This week, as the federal Liberals roll out their latest plan to fix housing in Canada, they face a Sisyphean task, one they're unlikely to complete.

While the new government strategy makes a welcome political gesture toward solving problems created by the high cost of housing, there is evidence that the problem is bigger, more complicated and more intractable than any government can handle, even with this latest decade-long multi-billion-dollar plan.

Critics were quick to say why the plan was inadequate.

Never enough

"It's never enough," Jeff Morrison, executive director of the Canadian Housing and Renewal Association told Peter Armstrong on CBC's On The Money.

The criticisms could be grouped into four general categories. It wasn't enough. It was too late. It didn't do the right things. And it didn't help the right people.

All those critiques may be fair. But what no one, including the federal government, was going to admit was that solving the housing crisis is simply impossible.

Not yet Hong Kong density, but the Vancouver skyline is beginning to imitate the Asian city. (Darryl Dyck/Canadian Press) Like the mythological Greek Sisyphus, condemned to roll a boulder up hill repeatedly only to watch it roll down again, housing problems just don't stay solved.

The difficulty of the task is sometimes hidden by the simple-sounding solutions offered by critics — including in the comment section of any story on the subject — many of them contradictory. Open more of Canada's farmland to construction. End immigration. Build more affordable housing. Kick out foreign investors. End all rent controls. Impose more rent controls.

Canadian Prime Minister Justin Trudeau visits a housing development in Toronto's Lawrence Heights neighbourhood ahead of the policy announcement on Wednesday. It's unlikely any government can solve housing. (Chris Young/Canadian Press) If the answers were so easy, there would be be no housing crisis. A wave of Prime Minister Justin Trudeau's magic wand would make us all content.

The all-purpose solution proposed by some is for the government to keep its hands off entirely and let the free market do its work. Certainly that would make the job simpler. But for some reason voters don't like the idea of some Canadian families living in cardboard boxes and others in mansions. And the government knows it.

Battling social and economic forces

Yet the market economy continues to rule in the housing sector. And within the matrix of that market economy, the government is battling enormous social and economic forces.

People, rich and poor, from other parts of the country and immigrants from other countries want to live in Canada's biggest cities.

That urge to migrate to the most expensive places is not limited to this time and this place.

Not just a <a href="https://twitter.com/hashtag/Canadian?src=hash&ref_src=twsrc%5Etfw">#Canadian</a> problem. Ambitious people want to go where the action is, despite the cost of housing. <br> <a href="https://t.co/KRtT4yPbpm">https://t.co/KRtT4yPbpm</a> via <a href="https://twitter.com/FT?ref_src=twsrc%5Etfw">@FT</a> —@don_pittis Recent articles in Britain's Financial Times describe how the young and vigorous continue to stream out of that country's crumbling towns and into its expensive cities, despite falling rents back home in the smaller centres.

A destination city like Hong Kong constantly worries that property prices are prohibitive, but a decades-long private and public building boom has failed to build enough and may have encouraged the influx.

Rents continue to soar. New York and San Francisco and Mexico City face similar fears, and still people come.

Advantages don't go away

"Toronto and other big cities ... have advantages that don't go away just because it gets more and more expensive," Winnipeg economist Wayne Simpson once told me when I was researching the impact of rent control.

In Vancouver and Toronto, the construction industry working in high gear has as yet failed to satisfy demand.

The Canadian construction industry is already hot, with projects such as Canoe Landing in Toronto trying to meet a demand for housing that has not yet been satisfied. (Don Pittis/CBC) The amounts of money involved are hard to conceive. The critics who say government spending "isn't enough" are surely right. The multi-billion dollar spending plan sounds big, but spread over a decade and over a country, the money is dwarfed in a market where a single month's turnover of just resale houses, in greater Toronto alone , is worth more than $5 billion.

Critics who say the government is doing the wrong thing are probably right as well, since no one really knows how to solve the problem of housing.

As we have seen with the Bank of Canada and interest rates, an effort to stimulate the economy by making money easier to borrow has only served to make houses more expensive.

Similarly, giving tax money to help poorer people pay high rents will work through the market economy to bid up the price of rental housing.

Making busy cities more welcoming with lower rents will make them even more dynamic, encouraging the cycle of in-migration.

As we have noted previously, Canada is going through a difficult transition that others have gone through before. There is no longer room for every family to have its suburban picket fence.

Get used to higher density

Increased housing density is blocked by people living in single family dwellings they never could afford to buy. Like elsewhere in the world urban dwellers will eventually become accustomed to higher-density housing going up next door.

People will become used to living and raising families in smaller spaces. The average for new apartments in Hong Kong is now about 600 square feet (57 sq m).

But that adjustment will take time.

In the near term, the one thing that could solve the Canadian housing crisis is a sudden crash in prices with the much-predicted popping of the property bubble.

Then the complaint that federal spending plan is too late will become a virtue.

With parts of the spending plan scheduled to start in 2020, the government's new strategy could kill two birds with one stone, adding to Canada's stock of affordable housing and bailing out a shattered real estate industry adjusting to a new reality.​

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