To prove: Uber cannot be cheaper than driving your own vehicle. Proof of negation of the TP using counterexample: 1. Monthly insurance cost for own vehicle =

To prove: Uber cannot be cheaper than driving your own vehicle. Proof of negation of the TP using counterexample: 1. Monthly insurance cost for own vehicle = a few hundred dollars = $k. Monthly insurance cost for Uber = $0. 2. Assume an extreme case where you don't travel at all in the entire month. Total cost of transportation for owning a car = $k. Total cost of transportation for Uber-ing everywhere = $0. 3. Assuming that the costs are proportional to the kms you have traveled you get this: http://imgur.com/A61dXx9 http://imgur.com/A61dXx9 The inflection point where Uber is no longer cheaper than driving is (k / (mu - mc)), where mu and mc are the slopes for the lines for Uber and own car, and "k" is the insurance intercept.