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pounds. Cost. To. Time. pounds. Bm. Cost. Bc. Bol. To. Tm. Time. pounds. Bm. Cost. Bc. Bol. Tm. Time. pounds. Bm. Bc. Bol. Cost. Tm. Time. Tc. Tol. pounds. Bd. Bs. Bd’. Cost. Td. Time. Ts. Td’l. Patent races. Patent races. Time of Innovation T(X). T(X).
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pounds Cost To Time
pounds Bm Cost Bc Bol To Tm Time
pounds Bm Cost Bc Bol Tm Time
pounds Bm Bc Bol Cost Tm Time Tc Tol
pounds Bd Bs Bd’ Cost Td Time Ts Td’l
Time of Innovation T(X) T(X) Expenditures X
Present value of Benefits Bpv Bpv(X)=X Bpv(X) X* Xe
Duration of patents pounds B20 Cost B0 B7 T7 T20 Time
I 1. No one innovates 2. one innovates (no market failure) 3. both innovate (market failure) 4. both innovate 1 alpha
Patent length p CSo c M DL c-x a a-c a-(c-x) Q
p 1/4 Po xH xL 1 x
profits 4/27 x 2/3