plz plz help

There are 10 billion barrels of oil in an oil field. A large number of oil companies have the capability of extracting oil. To extract oil, each company needs to spend $2 per barrel plus a fixed cost of $1 billion reflecting set-up costs. Crude oil is sold at $10 per barrel. Each company is able to extract all of the oil under the field. If more than one company simultaneously work the field then each company extracts an equal fraction of the oil. If, that is, N companies work the field then each company extracts 10/N billion barrels. 1. Consider the following thought experiment. There are two companies working the field, and then a third enters. What are the entrant's profits? What is the quantitative effect of entry on the aggregate profits of the two incumbent companies? (10 pts.) 2. Suppose a social planner wants to minimize the social cost of extracting the oil from the field, subject to the constraint that the field is developed (i.e., that at least one company works the field). How many oil companies would the social planner license (i.e., allow to work the field)? (10 pts.) 3. Suppose the oil field lies in international waters, so that any oil company can work the field if it chooses. How many oil companies will be working the field? (10 pts.) 4. Suppose the oil field lies within the domain of one nation, who can license companies to work the field. Suppose that nation maximizes the proceeds from the license sale. How many oil companies will the nation license, and how much will a license cost? (10 pts.)