SHANGHAI, China’s financial centre, does not make it easy on outsiders wishing to buy homes. Non-residents who are single are banned from buying property. The married are welcome but only so long as they have paid local taxes for two years and make nearly a third of the purchase in cash. Shenyang, China’s biggest northern city, is far more welcoming. Anyone can buy a home there. All to little effect: housing prices in Shanghai, five times more expensive than those in Shenyang, have risen by 20% over the past year; those in the northern city have edged down.

This bifurcation is a worry for the government, which wants to spur growth without inflating bubbles. A divergence in housing prices between wealthy cities and the hinterland is a familiar problem in other countries—just look at London and Lincolnshire, say, or New York and Nebraska. But the divisions are starker in China. In its most prosperous cities, already giddy prices continue to shoot up, while unsold flats pile up in markets where valuations were low to begin with. Moreover, construction has long been one of the economy’s main engines, accounting for as much as a quarter of GDP growth until recently. This makes it especially important that the government get the balance right. Doing so is proving hard.

Over the past half-year, the government has unveiled a series of measures to support the housing market that specifically exclude China’s five hottest markets (Beijing, Guangzhou, Sanya, Shanghai and Shenzhen). People buying homes need only make a 20% down-payment to obtain a mortgage, except in the five conurbations, where they must put down 30%. By the same token, in most of the country transaction taxes have been cut by as much as two-thirds for people buying second homes; in the five outliers they have been left unchanged. In Shenzhen, a southern tech hub that is the frothiest market, with prices up by 53% in the past year alone, local officials have vowed to crack down on speculators and expand the supply of affordable housing.

The results of this two-tier system have been meagre so far. The frenzy in the biggest cities stems from the central bank’s steady loosening of monetary policy over the past 18 months. Although warranted from an economic perspective, it was inevitable that low interest rates would drive asset prices higher. Initially, much of the credit pumped out by banks ended up in the stockmarket, but following its crash last summer, property beckoned as one of the few decent investment options in China (capital controls, which have been further tightened recently, make it hard for Chinese savers to invest their money abroad).

For speculators looking at property, the excess supply in smaller cities was all too evident, so they turned instead to the megalopolises. Du Jinsong of Credit Suisse describes it as a form of groupthink. “Everybody—investors, developers, policymakers and bankers—thinks that first-tier cities are safe,” he says.

Even as the government tries to restrain the excesses, however, it does not want to snuff out the rally in the big cities altogether, for they tend to influence sentiment elsewhere. There are signs that this is beginning to happen. Housing prices started rising month on month in the biggest cities a year ago. In midsized cities (in China, those with populations of 5m-10m), prices have been rising for the past four months. In smaller cities (mere hamlets of 1m-5m), gains have been evident only for the past two months (see chart).

If this upturn lasts, some investors reckon it will spur construction. Commodities used to build apartment blocks, such as iron (girders) and copper (wires), have recovered slightly from their recent swoon, partly in the hope that China’s property market is also stirring (see article). Indeed, a series of mini-cycles in the Chinese housing sector over the past decade followed this sort of pattern: rising housing sales led to new building starts, which in turn pushed commodity prices higher. Figures from the China Index Academy, a data provider, show that the stock of unsold homes has decreased recently, from nearly 30 months’ worth of sales early last year to 15 now. “A housing market with rising volume and prices clearly does not support the view that, on a macro level, China’s housing market is oversupplied,” notes Liang Hong of China International Capital Corp, an investment bank. But there is a further vast increment of supply on the verge of coming to market, because developers slowed the pace of construction in recent years and in some cases halted it altogether. There were 4.7 billion square metres of housing under construction but not yet available for sale at the end of last year, up by 25% from the end of 2011; 452 million square metres of housing were on sale, nearly three times as much as at the end of 2011. Some provinces and cities are drafting plans to convert unsold homes into subsidised housing for poorer residents. Xi Jinping, China’s president, has said that reducing property inventory is a “battle of annihilation” that must be won to revitalise the economy. Revived demand for new construction, in short, is a long way off. The exception is sure to be China’s biggest cities, where there clearly is an imbalance between supply and demand. Shenzhen and Shanghai, in particular, are popular with the young and the highly educated, just the kinds of people that push up housing prices. They are two of China’s best-run cities, offering good transport links, good jobs and, by Chinese standards, good air. Unsold housing inventories cover just about five months of demand at the current pace of sales, indicating that more construction is needed.