5. [Perfect Competition] Demand for the good produced in a perfectly competitive industry is given by
P(Q) = 59 - Q. The optimal technology for minimizing LRATC is given by TC($q_i$) = 100 - $q_i$ + 0.5$q_i$^2.
How many firms are in this industry in the long run?
(a) $P^{be}$ = 13.14, Q = 45.86, leads to N ? 3.24. If we restrict ourself to integer numbers of firms, that
leaves us with three firms, as the fourth could not enter profitably.