You own a piece of raw land in an up-and-coming area in Gotham City. The costs to construct a building increase disproportionately with the size of the building. A building of q square feet costs 0.1 x q2 to build. After you construct a building on the lot, it will last forever but you are committed to it: You cannot put another building on the lot. Buildings currently rent at $100 per square foot per month. Rents in this area are expected to increase in five years. There is a 50% chance that they will rise to $200 per square foot per month and stay there forever, and a 50% chance that they will stay at $100 per square foot per month forever. The cost of capital is fixed at 12% per year.

a. Should you construct a building on the lot right away? If so, how large should the building be?

b. If you choose to delay the decision, how large a building will you construct in each possible state in five years?