According to reliable estimates, cars are unused most of the time; and scores of bedrooms go unused every evening. Many startups have jumped into this void to create a sharing economy for cars, housing, and other goods. Let’s analyze this sort of market, using the market for rooms as an example.
Suppose there are two groups of rooms that could be made available for rent, a commercial sector (hotels) and a residential sector (consisting of rooms in places like your house). Hotels have a supply schedule, and let’s say it’s given by P = 20 + 0.5Q, where Q is the number of rooms they rent in some given time period.
Homeowners also have rooms. If there were a market for such things, many homeowners would be willing to rent out rooms for the night. Many of these owners would be willing to rent out a room at a lower rate than even low-cost hotel rooms. But some people would not.
Suppose that, collectively, homeowners have the following supply scheduled for rooms: P = 10 + Q.
Finally, suppose that demand for rooms is given by P = 100 – Q.
First, calculate the equilibrium price and quantity of rooms when only the commercial sellers are in the market. Calculate CS and commercial seller PS.
Next, find the overall supply curve for rooms when the residential sellers enter the market.
Calculate the equilibrium price and quantity when the residential sellers are in.
Calculate CS, as well as the PS for residential and commercial sellers, respectively.
 See, for example, http://www.economist.com/news/leaders/21573104-internet-everything-hire-rise-sharing-economy .