Demand for housing in Washington, D.C., is going through the roof. Over a thousand people move to the nation's capital every month, driving up the cost of housing, and turning the city into a construction zone. Tower cranes rising high above the city streets have become so common, they're just part of the background.

But as fast as the cranes can rise, demand for housing has shot up even faster, making DC among the most expensive cities in the United States. With average home prices at $453 per square foot, it's every bit as expensive as New York City. And the struggles of one homebuilder shows just why the city's shortage looks to continue for a long time.

"I got driven down the tiny house road because of affordability, simplicity, sustainability, and then mobility," says Jay Austin, who designed a custom 140-square-foot house in Washington, D.C. Despite the miniscule size, his "Matchbox" house is stylish, well-built, and it includes all the necessities (if not the luxuries) of life: a bathroom, a shower, a modest kitchen, office space, and a bedroom loft. There's even a hot tub outside.

Clever design elements make the most of minimalism. The Matchbox's high ceilings, skylight, and wide windows make the small space feel modern, uncluttered, and open.

At a cost that ranges from $10,000 to $50,000, tiny homes like the Matchbox could help to ease the shortage of affordable housing in the capital city. Heating and cooling costs are negligible. Rainwater catchment systems help to make the homes self-sustaining. They're an attractive option to the very sort of residents who the city attracts in abundance: single, young professionals without a lot of stuff, who aren't ready to take on a large mortgage.

But tiny houses come with one enormous catch: they're illegal, in violation of several codes in Washington D.C.'s Zoning Ordinance. Among the many requirements in the 34 chapters and 600 pages of code are mandates defining minimum lot size, room sizes, alleyway widths, and "accessory dwelling units" that prevent tiny houses from being anything more than a part-time residence.

That's why Austin and his tiny house-dwelling neighbors at Boneyard Studios don't actually live in their own homes much of the time. To skirt some of the zoning regulations, they've added wheels to their homes, which reclassifies them as trailers – and subjects them to regulation by the Department of Motor Vehicles. But current law still requires them to either move their homes from time to time, or keep permanent residences elsewhere.

The DC Office of Zoning, the Zoning Commission, the Zoning Administrator, the Board of Zoning Adjustment, and the Office of Planning all declined to comment on the laws that prevent citizens from living in tiny houses. But their website offers a clue:

Outdated terms like telegraph office and tenement house still reside in our regulations. Concepts like parking standards and antenna regulations are based on 1950s technology, and new concepts like sustainable development had not even been envisioned.

Complex as it is, the Zoning Ordinance of the District of Columbia was approved in 1958. That's over five decades of cultural change and building innovations, like tiny houses, that the code wasn't designed to address.

Exemptions and alterations to the code are possible—many are granted every year—but they don't come cheaply. Lisa Sturtevant of the National Housing Conference estimates that typical approvals add up to $50,000 to the cost of a new single-family unit. That's why large, wealthy developers enjoy greater flexibility to build in the city, but tiny house dwellers… not so much.

Fortunately, a comprehensive rewrite of the zoning code has been in the works for much of the last decade. Efforts to allow more affordable housing are underway, although many of these solutions favor large developers. Future plans still forbid tiny houses. Austin estimates that, given the current glacial pace of change among the city's many zoning committees, tiny houses are "many years, if not decades out" from being allowed in the city.

For now, Jay Austin is allowed to build the home of his dreams – he just can't live there. The Matchbox has become a part-time residence and a full-time showpiece. The community of tiny houses at Boneyard Studios are periodically displayed to the public in the hopes of changing a zoning authority that hasn't updated a zoning code in 56 years.

Runs about 10:30

Produced, shot, written, narrated, and edited by Todd Krainin.

Additional music by Lee Rosevere.

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