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Profit Maximization
Ed. 7: Ch. 8, pgs 264-265, pgs 277-300
Ed. 6: Ch. 8, pages 265-266, pgs 278-304
1
Profit Maximization assuming:
1. Firm must charge every consumer the same price (i.e., no price discrimination)
2. No Strategic Interaction among Firms
We will consider two industry structures: Monopoly Monopolistic Competition
2
Profit Maximization ExampleQ FC VC TC AFC AVC ATC MC
0 100 0 100 - - - 50
1 100 50 150 100 50 150
30
2 100 80 180 50 40 90
20
3 100 100 200 33.3 33.33 66.7
10
4 100 110 210 25 27.5 52.5
20
5 100 130 230 20 26 463
Q FC VC TC AFC AVC ATC MC
5 100 130 230 20 26 46
30
6 100 160 260 16.7 26.67 43.3
40
7 100 200 300 14.3 28.57 42.9
50
8 100 250 350 12.5 31.25 43.8
60
9 100 310 410 11.1 34.44 45.6
70
10 100 380 480 10 38 48 4
Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue (MR) for each unit the firm sells is $55? What are these profits?
8 55*8-43.75*8=90
5
Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue for each unit the firm sells is $35? What are these profits?
6 35*6-43.33*6=-50
Produce an output of 6 in short-run if fixed costs are sunk.
6
Q AFC AVC ATC MC 0 - - - 50
1 100.00 50.00 150.00 30
2 50.00 40.00 90.00 20
3 33.33 33.33 66.67 10
4 25.00 27.50 52.50 20
5 20.00 26.00 46.00 30
6 16.67 26.67 43.33 40
7 14.29 28.57 42.86 50
8 12.50 31.25 43.75 60
9 11.11 34.44 45.56 70
10 10.00 38.00 48.00
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10
Q
$/Q
MC
ATC
AVC
AFC
What output maximizes profits if the marginal revenue for each unit the firm sells is $25? What are these profits?
5? 25*5-46*5=-105
Better off producing 0 so profits=-FC=-100 7
Short-Run Profit Maximizing Rule
Produce at an Output where
Marginal Revenue = Marginal Cost
(MR) (MC)
if Total Revenue > Variable Cost
[When the firm cannot price discriminate, this is the same thing as saying as long as
Price > AVC (from P*Q > AVC*Q) ]
8
Monopoly Characteristics
1. There is a single seller
2. There are no close substitutes for the good
3. There are extremely high barriers to entry
9
Natural Monopoly (type of monopoly where there exists large economies of scale)
Quantity0
$/unit
Long Run Average Total Cost
ATCone big firm
ATC1/2 big firm
Qbig firmQ1/2 big firm
when a single firm can supply a
good or service to an entire
market at a smaller cost than could
two or more firms.
10
Monopolist Marginal Revenue (with no price discrimination)
P Q TR MR
10 0 0
9 1 9
8 2 16
7 3 21
6 4 24
5 5 25
4 6 24
3 7 21
2 8 16
1 9 9
0 10 0
+7+5+3
+1-1-3-5-7-9
Q
TRMR
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
D
+9
MR
Q
Note that Marginal Revenue for a given unit is plotted at the midpoint of that unit.11
Use Calculus to Obtain MR curve for Linear
Demand Curve Demand Curve:
P=a-bQ TR = (a-bQ)Q =aQ-bQ2
MR =ΔTR/ ΔQ =∂TR/ ∂Q
=a-2bQ[In prior graph, a=10 and b=1]
Slope of D
Slope of MR
12
Monopoly If the firm’s goal were to
maximize total revenue, where would it produce?
The elastic and inelastic portions of the demand curve are labeled. How do these relate to MR?
P=$5; D=-1; TR=$25
Elastic: MR>0 Inelastic: MR<0 Will a monopolist ever produce
on the inelastic portion of the demand curve? No.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
D
Elastic
Inelastic
Q
MR
13
Own Price Elasticity of Demand
0123456789
101112
0 1 2 3 4 5 6
Q
P ($
/Q)
A
B
C
D
EF
G
Pt Q P d TR
A 0 12 -∞
B 1 10 -5
C 2 8 -2
D 3 6 -1
E 4 4 -1/2
F 5 2 -1/5
G 6 0 0
0
10
16
1816
10
0
0123456789
10111213141516171819
0 1 2 3 4 5 6
Q
TR
=T
E
MR
10
6
2-2-6
-10
14
TR
MATH BEHIND: Maximizing Revenue and Own Price Elasticity equaling -1
MaxQ TR = MaxQ P(Q)Q
Q
TR0
PQQ
P,PQ
Q
P
so
Q
P
P
Q
1,P
QPQ
Own Price Elasticity of Demand
15
Monopoly Maximizing Profits
If the monopolist maximizes profits, where would it produce?
At an output where MR=MC as long as P>AVC.
This is at an output of Q=4 so a price of P=6.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
16
MATH BEHIND: Maximizing Profits being where MR=MC
MaxQ Profits = MaxQ TR(Q)-TC(Q)
so profits are maximized where
Or where,
Applies when Q>0
0
MCMRQ
TC
Q
TR
MCMR
17
Monopoly Maximizing Profits At Q=4 and P=6, what
is Total Revenue?TR=P*Q=6*4=24 At Q=4, what are Total
Costs?TC=ATC*Q=4.5*4=18 At Q=4 and P=6, what
are Profits?Profits=TR-TC=24-18=6OrProfits=P*Q-ATC*Q
=(P-ATC)*Q=(6-4.5)*4=6
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
TR
TC
Profits
18
Monopoly Maximizing Profits
What is the difference between these costs and the costs on the prior slide? FC are greater on the costs depicted to the right.
If the monopolist maximizes profits, where would it produce?
Q=4 so set P=6. Profits would be:TR-TC=6*4-8*4= -8
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
MR
Profits
19
Monopolist in Long Run What should this
monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Keep producing Q=4 or change plant size depending if there is a plant size that would result in greater profits.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
Q
MR
Profits
20
Short Run and Long Run ATCs
Q 21
Monopolist in Long Run
What should this monopolist do in the Long Run assuming that the monopolist thinks his costs will not change and neither will demand?
Exit the industry or change plant size depending if there is a plant size that would result in positive profits given demand curve.
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10 11 12
AVC
MC
ATC
D
MR
Profits
22
Monopolistic Competition Characteristics1. There are many buyers and seller
2. Each firm in the industry produces a differentiated product
3. There is free entry into and exit from the industry
[Think bakery or coffee shop in big city.]
23
Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Short Run
If bakery maximizes profits, where would it produce?
Where MR=MC which is at an output of Q=3.5 so a price of P=8.
What are the bakery’s profits?
TR-TC=P*Q-ATC*Q=8*3.5 - 6.25*3.5 = 6.12
0123456789
10111213
0 1 2 3 4 5 6 7 8 9
10Q
MC
ATC
AVC
D
MR24
Bakery in a Monopolistically Competitive Industry Maximizing Profits in the Long Run
In long-run if the bakery is making positive economic profits, we would expect other bakeries to enter causing a reduction in demand.
What are maximum profits when demand is D’?
Q=3 so a price of P=6.67.Profits=P*Q-ATC*Q
=6.67*3-6.67*3=00123456789
101112
0 1 2 3 4 5 6 7 8 9
10 Q
MC
ATC
AVC
MR
D’
25
Review of Profit Maximization (when setting a single price)
26
Marginal Revenue from 5th Unit is just the shaded area below. This area is $11.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
When the MR curve is linear, the area under the MR curve can be obtained by just taking the MR at the midpoint of the quantities – in this case at 4.5.
The orange area is the same as the purple area. 27
Marginal Cost of 5th Unit is just the shaded area below. This area is $9.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MRThe purple area is the same as the red area
When the MC curve is linear, the area under the MC curve can be obtained by taking the MC at the midpoint of the quantities – in this case at 4.5.
28
Change in Profits associated with producing 5 Units rather than 4 units.
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
Yellow area is change in profits associated with producing 5 units rather than 4 units. This area is $2.
Subtract MC of 5th unit from MR of 5th unit– brown area from purple. 29
Review of Profit Maximization (when setting a single price)
30
PROFIT MAXIMIZATION
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Q
$/u
nit
MC
ATC
AVC
D
MR
11.2
15
Profits are maximized at an output where MR=MC which is Q=5. Price is 15 and ATC is 11.2 at Q=5.
Profits are then 15*5-11.2*5=19
31
