Total Revenue, Average Revenue
and Marginal Revenue
• Wealth-maximizing
• Each seller has sufficient market power to
set the selling price higher and sell less OR
set the selling price lower and sell more
• The demand curve facing the price searcher
is downward sloping
Total Revenue, Average Revenue
and Marginal Revenue
• Total revenue ( TR ) is the total amount of
money(or some other good) that a firm
receives from the sale of its goods. It the
firm practices single pricing rather than
price discrimination, TR = total expenditure
of the consumer = P x Q
Total Revenue, Average Revenue
and Marginal Revenue
• Average revenue ( AR ) is the total amount
of money(or some other good) that a firm
receives from the sale divided by the
number of units of goods sold.
• AR = TR/Q, since TR=P x Q, then AR = P
for single pricing practice
• And since MUV = DD = P, then
• MUV = DD = P = AR
Total Revenue, Average Revenue
and Marginal Revenue
• Marginal revenue ( MR ) is the change in
total revenue resulting from selling an extra
unit of goods.
• MR = TR/Q, where TR = change in TR
due to change in Q, Q = change in Q
To find T R from the M R curve
• For a certain known quantity transacted, the
area under the MR and above the horizontal
axis is the T R . (I.e. the sum of the Marginal
Revenues of all units of goods.)
• The slope of the TR curve is MR. Why?
• And, MR is always smaller Price for single
pricing arrangement (I.e. MR < P) Why?
(Hint MR<AR, AR=P for single pricing)
Price
A
For a certain known quantity transacted, the area under the
MR and above the horizontal axis is the T R .
(I.e. the sum of the Marginal Revenues of all units of goods,
I.e. area 0ACQ)
Also, TR = AR x Q, I.e. area 0PBQ
B
P
C
MR
0
Q
AR
Quantity
The slope of the TR curve is MR
$
Slope at point E =
MR
E
TR
slope =AR
0
The relations between TR, AR and MR
Quantity
Total Revenue, Average Revenue
and Marginal Revenue
• The slope of Marginal revenue ( MR ) is
twice the slope of AR.
• Why? (See next slide)
• (The relations between TR, AR and MR can
also be applied to TUV, AUV and MUV)
P, AR, MR
AR
MR curve
curve
=
AR
Total
TR
Revenue
MUV = DD = P = AR
Q
Quantity
P, AR, MR
AR
MR curve
curve
AR
Total
TR
Revenue
TR
=
MUV = DD = P = AR
Q
Quantity
P, AR, MR
AR
curve
=
AR
MR
curve
MUV = DD = P = AR
Q
Quantity
Total Revenue, Average Revenue
and Marginal Revenue
• The areas of the 2 triangles must be the same
for total revenue should be the same.
• The two triangles must be the same only if
the MR cuts the midpoint of the
perpendicular line drawn from the DD to the
vertical axis.
• Hence, the slope of Marginal revenue ( MR )
is twice the slope of AR.
The relationship between AR and MR
• The slope of MR is twice the slope of AR
• MR curve is not the demand curve (the
relationship between price and quantity).
• However, if the price searcher practises price
discrimination or All-or-Nothing Pricing
Arrangement, then All-or-nothing pricing =
• All-or-nothing DD = AUV , which is >
MUV , and also downward-sloping
Revision on different pricing arrangement
•
•
•
•
•
Single Pricing Arrangement
with Consumer Surplus = TUV - TEV
MUV = DD = AR = P [>MR] {<AUV}
All-or-Nothing Pricing Arrangement
All consumer surplus will be extracted, so
that TUV = TEV
• hence, All-or-Nothing DD curve =
All-or-nothing pricing = AUV {>MUV}
REVISION
Single Pricing
Arrangement
AUV
All-or-nothing Pricing
Arrangement
P
DEMAND
AUV = AR
P
MR
DEMAND
MUV = AR
Q
TUV= TEV + CS
MUV = MR
Q
TUV= TEV
A Price -Searcher = Price-Searcher’s Market
Price
MR cuts the midpoint of the perpendicular
line drawn from the AR to the vertical axis.
MR
AR
Quantity