Down a ramshackle alleyway, with no running water or toilet, and filled with rubbish, lies a cramped, 13-square-metre room few wealthy Chinese would deign to occupy. It is for sale at nearly $600,000.

The space has one particular feature that makes it a spectacularly desirable residence: ownership entitles the buyer's child to a place at the nearby Huangchenggen Primary School, considered one of the best in the People's Republic.

The asking price of 3.8 million yuan is equivalent to $45,000 per square metre (nearly $4,200 per square foot) -- comparable to some properties in Mediterranean tax haven Monaco.

Even so, "it's going to move quickly," said an estate agent showing the space, adding he had already sold two adjacent rooms.

Chinese parents are renowned for the high value they put on education, but the astronomic prices the rich are willing to pay to ensure their children get into the best schools have raised a furore over equality of opportunity.

The room's price is more than the cost of sending a student to Harvard for both an undergraduate degree and law school.

The phenomenon is the natural outcome of a system that "emphasises that children must win from the starting line", said Tao Hongkai, director of an education research centre at Central China Normal University.

Parents are "investing two-thirds of their income in their child's education", he said, adding that "since they only have one child, they put everything into them".

Only owning guarantees a spot at the exclusive schools, not renting, so that the best schools are increasingly reserved for China's wealthy.

"Before, educational resources were relatively balanced. Now, it's completely education for aristocrats," said Tao.

- 'Better if it's liveable' -

Reports that a buyer paid 5.3 million yuan for an 11.4-square-metre room in Wenchang Alley, with similar access privileges at Beijing Number Two Experimental Primary School, ignited controversy last week.

The schools' catchment areas, where property-owning families with Beijing residency are guaranteed a free place, are restricted to only a few streets, with other hopefuls having to apply -- and pay -- for one of the coveted slots.

Beijing Number Two takes in around 800 children a year, many of whose parents are government officials.

As is common in the capital's central neighbourhoods, many of the centuries-old courtyard dwellings have been chopped into a dozen or more small rooms.

Red doors with lion head knockers open into a maze of narrow junk-filled passageways, crisscrossed by ropes heavy with drying laundry, sausages, or dead ducks.

As many as three generations crowd into the tiny spaces, using nearby public bathrooms.

Even so eager buyers plaster the courtyards' walls with fliers, desperate for rooms as small as seven metres square.

Any space will do, said one ad, offering to pay cash for an "appropriate" accommodation. "Of course, it's better if it's liveable," it added.

But the costs are worth it, said Xiong Bingji, of the 21st Century Education Research Institute.

"In China, educational resources are unbalanced. A school district apartment lets kids go to a really great elementary school and get a high quality education," he said, adding they might also offer a profit when the school place is no longer needed.

"After five or six, years... it's possible prices will be even higher".

- 'Insane' -

Wenchang Alley exists in a surreal space between China's past and its present. To the north, luxury sedans idle behind gleaming office towers housing the banks that helped finance China's transformation from a destitute socialist backwater into the world's second-largest economy.

To the south a stately old courtyard home hosts a museum celebrating the life of Li Dazhao, who co-founded the Communist Party of China in 1921.

The Beijing Number Two school is sandwiched between the two, a modern and well maintained facility, fitted with solar panels and picture windows.

Children play on new basketball courts beneath signs exhorting them to "bravely explore" and "venerate civilisation", as well as a list of "core" socialist values, including both "prosperity" and "equality".

Two kilometres (a mile) away, at the annual meeting of China's Communist-controlled legislature, delegate Li Chanming, the director of one of Beijing's best middle schools, decried the sums being paid for the "school rooms".

The money would be better spent on "improving the quality and amount" of the children's extracurricular tuition, he told a press conference on social policy.

At Beijing Number Two, parents politely disagreed.

"The school pays more attention to the kids' all-around education and comprehensive development," said one mother waiting to collect her child. "They don't just focus on kids' grades."

She and other parents declined to comment on their family incomes or how they secured their places.

Other neighbourhood residents were less circumspect.

"You could fit a bed and a dresser in it, but then you wouldn't have space to move," one man said of the 5.3 million yuan room. "It's insane."