BOGO* coupons
•
p
1
= 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
x
2
< 1 in this range
*Buy one get one