Question: coase theorem question specifically e amp f suppose that a...
Coase theorem question. Specifically e & f
Suppose that a rancher is raising cattle (X) next to a farmer. The profits of the rancher are given by π(X) = 100X −X2 for 0 ≤ X ≤ 100 and the utility of the farmer is given by: U(W,X) = W(100 − X) for 0 ≤ X ≤ 100 where W is her level of wealth. Assume initially W = 50.
a) Suppose the rancher has the right to run as many cattle as she likes. How many cattle will she choose?
b) Suppose the farmer has the right to dictate how many cattle will be run. How many cattle will she choose?
c) What is the efficient number of cattle to run? (i.e. Solve the social planner’s problem)
d) Suppose the government will tax the rancher $T per cow. At what tax rate $T∗ will the rancher choose to run the efficient number of cattle?
e) Suppose the farmer chooses the number of cattle, and the farmer is paid $S per cow by the rancher. (The amount paid to the farmer enters her wealth.) How many cows will the farmer choose to run?
f) Bonus: Why do the answers to c) and e) differ?