Consumer Surplus
• We have defined
Consumer Surplus
in terms of demand
curves.
• Can we provide a
formal definition inP
terms of utility
functions?
Consumer Surplus and
Indifference Curves
Managerial Economics-Charles W. Upton
D
Consumer Surplus and
Indifference Curves
A Formal Definition
Q
A Formal Definition
X
X
Budget
Xo
Xo
Widgets
Widgets
Consumer Surplus and
Indifference Curves
Consumer Surplus and
Indifference Curves
A Formal Definition
A Formal Definition
X
X
X1
Xo
Xo
Widgets
Consumer Surplus and
Indifference Curves
Widgets
Consumer Surplus and
Indifference Curves
1
A Formal Definition
The Equation
X
• A consumer has income of xo
X1
Xo
Consumer Surplus =
X1 - Xo
Widgets
Consumer Surplus and
Indifference Curves
Consumer Surplus and
Indifference Curves
The Equation
• A consumer has income of xo
• He gets the chance to purchase at a price p o
• He purchases q o
The Equation
•
•
•
•
•
A consumer has income of xo
He gets the chance to purchase at a price p o
He purchases q o
Let his utility function be U(X, q)
∆ defines consumer surplus
U(xo -poqo , qo ) = U(xo +∆, 0)
Consumer Surplus and
Indifference Curves
Consumer Surplus and
Indifference Curves
The Equation
The Equation
U(xo-poqo, qo) = U(xo +∆, 0)
U(xo-poqo, qo) = U(xo +∆, 0)
Units of
good
purchased
Consumer Surplus and
Indifference Curves
Amount to Units of
spend on
good
other
purchased
goods.
Consumer Surplus and
Indifference Curves
2
The Equation
U(xo-poqo, qo) = U(xo +∆, 0)
Amount to Units
ofthat would
Dollars
spend on
good an equal
represent
other
purchased
increase in utility.
goods.
Consumer Surplus and
Indifference Curves
One of a Kind
• A consumer has income of xo
• He gets the chance to buy a one of a kind
item for p o
• His Utility Function is
U(x,N)
X = Dollars spend on
everything but the item
Consumer Surplus and
Indifference Curves
An Application
• A consumer has income of xo
• He gets the chance to buy a one of a kind
item
• Let
One of a Kind
• A consumer has income of xo
• He gets the chance to buy a one of a kind
item for p o
• His Utility Function is
U(x,N)
Consumer Surplus and
Indifference Curves
One of a Kind
• A consumer has income of xo
• He gets the chance to buy a one of a kind
item for p o
• His Utility Function is
U(x,N)
X = Dollars spend on
everything but the item
N= 0 (doesn’t buy)
N=1 (buys)
Consumer Surplus and
Indifference Curves
Willingness to Pay
• A consumer has income of xo
• He gets the chance to a buy a one of a kind
item
U(xo -po , 1) = U(xo +∆, 0)
• ∆ defines consumer surplus
Consumer Surplus and
Indifference Curves
Consumer Surplus and
Indifference Curves
3
Willingness to Pay
• A consumer has income of xo
• He gets the chance to a buy a one of a kind
item
• Let
U(xo - θ, 1) = U(xo , 0)
A Comparison
Consumer Surplus
U(xo -po , 1) =
U(xo +∆, 0)
• θ defines the maximum amount he is
willing to pay
Consumer Surplus and
Indifference Curves
A Comparison
Consumer Surplus
U(xo -po , 1) =
U(xo +∆, 0)
Willingness to Pay
U(xo - θ, 1) =
U(xo , 0)
Consumer Surplus and
Indifference Curves
A Comparison
Consumer Surplus
U(xo -po , 1) =
U(xo +∆, 0)
Willingness to Pay
U(xo - θ, 1) =
U(xo , 0)
∆ + po ≠ θ
Consumer Surplus and
Indifference Curves
A Comparison
Consumer Surplus
U(xo -po , 1) =
U(xo +∆, 0)
Willingness to Pay
U(xo - θ, 1) =
U(xo , 0)
∆ + po ≅ θ
Consumer Surplus and
Indifference Curves
Consumer Surplus and
Indifference Curves
A Comparison
Consumer Surplus
U(xo -po , 1) =
Willingness to Pay
U(xo - θ, 1) =
U(x , 0)
U(xo +∆, 0)
Suppose I amo
given a rare
beautiful painting.
Consumer Surplus and
Indifference Curves
4
A Comparison
Consumer Surplus
U(xo -po , 1) =
Willingness to Pay
U(xo - θ, 1) =
U(x , 0)
U(xo +∆, 0)
Significant o
consumer surplus.
Consumer Surplus and
Indifference Curves
A Comparison
Consumer Surplus
U(xo -po , 1) =
Willingness to Pay
U(xo - θ, 1) =
But0)wouldU(x
I be , 0)
U(xo +∆,
o
willing to pay that
much?
Consumer Surplus and
Indifference Curves
End
©2003 Charles
W. Upton
Consumer Surplus and
Indifference Curves
5