pounds

1
pounds
Cost
To
Time
2
pounds
Bm
Cost
Bc
Bol
To
Tm
Time
3
pounds
Bm
Cost
Bc
Bol
Tm
Time
4
pounds
Bm
Bc
Bol
Cost
Tm
Time
Tol
Tc
5
pounds
Bd
Bs
Bd
Cost
Td
Time
Tdl
Ts
6
Patent races
7
Patent races
8
Time of Innovation T(X)
T(X)
Expenditures X
9
Present value of Benefits Bpv
Bpv(X)X
Bpv(X)
X
Xe
10
Duration of patents
pounds
B20
Cost
B0
B7
T7
T20
Time
11
I
1. No one innovates
2. one innovates (no market failure)
3. both innovate (market failure)
4. both innovate
1
alpha
12
Patent length
p
CSo
c
M
DL
c-x
a
a-c
a-(c-x)
Q
13
p
1/4
Po
xH
1
xL
x
14
profits
4/27
x
2/3