Three individuals consume a public good, and their demands are express

Three individuals consume a public good, and their demands are expressed as:

P1 = 1.5 – 0.005Q (for Q < 300 ); P2 = 4.5 - 0.007Q (for Q < 643 ); P3 = 3.0 - 0.002Q (for Q < 1500 ), where P represents price in dollars per unit and Q represents output in units per day. The marginal cost of providing the service is given as a constant $5.00 per unit. Determine the efficient level of output of this public good.   ANSWER

The efficient level occurs where the total demand curve intersects MC. The total demand is the vertical sum of the individual demands. The following curve applies for output up to Q = 300 only.
Demand P = 9.0 – 0.014Q. (0 ≤ Q ≤ 300 )
The efficient output of the good is determined at the intersection of demand and MC.
9.0 – 0.014Q = 5.00
Q = 285.7 or 286 units per time period
For output rates above Q = 300, only the second and third demands apply, and for outputs above Q = 643, only the third demand applies.