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Revenue and
Profit
Revenue
• Defining total, average and marginal
revenue
– TR = P × Q
– AR = TR / Q
– MR = TR / Q
• Revenue curves when firms are price
takers (horizontal demand curve)
– average revenue (AR)
– marginal revenue (MR)
S
AR, MR (£)
Price (£)
Deriving a firm’s AR and MR: price-taking firm
Pe
D
O
Q (millions)
(a) The market
O
Q (hundreds)
(b) The firm
S
AR, MR (£)
Price (£)
Deriving a firm’s AR and MR: price-taking firm
D = AR
= MR
Pe
D
O
Q (millions)
(a) The market
O
Q (hundreds)
(b) The firm
Revenue
• Defining total, average and marginal
revenue
– TR = P × Q
– AR = TR / Q
– MR = TR / Q
• Revenue curves when firms are price
takers (horizontal demand curve)
– average revenue (AR)
– marginal revenue (MR)
– total revenue (TR)
Total revenue for a price-taking firm
Quantity Price = AR
(units) = MR (£)
6000
0
200
400
600
800
1000
1200
TR (£)
5000
4000
3000
5
5
5
5
5
5
5
2000
1000
0
0
200
400
600
Quantity
800
1000
1200
Total revenue for a price-taking firm
Quantity Price = AR
(units) = MR (£)
6000
0
200
400
600
800
1000
1200
TR (£)
5000
4000
3000
5
5
5
5
5
5
5
TR
(£)
0
1000
2000
3000
4000
5000
6000
2000
1000
0
0
200
400
600
Quantity
800
1000
1200
Total revenue for a price-taking firm
Quantity Price = AR
(units) = MR (£)
6000
0
200
400
600
800
1000
1200
TR (£)
5000
4000
3000
5
5
5
5
5
5
5
TR
TR
(£)
0
1000
2000
3000
4000
5000
6000
2000
1000
0
0
200
400
600
Quantity
800
1000
1200
Total revenue for a price-taking firm
TR
6000
TR (£)
5000
4000
3000
2000
1000
0
0
200
400
600
Quantity
800
1000
1200
Revenue
• Revenue curves when price varies
with output (downward-sloping
demand curve)
– average revenue (AR)
– marginal revenue (MR)
AR and MR curves for a firm facing a downward-sloping
demand curve
Q P =AR
(units) (£)
8
1
7
2
6
3
5
4
4
5
3
6
2
7
8
AR, MR (£)
6
4
2
AR
0
1
-2
-4
2
3
4
5
6
7
Quantity
AR and MR curves for a firm facing a downward-sloping
demand curve
Q P =AR
(units) (£)
8
1
7
2
6
3
5
4
4
5
3
6
2
7
8
AR, MR (£)
6
4
2
TR MR
(£) (£)
8
6
14
4
18
2
20
0
20
-2
18
-4
14
AR
0
1
2
3
4
5
6
7
-2
-4
MR
Quantity
Revenue
• Revenue curves when price varies
with output (downward-sloping
demand curve)
– average revenue (AR)
– marginal revenue (MR)
– total revenue (TR)
TR curve for a firm facing a downward-sloping D curve
20
16
Quantity P = AR
(units)
(£)
TR (£)
12
1
2
3
4
5
6
7
8
4
TR
(£)
8
7
6
5
4
3
2
8
14
18
20
20
18
14
5
6
0
0
1
2
3
4
Quantity
7
TR curve for a firm facing a downward-sloping D curve
20
16
Quantity P = AR
(units)
(£)
TR (£)
12
1
2
3
4
5
6
7
8
4
TR
TR
(£)
8
7
6
5
4
3
2
8
14
18
20
20
18
14
5
6
0
0
1
2
3
4
Quantity
7
Revenue
• Revenue curves when price varies
with output (downward-sloping
demand curve)
– average revenue (AR)
– marginal revenue (MR)
– total revenue (TR)
– revenue curves and price elasticity of
demand
AR and MR curves for a firm facing a downward-sloping
demand curve
8
Elastic
Elasticity = -1
AR, MR (£)
6
4
Inelastic
2
AR
0
1
2
3
4
5
6
7
-2
-4
MR
Quantity
TR curve for a firm facing a downward-sloping D curve
Elasticity = -1
20
16
TR
TR (£)
12
8
4
0
0
1
2
3
4
Quantity
5
6
7
Revenue
• Revenue curves when price varies
with output (downward-sloping
demand curve)
– average revenue (AR)
– marginal revenue (MR)
– total revenue (TR)
– revenue curves and price elasticity of
demand
• Shifts in revenue curves
Profit Maximisation
• Using total curves
– maximising the difference between TR
and TC
Finding maximum profit using total curves
24
TR, TC, TP (£)
20
16
12
8
4
0
1
-4
-8
2
3
4
5
6
7
Quantity
Finding maximum profit using total curves
24
TR, TC, TP (£)
20
16
TR
12
8
4
0
1
-4
-8
2
3
4
5
6
7
Quantity
Finding maximum profit using total curves
TC
24
TR, TC, TP (£)
20
16
TR
12
8
4
0
1
-4
-8
2
3
4
5
6
7
Quantity
Profit Maximisation
• Using total curves
– maximising the difference between TR
and TC
– the total profit curve
Finding maximum profit using total curves
TC
24
TR, TC, TP (£)
20
16
TR
12
8
4
0
1
2
3
4
5
6
-4
-8
TP
7
Quantity
Finding maximum profit using total curves
TC
24
b
TR, TC, TP (£)
20
16
TR
a
12
8
4
c
0
1
d
2
3
4
5
6
-4
-8
TP
7
Quantity
TR, TC, TP (£)
Finding maximum profit using total curves
24
22
20
18
16
14
12
10
8
6
4
2
0
-2
-4
-6
-8
TC
d
TR
e
f
1
2
3
4
5
6
TP
7
Quantity
Profit Maximisation
• Using total curves
– maximising the difference between TR
and TC
– the total profit curve
• Using marginal and average curves
Profit Maximisation
• Using total curves
– maximising the difference between TR
and TC
– the total profit curve
• Using marginal and average curves
– stage 1:
profit maximised where MR = MC
Finding the profit-maximising output using marginal curves
16
Costs and revenue (£)
12
8
4
0
1
-4
2
3
4
5
6
7
Quantity
Finding the profit-maximising output using marginal curves
16
MC
Costs and revenue (£)
12
8
4
0
1
-4
2
3
4
5
6
7
Quantity
Finding the profit-maximising output using marginal curves
16
MC
Costs and revenue (£)
12
8
4
Profit-maximising
output
e
0
1
-4
2
3
4
5
6
7
MR
Quantity
Profit Maximisation
• Using total curves
– maximising the difference between TR
and TC
– the total profit curve
• Using marginal and average curves
– stage 1:
profit maximised where MR = MC
– stage 2:
using AR and AC curves to measure
maximum profit
Measuring the maximum profit using average curves
16
MC
Costs and revenue (£)
12
8
4
0
1
-4
2
3
4
5
6
7
MR
Quantity
Measuring the maximum profit using average curves
16
MC
Costs and revenue (£)
12
8
4
AR
0
1
-4
2
3
4
5
6
7
MR
Quantity
Measuring the maximum profit using average curves
16
MC
Total profit =
£1.50 x 3 = £4.50
Costs and revenue (£)
12
AC
8
a
6.00
TOTAL PROFIT b
4.50
4
AR
0
1
-4
2
3
4
5
6
7
MR
Quantity
Profit Maximisation
• Some qualifications
– long-run profit maximisation
– the meaning of 'profit'
• What if a loss is made?
– loss minimising:
still produce where MR = MC
Loss-minimising output
MC
Costs and revenue (£)
AC
AC
LOSS
AR
AR
O
Q
MR
Quantity
Profit Maximisation
• Some qualifications
– long-run profit maximisation
– the meaning of 'profit'
• What if a loss is made?
– loss minimising:
still produce where MR = MC
– short-run shut-down point:
P = AVC
Costs and revenue (£)
The short-run shut-down point
AC
AVC
P=
AVC
AR
O
Q
Quantity
Profit Maximisation
• Some qualifications
– long-run profit maximisation
– the meaning of 'profit'
• What if a loss is made?
– loss minimising:
still produce where MR = MC
– short-run shut-down point:
P = AVC
– long-run shut-down point:
P = LRAC