Make vs Buy in a Monopoly with Demand or Cost Uncertainty

The issue of technical progress under uncertainty is nested into the debate on vertical integration vs outsourcing, to show that, in general, the former is preferable to the latter in terms of both expected profits and technological efficiency. It is then shown that there exist (i) an optimal two part tariff where the unit price set by the upstream firm is conditional upon its R&D effort, and (ii) an optimal contract specifying the input price in terms of the initial capabilities of the sub-contractor, whereby the industry replicates the same performance as the vertically integrated firm as for both profits and R&D efforts.