(4) Suppose that the government allocates the N licenses by an auction. Every firm bids for a license. The top N bidders get the licenses. If there are more than N firms bidding the same amount, then the government uses a lottery to decide the winner. How much at most will a firm bid for the license? (it is a function of N.) (5) If the government wants to allocates the licenses by auction and also maximize the total revenue from the licenses (= Nx license fee), what is the optimal amount of N (it can be non-integer)? (4) Suppose that the government allocates the N licenses by an auction. Every firm bids for a license. The top N bidders get the licenses. If there are more than N firms bidding the same amount, then the government uses a lottery to decide the winner. How much at most will a firm bid for the license? (it is a function of N.) (5) If the government wants to allocates the licenses by auction and also maximize the total revenue from the licenses (= Nx license fee), what is the optimal amount of N (it can be non-integer)