Quality choice and capacity rationing in advance selling

Figure 1.  Sequence of events

Figure 2.  Value of rationing

Figure 3.  Value of flexibility on quality choice

Figure 4.  Value of flexibility on quality choice when capacity rationing is prohibited

Figure A1.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ T\leq\frac{N}{3} $

Figure A2.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{3}<T\leq\frac{N}{2} $ and $ N_{1}\leq\frac{3T-N}{2} $

Figure A3.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{3}<T\leq\frac{N}{2} $ and $ \frac{3T-N}{2}<N_{1}\leq\overline{N}_{1} $

Figure A4.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{3}<T\leq\frac{N}{2} $ and $ N_{1}>\overline{N}_{1} $

Figure A5.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{2}<T\leq\overline{T} $ and $ N_{1}\leq\frac{3T-N}{2} $

Figure A6.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{2}<T\leq\overline{T} $ and $ \frac{3T-N}{2}<N_{1}\leq\overline{N}_{1} $

Figure A7.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{2}<T\leq\overline{T} $ and $ N_{1}>\overline{N}_{1} $

Figure A8.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ T>\overline{T} $