The cost (supply) of each "unit" of NPR (National Public Radio) is P=2. Derek's valuation for each unit of NPR (demand) is given by PD=10-Q, and Kim's valuation is given by PK=4-0.5Q. The total social valuation (demand) of NPR is Ps= Q. The socially optimal amount of NPR is units. Without intervention, the private market would lead to an under-provision of NPR