How are resources allocated across different R&D areas? We show that under a plausible set of assumptions, the competitive market allocates excessive innovative efforts into high returns areas, meaning those with higher private (and social) payoffs. The underlying source of market failure is the absence of property rights on problems to be solved, which are the source of R&D value. The competitive bias towards high return areas comes three distortions. The first two are familiar in the context of a single innovation line: the cannibalization of returns of competing innovators and duplication costs. The third one is new to the innovation literature: excessive entry into high return areas results as the market does not take into account the future value of an unsolved problem while a social planner does. Allocation of resources to problem solving leads to a stationary distribution over open problems. The distribution of the socially optimal solution stochastically dominates that of the competitive equilibrium. A severe form of rent dissipation occurs in the latter, where the total value of R&D activity equals the value of allocating all resources to the least valuable problem solved. Joint with Francesco Squintani.