The verification of my solution Farmer Smith's cattle wander into Farmer Jones' land once a month and cause $\$3,000$ of damage. If Smith reduced the size of his herd by half it would reduce the damage by half but it would also reduce his profits from $\$7,500$ to $\$3,500$. If Smith left the cattle business entirely, he would lose the entire $\$7,500$. If the two parties could negotiate at zero transactions cost, what would be the resulting size of the herd? If there are large transactions costs, Jones hires a lawyer and sues Smith for damages. You are the local judge. Should you allow Jones to collect damages from Smith? If so how much would you award?


I have this question. And I give the following answer. But I am not sure whether this following answer is enough or there are some mistakes.

If there are no transaction costs, then smith pays jones $3000 as compensation since it is profitale for him to do so. Notice that if he cuts his herd to hald, he loses 3500 and earns 4000 but if he pays up for the damages i.e. 3000 dollars he earns 7500-3000=4500 , i.e. he still earns 500 more in this situation.

Now the transaction cots are high. Yes I would allow jones to collect for the damages from smith since that way I am maximizing the society's payoff i.e. I am making Smith internalise the cost of damages that he has caused. I would tell smith to give $3500 to jones because

a. compensation to the damages

b. pay up the transaction costs

c. make him indifferent between cutting his herd to half and keeping the whole herd since this will mean no profit no loss situation which maximizes surplus of the society.

What do you think? Please share with me. thank you.
Zero transaction cost:


It is correct that the resulting herd will be $\$7,500$, but the transfer from Smith to Jones is not necessarily $\$3,000.$  For instance, the negotiation may result in the transfer amount of $\$4,000$, in which case Smith will be indifferent between producing the ``full-size'' herd and cutting it down by half as $\$7.500 - \$4,000 = \$3,500$. The resulting transfer depends on the negotiation powers of the parties and can be anything between $\$3,000$ and $\$4,000$. 


  High transaction cost:


Notice that your decision as a judge should depend on the value of the transaction cost.  Suppose the transaction cost is $\$4,000$, then what would be your decision? Can (or should) you make Smith indifferent in this case? Hope this will help you with the solution.