A railroad can operate zero, one, or two trains a day along a certain stretch of track that borders a farmer's field, but the trains occasionally emit sparks that set fire to the crops. The following table shows the railroad's total profit and the farmer's total fire damage (in dollars) as functions of the number of trains:
(a) What is the socially optimal number of trains?
(b) Assume bargaining costs between the railroad and farmer are zero. Describe the outcome under the following two situations:
(i) The railroad has the right to operate any number of trains, protected by a property rule;
(ii) The farmer has the right to be free from crop damage, protected by a property rule.
(c) Assume bargaining costs between the railroad and farmer are high. Describe the outcome under the following situations:
(i) The railroad has the right to operate any number of trains, protected by a liability rule;
(ii) The farmer has the right to be free from crop damage, protected by a liability rule.