Exercise 15.12. (1) Prove Proposition 15.7. In particular, use equation (15.9) and show that when (15.37) is not satisfied, both free entry conditions cannot hold simultaneously. Then show that if σ < 1/δ, there will be greater incentives to undertake research for the technology that is relatively scarce, and the opposite holds when σ > 1/δ. (2) Interpret the economic significance of the condition σ < 1/δ. [Hint: relate this to the fact that When σ < 1/δ, ∂ ¡ Nδ HVH/Nδ LVL ¢ /∂ (NH/NL) < 0, but the inequality is reversed when σ > 1/δ].