Answer to Question #15559 in Economics of Enterprise for Chris Callahan

Question

Rancher Profit Function: Π(X) = 100X – X² for 0 ≤ X ≤ 100

Farmer Utility Function: U(W,X) = (W)(100 – X) for 0 ≤ X ≤ 100

What is the efficient number of cattle to run?

Suppose the rancher gets to choose how many cattle to run, but the government charges him a
tax T on each cow. At what tax rate T* will the rancher choose to run the efficient number of
cattle?