Proof of Proposition Sample Clauses

Proof of Proposition. 4. The first part follows directly from the subgame Γ1,G (see payoffs given in figure 1). After loosing to G1, brand would launch a generic if ΠT1 + ΠT1 − θ + δ(ΠT1 + ΠT1) ≥ 0 0 ΠD0 +δΠT0. Rearranging the terms gives the required result θ ≤ (ΠT1 +ΠT0 −ΠD0)+δ·(ΠT1 +ΠT1 − 0 ΠT0) = θ∗∗(κ). Similarly, the second part follows from the subgame Γ1,B. After winning against 0 G1, the brand launches a generic in post-patent period if ΠM + δ(ΠT1 + ΠT1 − θ) ≥ ΠM + δ(ΠT0). Rearranging gives the required result θ ≤ (ΠT1 + ΠT1 − ΠT0) = θ∗(κ). Q Appendix C. Extension to the Game Tree‌ 0 2

Proof of Proposition. 2. Substituting the instrument values into the welfare function,