2. (40 points) A lumber mill supplies an Ikea furniture factory. The furniture factory makes minimalist tables and sells them for $230 (customers pick the tables up from the factory in this example). The factory expects to sell 1000 tables. The lumber for a table costs $100 to make and $50 to ship to the factory (Shipping cost paid by the mill). The market price for the lumber of one table is $180 (the factory can buy on the open market for this price, and the lumber mill can sell on the open market for this price. Ex Ante A. What is the maximum total profit generated by both firms working together? Find the outside option profit for each firm. B. Now consider that the lumber mill can build a new mill right next to the factory for $10,000. This eliminates the shipping cost when selling to the Ikea factory but not the shipping cost on the open market. What is the maximum total profit generated by both firms together if the new mill gets made? C. Find the nash bargaining profit for each firm. What is the corresponding price at which the lumber mill will sell to the factory. Ex Post D. Now assume that the lumber company has already spent the $10,000 to build the mill next to the Ikea factory. Find the new outside option for each firm. E. Find the new nash bargaining profit for each firm. What is the corresponding price at which the lumber mill will sell to the factory.