Sarah Holder has written an excellent piece for CityLab about the effects of AirBnB on local housing prices.   I'd like to expand on one piece of her discussion and relate this to the recent literature in economics on misallocation and "wedges" that arise due to taxes and market distortions.

Labor economists model a person's time allocation decision.  There are 24 hours in a day and each of us can either work or take leisure.   Given our skill set, we can earn a given wage perhaps $20 an hour.   If the tax rate is 25% then your after tax hourly pay is $15 an hour and an economist would say that the "price" of an hour of leisure is $15 (opportunity cost).

In Gary Becker's work on household production, time spent at home is not just leisure. It can also be invested in raising children or other household activities such as cooking.   A key point is that the household sector isn't taxed.  When market work is taxed, this is an implicit subsidy for investing more of your scarce time in home production.

As Sarah Holder's piece argues, AirBNB is "home production". If I rent out one of the bedrooms in my house and then after the guest leaves, I vacuum and clean up --- I am investing my labor in household production that isn't taxed.

She points out in her piece that AirBNB units compete with hotels that pay workers who pay taxes and the workers are unionized.

The point of this blog post is that the high tax states (such as California) also have high union protection and these two forces together create a wedge that allows AirBNB to prosper.

Let me explain;

Assume that all workers are equally productive in cleaning a room.  This room can either be in the hotel or in a house.   Assume that Union workers are paid a 30% premium over non-union workers and assume that everyone who works pays 25% in taxes.  Assume that one worker can clean 1 room per hour and the hourly wage for non-union workers is $14.

Each union worker is paid 1.3*14 per hour and her after tax hourly income = .75*1.3*14

Each hotel who hires union workers is paying 1.3*14 to clean each room and this cost will be reflected in the firm's marginal cost function and thus will set the price the firm charges per hotel room depending on the shape of the residual demand curve it faces.

Each home owner who thinks about renting out a room and then cleaning it has an opportunity cost = .75*14.  I'm assuming he wouldn't be able to find a union job.

Given this lower cost structure, the AirBNB entrant can charge a lower price than the hotel and attract renters because he doesn't pay a union wage premium to himself and he doesn't pay taxes on his household production!

So, the people of Silicon Valley have figured out a way (through creating AirBNB) to arbitrage two distortionary wedges in our economy (the union wage premium and the tax on market work). 

Update:

Define P_hotel =  nightly price for staying in the hotel
P_airbnb =  nightly price for staying in the airbnb

The marginal profit on hotel room =  P_hotel - 1.3*14

The marginal profit on AirBNB room =  P_airbnb- 14*(.8)

Since the AirBNB room is in a person's house, the owner of the house can hire a worker to show up and clean and pay them in cash 80% of $14 as this makes them both better off.  The worker doesn't pay taxes on this home production.

So this algebra highlights the double wedge that allows AirBNB to charge lower prices than hotels and this approach under-cuts unionized labor and lowers the tax revenue that the government collects per room.  Government might collect more revenue if the price elasticity of demand for rooms is large.