Patents & Technological Change
How much R&D exists without patents?
 How do patents perform as an incentive
system relative to alternatives?
 How long should patents last?

This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Some Distinctions…
Patents
 Copyrights
 Trademarks

This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Incentives for Innovation
Public Goods and ideas
 Without patents why develop a new drug?
 Virtues of Patents



Research
Disclosure
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Modeling Research & Development

Assumptions








Identical firms, 1 research project each
n: Current number of firms/projects
Constant MC = m = 1
C(n) = total research cost = nm = n
ρ(n) = probability of at least one success
R&D occurs at t=0. If successful, then society
benefits in later periods (t=1,2,…)
B = social benefit of the discovery
B ρ(n)= expected social benefit
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Table 16.4: Socially Optimal R&D
Number of
projects n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
24.84
25
Expected
Expected Probability
Expected
Net Social
Social Cost
Marginal
Payoff with of Success Social Benefit
Benefit
C(n)
Social Benefit
Prize B
ρ(n)
Bρ(n)
Bρ(n)-C(n)
4.14
3.38
2.76
2.25
1.84
1.5
1.23
1
0.82
0.67
0.54
0.44
0.36
0.3
0.24
0.2
0.16
0.13
0.11
0.09
0.07
0.06
0.05
0.04
0.03
0.03
4.60
4.17
3.8
3.48
3.19
2.93
2.71
2.51
2.33
2.17
2.03
1.9
1.79
1.68
1.59
1.5
1.42
1.35
1.29
1.23
1.17
1.12
1.08
1.03
1
0.99
0.184
0.334
0.456
0.556
0.638
0.704
0.759
0.803
0.839
0.869
0.893
0.912
0.929
0.942
0.952
0.961
0.968
0.974
0.979
0.983
1.066
0.988
0.991
0.992
0.994
0.994
4.60
8.35
11.41
13.91
15.94
17.61
18.97
20.08
20.98
21.72
22.32
22.81
23.22
23.54
23.81
24.03
24.21
24.35
24.47
24.57
26.65
24.71
24.77
24.81
24.84
24.84
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
24.84
25
3.60
6.35
8.41
9.91
10.94
11.61
11.97
12.08
11.98
11.72
11.32
10.81
10.22
9.54
8.81
8.03
7.21
6.35
5.47
4.57
5.65
2.71
1.77
0.81
0.00
-0.16
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Figure 16.1-Total Benefits, Costs
30
Expected Social Benefits, Bρ(n)
25
20
Social Costs, C(n)
15
10
Net Social Benefits Bρ(n)-C(n)
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Figure 16.1-Marginal Benefits, Costs
5
4.5
Expected payoff with prize B
4
3.5
3
2.5
2
1.5
Marginal Cost
1
0.5
Marginal Social Benefits
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
No Government Incentives

How much research will private firms do
without government subsidies?
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Government Incentives for R&D
R&D tax deductions
 Prizes
 Joint ventures
 Patents

This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Optimal Patent Length
Demand:
p  6 - 5Q
Marginal Cost:
MC  1
 Pm  $3.50;
Qm  0.5;
T
V(T) = Value of Patent  
t 1
 m  $1.25
m
1  r 
t
Longer Patents produce encourage more research, but
they also increase the period of post development
deadweight loss.
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
How much research is done?
Firm's will choose to do projects as long as:
  (n+1)- (n) V (T )  m  1
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.
Table 16.5: Optimal Patent Length
Length of
Patent
5.35
5.71
6.53
7.47
8.56
9.00
9.87
10.00
11.00
11.11
11.45
12.00
13.00
13.40
14.00
15.94
19.51
23.36
Number Net Social
of Projects Benefit
0
1
2
3
4
4
5
5
5
6
6
6
6
7
7
8
9
10
0.00
3.20
5.35
6.91
7.91
7.84
8.44
8.42
8.29
8.61
8.61
8.53
8.41
8.47
8.39
8.08
7.48
6.72
This slideshow was written by Ken Chapman, but is substantially based on concepts from
Modern Industrial Organization by Carlton and Perloff, 4th edition, McGraw-Hill.