Although Uber and Lyft are known for their flexible “surge pricing,” they are surprisingly rigid in another way: each firm takes a constant percentage of passenger fare whether or not there is a surge. In this paper, I investigate the possible reasons for, and the impact of, this rigidity. I study a market in which a profit‐maximizing intermediary facilitates trade between buyers and sellers. The intermediary sets prices for buyers and sellers, and keeps the difference as her fee. Optimal prices increase when demand increases, that is, shifts right. If a demand increase is due to an increase in the number of ex ante symmetric buyers, then the intermediary’s optimal percent fee decreases. If, instead, a demand increase is due to a reduction in the elasticity of demand, then the intermediary’s optimal percent fee increases. In either case, if the intermediary keeps a constant percent fee regardless of shifts in demand, as is the case with Uber and Lyft, then surge pricing (i.e., the ratio of price during high demand to price during low demand) is amplified on one side of the market and diminished on the other side.