Suppose a city has a parcel of scenic land that is now used as a park. A private company would like to buy the land to use for mining gravel.To keep things simple, suppose there are two periods, 0 and 1, and the land has only two uses, as a park or as a mine, and conversion to a mine is irreversible.
Use as a mine: The mining company is willing to pay $3 million to buy the land in either period. It will only pay once, at the time the land is sold. If the city sells the land it becomes a mine immediately and no longer produces any benefits as a park.
Use as a park: If left as a park in year 0, the land would produce $1 million of consumer surplus that year. If the land is a park in year 1, the consumer surplus that will be produced is unknown: there is a 30% chance it will be $9 million and a 70% chance it will be $1 million.
Finally, suppose the two periods are many years apart and the city uses a 100% interest rate in PV calculations involving period 1.
Please determine: (1) what the city would do if it had to make a permanent decision at 0; and (2) the option value of leaving the land as a park in period 0.