Steve Win has purchased land from the city of Atlantic City in the Marina section. There are stories of a new casino building boom in Atlantic City (MGeeM is also talking about entering, and Gump is opening his fourth casino). Some talk is circulating that Win will subdivide his new land purchase and perhaps three casinos will be built on the site.
Suppose Win subdivides his land into two parcels. He builds on one site and sells the other to another gambling entrepreneur. Win estimates that the demand for gambling in the Marina area of Atlantic City (after accounting for the presence of two existing casinos in the Marina and adjusting for the rest of the casinos in Atlantic City) is
P = 750 - 5Q
where P is the price associated with gambling and Q is the quantity of gambling (think of P as the average amount that a typical patron will net the casino, an amount paid for the entertainment of gambling, and Q as the number of gamblers).
Win, of course, does not sell the other parcel until his casino is built (or is significantly far along); thus he has a first-mover advantage.
Win's total cost (TCW) of producing gambling is
TCW = 20 + 40QW + 15.5Q2W
where QW is the number of gamblers in Win's casino and the total cost (TCR) of producing gambling for Win's rival is
TCR = 10 + 50QR + 20Q2R
where QR is the number of gamblers in the rival's casino and
QW + QR = Q
Would Atlantic City have done better to sell the land as two separate parcels rather than as a single parcel to Win (given that Win was going to subdivide, Win and his rival could not collude, and Win did not have the ability to produce as a monopolist)? You may assume that Win and his rival could have been Cournot duopolists. If Atlantic City could do better, show why and by how much. Carry all calculations to the thousandths decimal point.