This question investigates bargaining on a sinking ship. If a ship leaves port on a sunny day, it will not get caught in a storm and become disabled. If it leaves port on a stormy day, the probability that it will get caught in a storm and become disabled is 0.002 (1 in 500). The probability that a tugboat is sufficiently close by that it can tow a distressed boat to port is 1 - 1/(T + 1), where T is the number of tugboats per ship. If there is not a tugboat sufficiently close by to tow a distressed ship, the ship sinks at a cost of $5,000,000. A ship generates net revenue of $8500 per day when it leaves port (even if it gets distressed). Tugboats go out only on stormy days and do nothing other than roam the seas looking for distressed ships.. The cost per tugboat per stormy day is $2100.

The table below reports the net social benefit of a ship leaving port on a stormy day as a function of the number of tugboats per ship.

a) Indicate how one of these numbers in the above table is calculated.

The social optimum is therefore, on stormy days, to have ships leave port and for there to be one tugboat. The table below gives the number of tugboats and whether the ship will leave port, as a function of how much the ship captain pays the tugboat captain to be towed to shore. (M = millions of dollars).

no. of tugs/ship net revenue/ship expected cost of ship sinking cost of tugboats/ship net social benefit 0 1 -1500 1400 2 966 -300 payment 4.5M 4M 3.5M 3M 2.5M 2M exp cost of ship sink exp payment no. of tugs 3 leave port no 2 2 no 1 1 0 yes yes yes no 1.5 M IM no 0.5 M no no