Please solve all and show the work

1. Assume a market in which there are 9 1dentical firms with total production costs C (q1) = Y2 + q1. Entry 1s limited by the granting of administrative licenses (in fact the fixed part of the costs corresponds to the payment of the license) and 1t 1s known with certainty that the regulatory authority will not grant any further licenses in the future. The product that 1s marketed 1s perfectly homogeneous. Inverse demand is given by P (Q) = 10-Q, where Q 1s the aggregate output of all firms. Firms compete in quantities. a) Calculate the Nash equilibrium indicating the sales and profits of each firm . b) Suppose now that two firms in the sector are considering the possibility of a merger, so that when merged they would pay a single license (in addition the regulatory authority removes the surplus license, 1.e., does not grant 1t to a new company). Will it be profitable to carry out the merger? If these two firms decide to carry out the merger, how will 1t affect their competitors? ) What 1s the minimum number of firms that have to merge in order for the merger to be profitable? d) If the Competition Authority only cares about total surplus (defined as consumer surplus + profits net of fixed costs). Total surplus does not include income derived from administrative licenses. Would 1t allow a merger between five firms