Strategic R and D investments with uncertainty

I introduce uncertainty into the model of strategic cost-reducing R and D investments and reexamine welfare implications. I discuss two models. In one model an increase in expenditure decreases production costs when R\&D succeeds, and in the other model it increases probability of success. I show that two models yield completely different implications for tax-subsidy policies on R and D investments. In the former model equilibrium investment level is always too low from the viewpoint of social welfare, while in the latter model it can be either too low or too high and relatively risky (safe) investments should be subsidized (taxed).