Assume that a cogeneration heating distribution system can be constructed for $14600 per unit of capacity and can be operated at variable costs of $0 (heat is supplied by an industrial facility that operates 24 hours every day). Assume that during 8 hours of the day the on peak demand for heat is P=a-bQ. Assume that during the other 16 hours of the day (off-peak) the demand for heat is one-half of the demand during the peak period. Assume that the cost of capital, r, is 10% and that heating distribution system does not depreciate.

1. Assume on-peak demand is P=16-0.08Q, and off-peak demand is P=16-0.16Q. If the existing capacity (Q) were 120 units, what would be the socially optimal prices during the on-peak hours and during the off-peak hours?
2. What would be the optimal capacity? What would be the prices at this optimal capacity?