income may well exceed what had been anticipated.In fact，most investors have been doing very well under the xian system，particularly since 2000.In other words,with the economy growing and land rents rising，there are implied increases in income which fall into the hands of investors，workers and peasants.Judging from the shifts in the relative prices in favor of agricultural prod-ucts since 2003，these implied increases are very sub-stantial indeed.
The uniform17% level selected for the value-addedtax was reached after many rounds of negotiation with the different localities.It is clearly share rent and hencea clear case of sharecropping between the xians andinvestors on the one hand and between the xians and theupper levels on the other hand.There was an analyticalconundrumwhich took me months to resolve.I wrote The Theory of Share Tenancy 40 years ago，and one of the main points of departure from tradition was that Iallowed the sharing percentage to vary to obtain efficien-cy results.It was clear fromthe evidence in Asian agri-culture that sharing percentages varied significantlyaccording to land grades and localities.But nowthevalue-added tax，a share rent，is the same throughout the country.How can that lead to efficiency？If not，why would China have accelerated so much in growth under the sharing arrangement？
One night I recalled a footnote of Marshall which Iread as a graduate student，and jumped out of bed to findit.Marshall argued that share rent is less efficient than fixed rent，but he added a footnote:
If the 【share rent】landlord controls the amount【of capital】freely and in his own interest，and can bar-gain with his tenant as to the amount of labor heapplies，it can be proved geometrically that he will so adjust it as to force the tenant to cultivate the land just as intensively as he would under the English tenure 【fixed rent】，and his share will then be the same as under it.35
To this I responded in my sharecropping work:Marshall provided no geometric proof，and it is aninteresting conjecture whether he would have alteredthis footnote had he done so.This conjecture isinteresting because the results he conceived are cor-rect only in certain special cases，but as a matter ofgenerality they are incorrect.They are incorrectbecause Marshall did not allowthe rental percentageto vary.36
Based on Marshall’s footnote and my comment，andassuming the xian as the landlord，I asked myself what amount of ‘capital’ can the xian provide to guarantee anefficient solution when the sharing percentage is heldfixed and uniform.The answer，which I discoveredaround the end of 2004，is that the land price chargedby the xians（to investors as sharecroppers）can actuallybe negative!Taking land to be the capital contributed
【35】Alfred Marshall，Principles of Economics（8thed.，1920:London; Macmillan Co.1956），p.536，note 2.
【36】Cheung，The Theory of Share Tenancy,op.cit.，p.45.
by the landlord，the possibility of using a negative landprice means the landlord is offering infinite opportuni-ties for adjustment，under which the equi-marginal con-dition required for efficiency can always be attained aslong as the uniformsharing is within a reasonablerange.
By a negative land price，I mean that when an investorcomes to a xian to consider investment and production,the xian may not only give improved land to the investorfree of charge，they may even build the facilities gratis,or allow the investor a rebate over a number of years out of the value-added tax the xian is entitled to.Of course,not all xians are worth investing in，as there is no pointbuilding a factory in the hilly wilderness.Social returnsaside，the guideline of hownegative a land price can beoffered is a return high enough to cover the interest for-gone in the xian’s efforts to obtain and improve land forindustrial or co ercial usage.We will return to thisquestion in the next section.
Beijing’s prohibition on land prices going negative,imposed in 2006 for some xians，suggests that they didnot understand the working of the implicit sharecroppingsystem.But it may not be so.There is the problem that China’s population would be concentrated in the popularregions，to the detriment of a more even distributionwhich is more desirable in the long run.I wrote about the issue，but could offer no solution.There are mattersfor which market prices are not available to guide deci-sions，as Coase and I have expounded in our work on thefirm，and errors can only be discovered ex-post.
Ⅶ.The Sharing Formula and Its Effects
One evening in 2005，the head of a xian fromfar awaycalled，saying he happened to be in the neighborhoodand wanted to drop in for a visit.He came，took off his shoes，laid on the sofa，closed his eyes for some minutes,and then asked，“Professor，may I have a glass of wine？”Of course he may.
I knew what must have happened.Xian officials like this friend run all over the country soliciting investment.Whenever a business-inviting conference is held in a cer-tain city，the word would get around and officials from countless xians would arrive.It is not uncommon the sedays that xian officials dine at business occasions severaltimes in one evening.
A xian with a mere 300,000 in population would of ten employ 500 investment solicitors.In 2005 a xianin Anhui province held a beauty contest，selecting themost beautiful，charming and persuasive ladies to head the teams.Criticized all over the country，the head ofthat xian fought back: “Beauty is an asset，why not useit？”
