II. Budget constraint
- Economic theory of consumer = consumer choosing best bundle (=
consumer’s preferences) of affordable (= budget constraint) goods
II. a. Introduction & definitions
- Consumption choice set = collection of all consumption choices available to
consumer
- Consumption choice constrained by different factors/resource limitations (i.e.,
budget, time, calories etc.)
- Consumption bundle containing x1 units of commodity 1, x2 units of commodity
2… until xn units of commodity n vector x = (x1, x2, …, xn)
- Consumption bundle x = (x1, x2) with vector of commodity prices p = (p1, p2)
Consumption bundle x affordable at vector of prices p if
x1p1 + x2p2 ≤ M
with M = consumer’s disposable income
- Budget set = set of all affordable bundles
- Budget line = line connecting all consumption bundles on which whole budget
spent
x1p1 + x2p2 = M
- Composite-good interpretation: two-dimension space with x 1 = single good &
x2 = every other good/money for buying other goods
o Good 2 = composite good with price p2 = 1
II. b. The budget constraint equation
- Budget constraint equation
M p1
p1 x 1 + p2 x 2=M ⇒ x 2= − x
p2 p2 1
- Budget line slope
−p 1
p2
, - Slope of budget line measuring opportunity cost of consuming good 1
- Case of increasing consumption of good 1 by Δx 1
p1 Δ x 1+ p2 Δ x 2=0
− p1
Δ x 2= Δ x1
p2
So, if Δ x 1 >0 then Δ x 2 <0
- Budget line defined by two prices & one income with one redundant variable
- Interpretation: setting one of prices to 1 numeraire price (= price relative to
which measuring other prices & income)
II. c. Variations in the variables of the budget constraint equation
1) Income increase
- Increase in income (M) outward parallel shift of budget line
- ≠ change in slope of line
2) Price increase
- Increase in p1 with p2 & M remaining same good 1 = relatively more
expensive (= possibility of buying smaller quantity with same income)
p1
budget line rotating inward along x 1 axis slope value increasing from to
p2
p '1
p2
- Economic theory of consumer = consumer choosing best bundle (=
consumer’s preferences) of affordable (= budget constraint) goods
II. a. Introduction & definitions
- Consumption choice set = collection of all consumption choices available to
consumer
- Consumption choice constrained by different factors/resource limitations (i.e.,
budget, time, calories etc.)
- Consumption bundle containing x1 units of commodity 1, x2 units of commodity
2… until xn units of commodity n vector x = (x1, x2, …, xn)
- Consumption bundle x = (x1, x2) with vector of commodity prices p = (p1, p2)
Consumption bundle x affordable at vector of prices p if
x1p1 + x2p2 ≤ M
with M = consumer’s disposable income
- Budget set = set of all affordable bundles
- Budget line = line connecting all consumption bundles on which whole budget
spent
x1p1 + x2p2 = M
- Composite-good interpretation: two-dimension space with x 1 = single good &
x2 = every other good/money for buying other goods
o Good 2 = composite good with price p2 = 1
II. b. The budget constraint equation
- Budget constraint equation
M p1
p1 x 1 + p2 x 2=M ⇒ x 2= − x
p2 p2 1
- Budget line slope
−p 1
p2
, - Slope of budget line measuring opportunity cost of consuming good 1
- Case of increasing consumption of good 1 by Δx 1
p1 Δ x 1+ p2 Δ x 2=0
− p1
Δ x 2= Δ x1
p2
So, if Δ x 1 >0 then Δ x 2 <0
- Budget line defined by two prices & one income with one redundant variable
- Interpretation: setting one of prices to 1 numeraire price (= price relative to
which measuring other prices & income)
II. c. Variations in the variables of the budget constraint equation
1) Income increase
- Increase in income (M) outward parallel shift of budget line
- ≠ change in slope of line
2) Price increase
- Increase in p1 with p2 & M remaining same good 1 = relatively more
expensive (= possibility of buying smaller quantity with same income)
p1
budget line rotating inward along x 1 axis slope value increasing from to
p2
p '1
p2
