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

0.1q2

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

$95

per square foot per month. Rents in this area are expected to increase in five years. There is a

51%

chance that they will rise to

$198

per square foot per month and stay there forever and a

49%

chance that they will stay at

$95

per square foot per month forever. The cost of capital is fixed at

11.6%

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?