Question

1. Prof. Ronald Coase's seminal 1960 paper asks us to imagine the following scenario. A farmer and a cattle rancher are operating on neighboring properties. Inevitably, some of the rancher's cattle manage to stray onto the farmer's plot, damaging the crops and rendering them worthless. Now, consider the following numerical example: Suppose the cost to build a fence between the two properties that is strong enough to keep the cattle penned in is $10,000. The cattle rancher earns a profit of S300 per head of cattle, but the maximum number he can keep given the size of his property is 40. The farmer's crops are quite valuable, earning her a profit per ton of harvest of $1000. Further, suppose that the relationship between the total head of cattle the rancher keeps and the crop loss to the farmer (in the absence of a fence) is as follows Head of cattle Total crop loss (tons 20 30 40 10 Assume that bargaining does not incur any additional cost to either the farmer or the rancher. Now answer the following questions a. Suppose the local government intervened and insisted that the cattle rancher either build a fence to keep his cattle on his property or compensate the farmer for the value of her lost crops. Which would he choose? If it is to compensate the farmer, what would be the equilibrium payment and given this payment, how many head of cattle would he keep? Thoroughly explain your answer Suppose instead the local government told the farmer they didn't really care. Her choices are then either to build a fence to keep the cattle off her property or to pay the cattle rancher to reduce the size of his herd. Which would she choose? If it is to pay the rancher to reduce the size of his herd, what would be the equilibrium payment and, given this payment, how many head of cattle would the rancher keep? Thoroughly explain your answer. b. c. Do either the cattle rancher or the farmer have an incentive to build the fence under any circumstance? Why or why not'?

Answer 1

Q. 1. (a) If rancher builds fences then there is a fixed cost involved i.e. $10,000. We make a table to understand total profit to the rancher under different cases.

Heads of Cattle	Total crop loss (in tons)	Monetary value of loss=compensation	profit under compensation=revenue-compensation	profit under fence construction
10	1	1000	(300*10)-1000=2000	-9000
20	3	3000	(300*20)-3000=3000	-7000
30	6	6000	(300*30)-6000=3000	-4000
40	10	10,000	(300*40)-1000=2000	0

What we can see from the table is that if rancher goes to construct fence then he is left with zero profit in best case of having 40 cattle. So rancher will definitely not go for fencing.

Under compensation to the farmer, which he will choose to do, his maximum profit is when he is having 20 or 30 cattle. Hence he is indifferent in having 20 or 30 cattle.

(b) For this part also we do the same analysis. Once again if farmer fences then this fixed loss is $10,000. If he does nothing then rancher will have 40 cattle in which case profit of rancher will be 300*40=12000. But loss to farmer will be $10,000. So whether farmer does nothing or fences his loss is same $10,000. Now we consider alternate cases.

case1. If farmer restricts rancher to 30 cattle. then his loss is 6000 but then he will have to compensate rancher 3000 because rancher will earn 9000 from 30 cattle which other wise he could have earned 12000. Hence loss to farmer is 6000+3000=9000.

case 2. If farmer restricts rancher to 20 cattle. then his loss is 3000 but then he will have to compensate rancher 6000 because rancher will earn 6000 from 20 cattle which other wise he could have earned 12000. Hence loss to farmer is 3000+6000=9000.

case 3. If farmer restricts rancher to 10 cattle. then his loss is 1000 but then he will have to compensate rancher 9000 because rancher will earn 3000 from 10 cattle which other wise he could have earned 12000. Hence loss to farmer is 1000+9000=10,000.

Hence farmer will definitely not fence because then his loss is $10,000. But he can minimize his cost if he compensates to $9,000. hence he will compensate and restrict number of cattle to 20 or 30. He will be indifferent between these two numbers.

(c) No. None of them have incentive to build fence under any circumstances because under compensation both can do batter. It does not matter who has property right.