Who introduced inverse demand function in economics?

Suppose the state is trying to decide how many miles of a very scenic river it should preserve. There are 100 people in the community, each of whom has an identical inverse demand function given by P = 10-1.0q, where q is the number of miles preserved and P is the per mile price he or she is willing to pay for q miles of preserved river. If the marginal cost of preservation is $500 per mile, how many miles would be preserved in an efficient allocation?