There is a common area shared by residents in the village. The residents of the village would like to make use of the common area by investing in solar panels. The economic profit per solar panel depends on the number of panels that share the area. In particular, if N solar panels share the area, the gain from each of the N panels will be 20 - N. Suppose there are 20 residents, each at most can send one solar panel to the area. The marginal cost of installing an additional panel is constant at $4.

the socially optimal quantity (the quantity that maximizes total economic profit from solar panels for the village)