Posted by Nadia on Sunday, September 10, 2006 at 2:36am.
cattle rancher (A) owns a property next to an apple farm (B) cattle sometimes tent to roam into B's land and damage the trees. The rancher can choose the size of the herd. revenue form cattle is $6 per head. The following schedle lists A's marginal prodction cost(MPC) and the damage associated with each cattle is given by the MEC
Cattle# MPC$ MEC$
1 3 1
2 3 2
3 4 3
4 5 4
5 6 5
6 7 6
B can choose wether to farm or not.B's cost of prodction is $10 and revene is $12 when there is no cattle roaming loose. for each additional cattle B's revene is reduced by the margianl external cost MEC listed above.
1 what is the market outcome if there is no liablilty ( A does nopt pay for the damages caused)
2 what is the market outcome if A is liable for damages caused.
3 what is the efficient outcome
4 suppose that it is possible to bild a fence to enclose the ranch for the cost of $9. what is the efficient otcome in this case.
5 Suppose B can protect the trees by building a fence for the cost of $1 what is the efficient outcome.
if any one can please please help me that will be greatly appreciated
Assume both the farmer and rancher are both morally bankrupt and have no concern for the welfare of the other.
in 1) The rancher will produce where MC=MR. From the table, 5 cows. (or 4; the rancher is indifferent between the two levels).
Now the hard part. What does the farmer do. His total revenue is 12. His total cost given the rancher's 5 cows is 10+5=15. Now then, ask the question, can the farmer pay the rancher enough to cut back his herd size and yet still turn a production profit? The rancher would need to paid $9 to stop production completely. (Nadia, how did i arrive at this figure). Since the maximum profit for the farmer is $2, he will not produce at all.
2) Calculate production for the rancher when marginal costs include damages.
3) Both solutions are efficient. (Actually, because of lumpy-ness in the data, total combined profits under 1 are higher than under 2).
4) Who pays for the fence? Not the farmer because his total profit sans cattle is only $2. Not the rancher as his maximum profit from production is $9.
5) See reasoning in 4.
I want to revise my answer to question #3. Only the first solution is efficient. When the rancher must compensate for all of his damages is he will raise 2 cows and compensate the farmer $3. However, $3 exceeds the farmer's maximum profit. Thus, the rancher over-compensates.
Now then, if the rancher need only compensate for the economic loss to the farmer, he would limit his payment at $2. This becomes a fixed cost, and the rancher would raise 5 cows. This too is an efficient solution.
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