Profit Maximization课件
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$/Q
MC 50
100 90 80 70 60
8
55*8-43.75*8=90
MC
20 46.00 43.33 40 42.86 50 43.75 60 45.56 70 48.00 30
50 40 30 20 10 0
0 1 2 3 4 5 6 7 8
ATC AVC
AFC
9
Q
精品文档
10
What output maximizes profits if the marginal revenue for each unit the firm sells is $35? What are these profits?
Demand Curve:
Slope of D
P=a-bQ TR = (a-bQ)Q =aQ-bQ2 MR =ΔTR/ ΔQ =∂TR/ ∂Q Slope of MR
=a-2bQ
[In prior graph, a=10 and b=1]
精品文档
Monopoly
so profits are maximized where
TR TC MR MC 0 Q Q
Or where,
MR MC
精品文档
Applies when Q>0
Monopoly Maximizing Profits
At Q=4 and P=6, what is Total Revenue? TR=P*Q=6*4=24 At Q=4, what are Total Costs? TC=ATC*Q=4.5*4=18 At Q=4 and P=6, what are Profits? Profits=TR-TC=24-18=6 Or Profits=P*Q-ATC*Q =(P-ATC)*Q =(6-4.5)*4=6
10
Short-Run Profit Maximizing Rule
Produce
at an Output where Marginal Revenue = Marginal Cost (MR) (MC) if Total Revenue > Variable Cost
[When the firm cannot price discriminate, this is the same thing as saying as long as Price > AVC (from P*Q > AVC*Q) ]
精品文档
MR
P ($/Q)
Own Price Elasticity of Demand
Pt
A
Q
0
P
12
B
C D E F G
1
2 3 4 5 6
10
8 6 4 2 0
hd TR MR 0 -∞ 10 10 -5 6 16 -2
-1 -1/2 -1/5 0
12 A 11 10 9 8 7 6 5 4 3 2 1 0 0
Natural Monopoly (type of monopoly
where there exists large economies of scale)
$/unit
when a single firm can supply a good or service to an entire market at a smaller cost than could two or more firms.
Q 0 1 2 3 4 5 6 7 8 9 10 AFC 100.00 50.00 33.33 25.00 20.00 16.67 14.29 12.50 11.11 10.00 AVC 50.00 40.00 33.33 27.50 26.00 26.67 28.57 31.25 34.44 38.00 ATC 150.00 30 90.00 20 66.67 10 52.50
Long Run Average Total Cost
ATC1/2 big firm ATCone big firm
0
Q1/2 big精品文档 firm
Qbig firm
Quantity
Monopolist Marginal Revenue TR (with no price discrimination) MR
精品文档
Monopoly Characteristics
1. 2.
3.
There is a single seller There are no close substitutes for the good There are extremely high barriers to entry
精品文档
$/Q
MC 50
100 90 80 70 60
5?
25*5-46*5=-105
MC
10 52.50 46.00 30 43.33 40 42.86 50 43.75 60 45.56 70 48.00 20
50 40 30 20 10 0
0 1 2 3 4 5 6 7 8
ATC AVC
AFC
9
Q
Better off producing 0 so profits=-FC=-100 精品文档
Q
P 10 9 8 7 6 5 4 3 2 1 0 Q TR MR 0
10 9 8 7 6 5 4 3 2 1 0
+9 1 9 +7 2 16 +5 3 21 +3
4 5 6 24 +1 25 -1 24
0
D
Q
10 11 12 0 1 2 3 4 5 6 7 8 9
-3 7 21 -5 8 16 -7 9 9 -9
Q 0 1 2 3 4 5 6 7 8 9 10 AFC 100.00 50.00 33.33 25.00 20.00 16.67 14.29 12.50 11.11 10.00 AVC 50.00 40.00 33.33 27.50 26.00 26.67 28.57 31.25 34.44 38.00 ATC 150.00 30 90.00 20 66.67
10
What output maximizes profits if the marginal revenue for each unit the firm sells is $25? What are these profits?
Q 0 1 2 3 4 5 6 7 8 9 10 AFC 100.00 50.00 33.33 25.00 20.00 16.67 14.29 12.50 11.11 10.00 AVC 50.00 40.00 33.33 27.50 26.00 26.67 28.57 31.25 34.44 38.00 ATC 150.00 30 90.00 20 66.67
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
精品文档 480
10
38
48
What output maximizes profits if the marginal revenue (MR) for each unit the firm sells is $55? What are these profits?
10 0
MR
Note that Marginal Revenue for a given unit is plotted at the midpoint of that unit. 精品文档
Use Calculus to Obtain MR curve for Linear
Demand Curve
Profit Maximization
Ed. 7: Ch. 8, pgs 264-265, pgs 277-300 Ed. 6: Ch. 8, pages 265-266, pgs 278-304
精品文档
Profit Maximization assuming:
1. 2.
Firm must charge every consumer the same price (i.e., no price discrimination) No Strategic Interaction among Firms
MaxQ TR = MaxQ P(Q)Q so
TR P Q P 0 Q Q
P Q P, Q
Q Q P , P
Q P 1 P Q
精品文档
Own Price Elasticity of Demand
Monopoly Maximizing Profits
18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
B C D E F G 1 2 3 Q 4 5 6
10
0Байду номын сангаас
-10
TR=TE
18 16
2 -2 -6
TR 19
0
1
2
3
4
5
精品文档
Q
6
MATH BEHIND: Maximizing Revenue and Own Price Elasticity equaling -1
Inelastic
D
Q
10 11 12 0 1 2 3 4 5 6 7 8 9
Elastic: MR>0 0 Inelastic: MR<0 Will a monopolist ever produce on the inelastic portion of the demand curve? No.
We will consider two industry structures: Monopoly Monopolistic Competition
精品文档
Profit Maximization Example
Q 0 FC 100 VC 0 TC 100 AFC AVC ATC MC
100
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.
50
50
150 30
1
100
50
150
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
精品文档
230
20
26
46
Q 5
FC 100
VC 130
TC 230
AFC 20
AVC 26
ATC 46
MC
30 6 100 160 260 16.7 26.67 43.3 40
10 9 8 7 6 5 4 3 2 1
Elastic
If the firm’s goal were to maximize total revenue, where would it produce? P=$5; hD=-1; TR=$25 The elastic and inelastic portions of the demand curve are labeled. How do these relate to MR?
$/Q
MC 50
100 90 80 70 60
6
35*6-43.33*6=-50
MC
10 52.50 46.00 30 43.33 40 42.86 50 43.75 60 45.56 70 48.00 20
50 40 30 20 10 0
0 1 2 3 4 5 6 7 8
ATC AVC
AFC
9
Q
Produce an output of 6 in shortrun if fixed costs are sunk. 精品文档
10 9 8 7 6 5 4 3 2 1 0
10 11 12 0 1 2 3 4 5 6 7 8 9
MC ATC AVC D
Q
MR
精品文档
MATH BEHIND: Maximizing Profits being where MR=MC
MaxQ Profits = MaxQ TR(Q)-TC(Q)
10 9 8 7 6 5 4 3 2 1 0
10 11 12 0 1 2 3 4 5 6 7 8 9
TR
MC
Profits
ATC AVC D
Q TC
精品文档
MR
Monopoly Maximizing Profits
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
MC 50
100 90 80 70 60
8
55*8-43.75*8=90
MC
20 46.00 43.33 40 42.86 50 43.75 60 45.56 70 48.00 30
50 40 30 20 10 0
0 1 2 3 4 5 6 7 8
ATC AVC
AFC
9
Q
精品文档
10
What output maximizes profits if the marginal revenue for each unit the firm sells is $35? What are these profits?
Demand Curve:
Slope of D
P=a-bQ TR = (a-bQ)Q =aQ-bQ2 MR =ΔTR/ ΔQ =∂TR/ ∂Q Slope of MR
=a-2bQ
[In prior graph, a=10 and b=1]
精品文档
Monopoly
so profits are maximized where
TR TC MR MC 0 Q Q
Or where,
MR MC
精品文档
Applies when Q>0
Monopoly Maximizing Profits
At Q=4 and P=6, what is Total Revenue? TR=P*Q=6*4=24 At Q=4, what are Total Costs? TC=ATC*Q=4.5*4=18 At Q=4 and P=6, what are Profits? Profits=TR-TC=24-18=6 Or Profits=P*Q-ATC*Q =(P-ATC)*Q =(6-4.5)*4=6
10
Short-Run Profit Maximizing Rule
Produce
at an Output where Marginal Revenue = Marginal Cost (MR) (MC) if Total Revenue > Variable Cost
[When the firm cannot price discriminate, this is the same thing as saying as long as Price > AVC (from P*Q > AVC*Q) ]
精品文档
MR
P ($/Q)
Own Price Elasticity of Demand
Pt
A
Q
0
P
12
B
C D E F G
1
2 3 4 5 6
10
8 6 4 2 0
hd TR MR 0 -∞ 10 10 -5 6 16 -2
-1 -1/2 -1/5 0
12 A 11 10 9 8 7 6 5 4 3 2 1 0 0
Natural Monopoly (type of monopoly
where there exists large economies of scale)
$/unit
when a single firm can supply a good or service to an entire market at a smaller cost than could two or more firms.
Q 0 1 2 3 4 5 6 7 8 9 10 AFC 100.00 50.00 33.33 25.00 20.00 16.67 14.29 12.50 11.11 10.00 AVC 50.00 40.00 33.33 27.50 26.00 26.67 28.57 31.25 34.44 38.00 ATC 150.00 30 90.00 20 66.67 10 52.50
Long Run Average Total Cost
ATC1/2 big firm ATCone big firm
0
Q1/2 big精品文档 firm
Qbig firm
Quantity
Monopolist Marginal Revenue TR (with no price discrimination) MR
精品文档
Monopoly Characteristics
1. 2.
3.
There is a single seller There are no close substitutes for the good There are extremely high barriers to entry
精品文档
$/Q
MC 50
100 90 80 70 60
5?
25*5-46*5=-105
MC
10 52.50 46.00 30 43.33 40 42.86 50 43.75 60 45.56 70 48.00 20
50 40 30 20 10 0
0 1 2 3 4 5 6 7 8
ATC AVC
AFC
9
Q
Better off producing 0 so profits=-FC=-100 精品文档
Q
P 10 9 8 7 6 5 4 3 2 1 0 Q TR MR 0
10 9 8 7 6 5 4 3 2 1 0
+9 1 9 +7 2 16 +5 3 21 +3
4 5 6 24 +1 25 -1 24
0
D
Q
10 11 12 0 1 2 3 4 5 6 7 8 9
-3 7 21 -5 8 16 -7 9 9 -9
Q 0 1 2 3 4 5 6 7 8 9 10 AFC 100.00 50.00 33.33 25.00 20.00 16.67 14.29 12.50 11.11 10.00 AVC 50.00 40.00 33.33 27.50 26.00 26.67 28.57 31.25 34.44 38.00 ATC 150.00 30 90.00 20 66.67
10
What output maximizes profits if the marginal revenue for each unit the firm sells is $25? What are these profits?
Q 0 1 2 3 4 5 6 7 8 9 10 AFC 100.00 50.00 33.33 25.00 20.00 16.67 14.29 12.50 11.11 10.00 AVC 50.00 40.00 33.33 27.50 26.00 26.67 28.57 31.25 34.44 38.00 ATC 150.00 30 90.00 20 66.67
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
精品文档 480
10
38
48
What output maximizes profits if the marginal revenue (MR) for each unit the firm sells is $55? What are these profits?
10 0
MR
Note that Marginal Revenue for a given unit is plotted at the midpoint of that unit. 精品文档
Use Calculus to Obtain MR curve for Linear
Demand Curve
Profit Maximization
Ed. 7: Ch. 8, pgs 264-265, pgs 277-300 Ed. 6: Ch. 8, pages 265-266, pgs 278-304
精品文档
Profit Maximization assuming:
1. 2.
Firm must charge every consumer the same price (i.e., no price discrimination) No Strategic Interaction among Firms
MaxQ TR = MaxQ P(Q)Q so
TR P Q P 0 Q Q
P Q P, Q
Q Q P , P
Q P 1 P Q
精品文档
Own Price Elasticity of Demand
Monopoly Maximizing Profits
18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
B C D E F G 1 2 3 Q 4 5 6
10
0Байду номын сангаас
-10
TR=TE
18 16
2 -2 -6
TR 19
0
1
2
3
4
5
精品文档
Q
6
MATH BEHIND: Maximizing Revenue and Own Price Elasticity equaling -1
Inelastic
D
Q
10 11 12 0 1 2 3 4 5 6 7 8 9
Elastic: MR>0 0 Inelastic: MR<0 Will a monopolist ever produce on the inelastic portion of the demand curve? No.
We will consider two industry structures: Monopoly Monopolistic Competition
精品文档
Profit Maximization Example
Q 0 FC 100 VC 0 TC 100 AFC AVC ATC MC
100
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.
50
50
150 30
1
100
50
150
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
精品文档
230
20
26
46
Q 5
FC 100
VC 130
TC 230
AFC 20
AVC 26
ATC 46
MC
30 6 100 160 260 16.7 26.67 43.3 40
10 9 8 7 6 5 4 3 2 1
Elastic
If the firm’s goal were to maximize total revenue, where would it produce? P=$5; hD=-1; TR=$25 The elastic and inelastic portions of the demand curve are labeled. How do these relate to MR?
$/Q
MC 50
100 90 80 70 60
6
35*6-43.33*6=-50
MC
10 52.50 46.00 30 43.33 40 42.86 50 43.75 60 45.56 70 48.00 20
50 40 30 20 10 0
0 1 2 3 4 5 6 7 8
ATC AVC
AFC
9
Q
Produce an output of 6 in shortrun if fixed costs are sunk. 精品文档
10 9 8 7 6 5 4 3 2 1 0
10 11 12 0 1 2 3 4 5 6 7 8 9
MC ATC AVC D
Q
MR
精品文档
MATH BEHIND: Maximizing Profits being where MR=MC
MaxQ Profits = MaxQ TR(Q)-TC(Q)
10 9 8 7 6 5 4 3 2 1 0
10 11 12 0 1 2 3 4 5 6 7 8 9
TR
MC
Profits
ATC AVC D
Q TC
精品文档
MR
Monopoly Maximizing Profits
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