Question

4. (8) Double Moral Hazard

This question investigates bargaining over 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.

no. of tugs/ship	0	1	2	3
net revenue/ship
expected cost of ship sinking
cost of tugboats/ship
net social benefit	-1500	1400	966	-300

a) (4) Indicate how one of the numbers for net social benefit 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).

payment	4.5M	4M	3.5M	3M	2.5M	2M	1.5M	1M	0.5M
expected cost of ship sinking
expected payment
no. of tugs	3	2	2	1	1	0	0	0	0
leave port	no	no	yes	yes	yes	no	no	no	no

b) (4) Indicate how the indicated outcome with the payment of 4.5M by the ship's captain to the tugboat owner for towing the ship to shore is calculated.

* Please label which steps belong to part (a) and part (b).

Answer 1

Solution:

when the number of tugs is zero then the probability of tugboat is sufficiently closed.

Net revenue cost is 8500

Operating cost is 2100

The cost of boat sinks with probability is 0.002 is 20000

Net social benefit is 8500-20000 = -11500

As there is no tug, so that it means the operating cost is zero

When number of tugs is 1, then

Net social benefit is 8500 - (20000/2) -5000= -6500

When number of tugs is 2, then

Net social benefit is 8500 - (20000*2/3) -5000= -9833

When number of tugs is 3, then

Net social benefit is 8500 - (20000*3/4) -5000= -11500.

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