Taxation by auction: fund raising by 19th century Indian guilds

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Journal of Development Economics 74 (2004) 411–428

Taxation by auction: fund raising by 19th century

Indian guilds

Arijit Sena, Anand V. Swamyb,*

aCentre for Economic Studies and Planning, School of Social Sciences-II, Jawaharlal Nehru University,

New Delhi 110067, IndiabDepartment of Economics, Williams College, Williamstown, MA 01267, USA

Received 1 March 2001; accepted 1 July 2003

Abstract

We describe a unique institution used by 19th century Indian guilds to raise funds: on certain

holidays only one shop was allowed to operate; an auction would be held to sell this right, and the

winning bid would go to the guild fund. We compare this ‘‘taxation by auction’’ mechanism with

more conventional tax schemes and show that under certain conditions, not only will a majority of

guild members prefer to be taxed via an auction, but that this form of taxation will be more

equitable.

D 2004 Elsevier B.V. All rights reserved.

JEL classification: N85; O17

Keywords: Auctions; Fund raising; Indian guilds; Taxation

1. Introduction

Small communities often need to raise funds for the creation and maintenance of local

public goods. For instance, the residents of a village that is served by an irrigation canal

may have to contribute money and labor to maintain the facility; such contributions may

also be needed to enforce rules pertaining to the sustainable use of village forests; funds

may be required to construct or maintain the local school. However, even when such

cooperation is socially beneficial, it may not come about unless suitable institutions

emerge to allocate costs and benefits and punish opportunistic behavior (see Olson, 1965).

0304-3878/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jdeveco.2003.07.002

* Corresponding author.

E-mail addresses: [email protected] (A. Sen), [email protected] (A.V. Swamy).

A. Sen, A.V. Swamy / Journal of Development Economics 74 (2004) 411–428412

Recognizing this, development economists, among others, have sought to study the

institutional arrangements used by small communities to raise funds, and cooperate in

other ways.1 In this paper, we document and analyze one such arrangement: an ingenious

fund-raising method used by guilds in Gujarat (and other parts of India) in the 19th

century.

The Gujarati guilds were associations of producers/traders in a common line of business

in a city (see Section 2). Like any professional association, the guilds sought to raise funds

from their members for internal use, such as organizing dinners for guild members. In

addition, the richer guilds collected funds to provide various community-wide public

goods and services. Guild funds were used for charitable donations to religious institu-

tions, and to public institutions like animal hospitals, food kitchens, and drinking-water

facilities and resting places for travelers. Businessmen of the Jain faith continue to support

animal hospitals, known as pinjrapole, to this day.

To raise the funds, many guilds employed a mechanism that the Gazetteer of the city of

Surat, a prominent Gujarati trading and manufacturing center, described as follows

(Bombay Precidency, 1877, p. 321):

A favorite device for raising money is for men of the craft or trade to agree, on a certain

day, to shut all their shops but one. The right to keep open this one shop is then put up

to auction, and the amount bid is credited to the guild fund.

We call this mechanism ‘‘taxation by auction’’. Under this scheme, a guild in effect

taxed each of its members a day’s profits (except for the winner, who received some

information rents and was thus taxed only a part of his day’s profits). A crucial aspect of

implementing the scheme was to ensure that only the winning firm stayed open on the

holiday. This was achieved by the guild members agreeing to impose heavy fines on, and

even expel, offenders (see Section 2). The auction mechanism was thus supported by the

guild’s collective enforcement capacity.2

Auctions are much in the news these days, as they are being used by governments

across the world to divest public assets. The ‘‘spectrum auctions’’ in the US are a prime

example. Of course, auctions have long been used by governments and private parties to

sell (or lease) commodities as varied as food grains, forest timber, paintings, and oil tracts.

All these auctions have a common feature—an existing physical commodity is sold to the

highest bidder. In a different sphere, auctions have also been used to award ‘‘monopoly

rights’’ to firms and individuals. Many governments have auctioned off ‘‘trade quotas’’

1 Several such institutions are described and analyzed in a symposium on the management of local commons

in Journal of Economic Perspectives, Fall 1993. For Ostrom et al. (1994, p. 14), the task of eliciting contributions

for provision and maintenance of an irrigation system (say) is just one in the class of ‘‘supply-side provision

problems’’. Maclure (1994) discusses the difficulties associated with community participation in schools in

Burkina Faso.2 Another ingenious method for raising funds for a public good, used in the city-states of ancient Greece, is

succinctly described by Moore (1992, p. 195) as follows: ‘‘Someone nominated the man who was reputed to be

the richest. Let us call him Spyros. Spyros would then have to pay up, or claim ‘‘I not the richest, old Timon over

there is richer than me.’’ Then Timon was faced with a choice. Either he could pay, or he could insist that Spyros

exchange all his wealth with him, after which Spyros would have to pay’’.

A. Sen, A.V. Swamy / Journal of Development Economics 74 (2004) 411–428 413

and ‘‘licenses’’ to firms to enter new industries.3 More creatively, Jain temples in South

Asia and elsewhere have auctioned off the rights to perform certain religious ceremonies

(Banks, 1992). In principle, both kinds of auctions have served the dual purpose of

maximizing ‘‘seller revenue’’ and of allocating scarce resources efficiently.

The guild auctions differ from the above types of auctions in two major ways. First, the

item being auctioned is a monopoly right to work. Note that this monopoly position was

collectively created in the first place by the guild members who agreed to give up their

individual rights to work on a holiday. This is in contrast to other instances of auctioning

off monopoly positions, where these positions came into being as a result of the

environment and/or the technology.4 Second, the aim of the guild auctions was not so

much to maximize guild funds, but to collect a desired amount of funds via an auction

scheme rather than through more conventional forms of taxation.

In this paper, we present a theoretical analysis of the auction mechanism within a

formal model of guilds. Taking as given the amount of funds that a guild intends to raise,

we compare the payments that different guild members make under the auction vis-a-vis

other conventional taxes like a revenue tax. Given that many 19th century Indian guilds

engaged in collective decision making and that they desired to maintain equity (see

Section 2), our analysis identifies intuitive conditions under which (a) a guild will, at its

inception, prefer to adopt the auction mechanism over other tax schemes (ex ante majority

preference), (b) once the auction scheme is adopted, there will be no subsequent pressure

by a majority of the guild members to replace it by a conventional tax (interim majority

preference), and (c) the auction tax will be ‘‘more equitable’’ than a conventional tax.

The rest of the paper is organized as follows. In Section 2, we discuss the Indian guild

in its historical context, and document the ‘‘taxation by auction’’ arrangement. We present

a formal model of a guild’s alternative fund-raising mechanisms in Section 3. In Section 4,

we compare the ‘‘auction tax’’ to conventional taxation (specifically, to taxes on sales

revenue and inputs), and establish our central results. We discuss the implications of our

analysis in Section 5, and conclude.

2. Fund raising by Indian guilds, ca. 1890

The western Indian region of Gujarat has long been a major center of manufacturing

and trading. Guilds were active in this region until at least the early 20th century. In each

city, different occupations had their own guilds. There would be a grain-dealers’ guild, a

potters’ guild, a tobacco-sellers’ guild, a sweet-makers’ guild, and so on. In addition, a

citywide organization of merchants’ guilds, known as the Mahajan, provided important

administrative and dispute-resolution functions.

3 McAfee et al. (1999) document auctions held by the New Zealand government to allocate quota licenses in

the 1980s. The authors note that apart from raising revenues, such auctions had the potential to determine the

‘‘value’’ of such monopoly positions, which could then be used to convert quotas into ‘‘correctly priced’’ tariffs.4 In the case of quotas and licenses, independent economic arguments determined the creation of a monopoly

position. In the case of the temples, logistical considerations would likely dictate that the ritual be performed by

one or at most a few people.


Like guilds elsewhere, Gujarati guilds exercised a great deal of power over their

members.5 They regulated entry and working hours, some fixed sales quantities of

different guild members, and some explicitly set prices. Hopkins (1902, pp. 194–195)

reports that the artisan guilds routinely fixed prices. The Ahmedabad Gazetteer (vol. V, p.

109) refers to price-fixing by potters, barbers, and carpenters. Among the merchant guilds,

grain dealer and moneychanger guilds engaged in price-fixing (Hopkins, p. 194, p. 197).

Decision-making in a guild was to a large extent collective, and there is some evidence of

majority voting. Regarding guilds in the city of Ahmedabad, the Imperial Gazetteer of

India (p. 101) wrote: ‘‘Each of the different castes of traders, manufacturers, and artisans

forms its own trade-guild, to which all heads of households belong. Each member has the

right to vote, and decisions are passed by a majority’’.6 Violation of guild rules led to

severe fines, and in extreme cases, devastating social ostracism, which was imposed in

collaboration with other guilds. Hopkins (1902, p. 193) describes the punishment meted

out to the offender: ‘‘In the cities no dealer will serve him, no broker will act for him, no

servant will remain in his house. The carpenter, the baker, the confectioner, the blacksmith,

the tile-maker, the very potter, lowest of the lowly, refuse to take his orders, deliver goods

to him, or perform a service for him at any price’’.

There is ample anecdotal evidence that the guilds desired to maintain equity. The

methods used to achieve this objective included fixing prices, quantities, and working

hours. There is evidence that artisan guilds tried to allocate demand among different

members. Hopkins (1902, p. 197) writes: ‘‘The rates of sale and amount of marketable

material which can be made by each artisan are always settled in advance by the respective

guilds’’. According to the Ahmedabad Gazetteer (Bombay Precidency, 1879, p. 110)

‘‘. . . at the opening of the season the aldermen of the city tile-makers prescribe exactly

how many thousand tiles each member may make, and the minimum rate at which he may

sell them’’. The Gazetteer goes on to mention that because employment was scarce, the

bricklayers’ guild had forbidden its members from working overtime on any terms. It then

describes a practice wherein all handmade fabrics exported from Ahmedabad had to go

through about a dozen agents, who were forbidden from taking more than a certain

commission. Its interpretation of these practices is unambiguous: ‘‘It will be noticed that

the object of the above three edicts was the same, to distribute business among all alike

and to keep individuals from enriching themselves at the expense of the rest’’. At one

point, the Gazetteer (p. 111) accuses the guilds of ‘‘bigoted communism’’.

As mentioned earlier, the guilds raised funds from their members for guild functions

and celebrations as well as donations to public institutions. They used various conven-

tional methods such as entry fees, donations from members, and taxes on inputs and sales.

In Ahmedabad, confectioners were taxed on purchases of sugar and condensed milk. In

Broach, a tax that could be as high as a quarter of a dollar was placed on every bale of

5 For an overview of European guilds in the Middle Ages, see Thrupp (1965). For a recent interpretation of

the merchant guild as a mechanism that allowed rulers to commit to the security of merchants, see Greif et al.

(1994).6 In his survey of Indian guilds, Mukerjee (1923, p. 285), discussing the authority of the Mahajan, writes:

‘‘This authority is always exercised democratically. . .election and decision by majority is well-known among the

traders’ as well as the craftsmen’s guilds’’.


cotton. Every bill of exchange negotiated by a banker was taxed about 10 cents (Hopkins,

p. 191).7 Mukerjee (1922, p. 182) documents the use of sales taxes by guilds in the South

Indian city of Madura and reports on the custom of mahimai which are ‘‘fees on the

quantity of merchandise purchased and sold’’. He also provides a list of taxes on sale

proceeds imposed by the Sourashtra Sabha, a community association of artisans, traders

and bigger merchants.

Besides these conventional tax schemes, many observers noted the widespread use of

the ‘‘taxation by auction’’ mechanism described earlier. The Imperial Gazetteer of India

(volume 9, p. 25) provides the following account for Broach:

Money-changers, grain-dealers, grocers, and tobacco merchants make the observance

of their trade holidays—the 2nd, the 11th, and the last day of each fortnight—a source

of revenue to the general body. On the occasion of these holidays, only one shop is

allowed to stay open in each market. The right to open this shop is put up to auction,

and amount bid is kept for caste purposes.

The use of such auctions by Gujarati guilds is also mentioned by Gazetteer of

Ahmedabad (p. 111). An important source for this paper is Hopkins (1902), who, in

1896, conducted an ‘‘informal conference’’ with the heads of merchant and artisan

guilds in Ahmedabad, and supplemented this with information from other towns in

Gujarat. Hopkins (p. 190) describes the auctioning of the right to stay open on a holiday

as a ‘‘prime source’’ of revenue for ‘‘most guilds.’’ Finally, as late as in 1932, Desai

(1932, p. 220) writes: ‘‘Even now a considerable income is derived from the auction sale

of the right to keep shops open and do business on holidays’’. Similar auctions have

been used in other parts of India, including the city of Madura (Mukerjee, 1922, p. 182,

1923, p. 287).

The success of the auction scheme depended on a guild being able to ensure that only

the winning firm stayed open on a holiday. It would have been easy for a guild to observe

which of its members opened shop on a particular day, because they were usually clustered

in marketplaces.8 The Ahmedabad Gazetteer (p. 108) reports that the richer guilds had a

salaried clerk, gumasta, who was to ‘‘report to the aldermen all irregularities, such as non-

observance by any member of an appointed holiday’’. Given this, the fear of punishment

ensured that the holiday was observed by all except the winning firm. Hopkins (1902, p.

190) describes the treatment of firms which stayed open in violation of the guild’s dictates:

‘‘The fine is heavy for the violation of this right on the part of others; and if the offence is

repeated, the delinquent is sometimes expelled rather summarily’’.

7 Hopkins writes (p. 190): ‘‘Large guilds also get revenue from the purchases of the members, on which a tax

is levied. One quarter of one percent is the annual impost, but when paid in kind, as is often done, an approximate

amount, reckoned roughly according to this ratio, is taken by the guild. Thus from each cart bringing in a load of

grain, a few handfuls are taken out and cast in a heap at the city gate’’.8 The Gazetteer of Ahmedabad (p. 316) describes three ‘‘old markets’’ in the city: ‘‘In the Manekchok are the

chief bankers, jewelers, and native piece-good dealers. . .In the street east of the Three Gateways are European

piece-goods, hardware, sweetmeat, and vegetable shops. In the open space towards the Karanj where are grocery

and betel-leaf shops, the old weekly Juma or Friday market is still held. . .’’.


It should be clear from the above description that the auction scheme was a form of

taxation, where every firm was taxed a day’s profit (except for the winning firm, which

got to keep some ‘‘information rents’’) in order to raise money for the guild as a

whole. The rationale for this arrangement must therefore be sought by comparing it

with other conventional methods of taxation. That is what we do in the following

analysis. Specifically, recognizing the guilds’ proclivity towards collective decision

making and their concern for equity, we address the following questions in a formal

model: given that a guild wants to raise a certain sum of funds, when is it the case that

a majority of the guild members will prefer the use of the auction scheme as opposed

to any other tax scheme? When will the auction scheme be more equitable than other

kinds of taxes?

3. Fund raising mechanisms: a formal analysis

We start our formal analysis by recognizing the fact that in designing a fund-raising

mechanism, every guild most likely faced the following information constraint—it could

not perfectly observe the realized profits of its members. Even if sales could be

observed, the actual costs incurred by a firm within a specific time interval would

likely be private information (especially given that ‘‘family labor’’ was an important

input, whose opportunity cost at any point in time could hardly be commonly known).

Given that, our aim is to compare the performance of the auction scheme with that of

other schemes of taxing observable outcomes like revenue, sales, input purchases, etc. In

what follows, we focus primarily on the comparison between the auction and revenue

taxation. However, as we indicate subsequently, both our methodology and our

qualitative results carry over in comparing the auction to other conventional tax

schemes.

At the outset, recognize that an auction tax and a revenue tax can be so designed as to

be completely equivalent when the following conditions hold: (a) all firms in a guild are

identical in terms of costs incurred and revenues generated, and (b) the aggregate profits

generated by the guild members over any time interval is independent of the actual

number of firms in operation. If (a) and (b) jointly hold, then it is easy to see that if, for

example, profits are half the sales revenue for each firm, a 10% tax on the yearly sales

revenue of each firm will generate the same collection for the guild as when it employs

the auction scheme for one-fifth of the days in a year.9

However, the above conditions are very stringent. It is natural to expect that there

was ‘‘some’’ heterogeneity among guild members. Further, there is no reason to expect

that on any given day, if only one firm operated, it could serve the entire market and

generate the same amount of profits as when all guild members operated simultaneously.

Therefore, in our formal model, we study the efficacy of ‘‘taxation by auction’’ when

9 To see this, suppose that the total revenue generated on each day is S. Then the guild will collect 36.5S

under the revenue tax. This amount can be raised by holding an auction for 73 ‘‘holidays’’, since on each holiday,

a particular firm will win the auction by paying S/2 (since the winning firm will generate this amount as profits).

Note that the contributions made by each firm will also be identical under the two schemes.


there is heterogeneity among guild members and when aggregate profits depend on the

number of operating firms.

3.1. A model of a guild

Consider a guild of N firms, where N > 3. The firms operate at each instant in a time

interval [0, 1]. For any firm i, its instantaneous cost function is Ci( q) = hiqc, where hi is an

efficiency parameter privately known by firm i, and c is a commonly known returns-to-

scale parameter with cz 1. It is common knowledge that {h1, . . ., hN} are independently

and identically drawn from a symmetric distribution function F(�) on an interval [h�, h+],with h�>0. We let Eh denote the mean of each hi.

The instantaneous market demand is given by Q(P). The price that any firm can

charge at any instant is fixed by the guild at P0, and we normalize the corresponding

demand, Q(P0), to be unity. When multiple firms charge P0, they share the market

equally.10 We assume that P0 is large enough so that at any instant, each firm is

willing to meet its demand, no matter what its efficiency parameter is and no matter

how many other firms operate concurrently.11 Then, if m firms (with 1VmVN)

operate at any instant, the instantaneous profit of any firm i is p(hijm)uP0/m� hi(1/m)c; this will also be firm i’s aggregate profit if the m firms operate for the

entire time interval.

Let R be the amount that the guild wants to collect (in expected terms). In its fund-

raising effort, the guild faces the information problem that it cannot observe the realized

efficiency parameters of the N firms. Recognize that if it could indeed observe (and

verify) hi for every firm i, the guild could require each firm to donate x* fraction of its

realized profits, where

x* ¼ R=NpðEh j NÞ:12 ð1Þ

Then each firm i would pay x*p(hijN), and the guild would collect R (in expectation). We

will make use of this benchmark tax rate x* to facilitate our subsequent comparison of the

alternative fund-raising schemes that the guild can implement given its information

constraints.

Three comments about our model are in order. First, we have modeled a guild

consisting of heterogeneous members, where the precise differences across them are not

commonly known. The posited cost asymmetry among firms captures this. However,

while hi affects firm i’s costs (and thus profits) in a specific way in our model, it can be

thought of more generally as any privately observed variable that affects firm payoff

10 As mentioned before, there is ample evidence that many guilds fixed prices and allocated demand

equitably among their members. One way to think of the price P0 is to suppose that it is a ‘‘collusive’’ price that

maximizes the ex ante expected joint profits of the guild members: PQ( P)�NEh[Q( P)/N]c.11 When there are no taxes, the condition is satisfied for P0z ch+. We assume that P0 is bigger than this

threshold so that the condition is satisfied even when there are ‘‘small’’ taxes imposed by the guild.12 We take R to be small in relation to firm profits; specifically, we assume that R is less than the profits to

the highest-cost firm p(h+jN). This will ensure that x*, and the ‘‘auction tax’’ rate t* defined in Eq. (2), is

between 0 and 1.


within the time interval. Second, our aim is to model a scenario where a single firm

cannot generate the same profits that many firms operating concurrently can. An obvious

reason for this is diseconomies of scale in production. In addition, other factors like

consumer transportation costs, product differentiation, and client loyalty will also imply

that a single firm can serve only a part of the market. For the sake of brevity, we have

summarized these factors in a single returns-to-scale parameter c. Finally, our ‘‘single

period model’’ can be extended to study a dynamic environment where firms are in

business over a sequence of time periods (e.g., calendar years), where the guild wants to

collect R in each period. In that scenario, firms can have ‘‘permanent’’ cost differences, as

well as period-specific shocks to their costs. While we do not analyze such a case, we

will subsequently discuss how our results shed light on this dynamic model.

3.2. Taxation by auction

We model the auction scheme as follows: given the time interval [0, 1], the guild

declares a subinterval t (0 < t< 1) to be a ‘‘holiday’’, and decrees that one firm will have to

acquire the right to operate during this period by winning an auction (with the auction

proceeds going to the guild fund).13 We consider an open ascending auction with zero

reserve price.14 We also assume that the winning firm is required to charge the price P0

during the ‘‘holiday’’.15

For a given t, the value of winning the auction to any firm i is tp(hij1). Given {h1, . . .,hN}, let h(k) denote the kth order statistic (i.e., the kth lowest draw). Standard results in

auction theory (see, e.g., McAfee and McMillan (1987)) tell us that the most efficient

firm with h = h(1) will win the auction paying tp(h(2)j1), which is the value of winning to

the second-most efficient firm. The guild’s expected collection will thus be

tp(E(2)[h(2)] | 1), where E(2)[�] is the expectation operator with respect to the distribution

of h(2). So, to collect R, the guild will set the duration of the holiday at

t* ¼ R=pðEð2Þ½hð2Þ� j 1Þ: ð2Þ

The auction mechanism involves implicit taxation. Ex post, the most efficient firm pays

a tax of {t*p(h(1)jN)� t*[h(2)� h(1)]}, while all other firms j pay t*p(hjjN). Evaluated at

the ‘‘interim stage’’, i.e., the stage at which each firm knows its own ‘‘type’’ h but does not

13 In a dynamic scenario where there are successive periods, it will be appropriate to suppose that the guild

declares a fraction of time t in each period (e.g., 365t days in a year) to be a holiday, and at the beginning of each

period, auctions off the right to remain open on the holiday to a single firm.14 We have found no evidence suggesting the use of reserve prices. Given that, note that many different

forms of auction will yield the same expected contribution (by the Revenue Equivalence Theorem).15 We consider this a plausible assumption for two reasons. First, for many commodities raising the price

would merely lead to consumers postponing their purchases. Second, the guild was accountable to the community

for the price of its product. A price increase that was perceived as unfair would be resented and resisted. Indeed,

even the guild as whole could not always arbitrarily increase its price. The Ahmedabad Gazetteer (1879, p. 109)

documents an instance in which the potters’ guild in Ahmedabad was forced to rescind a price increase under

pressure from the merchants’ guilds. Having said that, we note that our results will hold with greater force in the

case where the winning firm is free to set a monopoly price; see footnote 18.


know the realized type of any other firm, the expected tax payment for firm i, denoted by

qAUC(hi), is

qAUCðhiÞ ¼ t*pðhi j NÞ � t*bðhiÞ; where bðhiÞ ¼ Prob½hi ¼ hð1Þ� fEð2Þ½hð2Þ j hð1Þ ¼ hi� � hig: ð3Þ

Thus, in terms of expected (interim) payments by any firm i, the auction scheme

involves a proportional tax t* on the realized profits of firm i less a ‘‘tax credit’’ of t*b(hi).This tax credit is the expected information rent to firm i from participating in the auction,

i.e., the probability that firm i wins times its expected winning payoff. The information

rent is positive for all firms with h < h+, and is strictly decreasing and strictly convex in

h.16

3.3. Revenue taxation

Assuming that the guild can observe firm’s instantaneous sales revenue, consider the

scheme where the guild allows all N firms to operate over the time interval [0, 1], and taxes

R/P0 fraction of each firm’s revenues. Under this ‘‘revenue tax scheme’’, each firm makes

a lump-sum contribution of R/N, and the total collection is R. To facilitate subsequent

comparison, we will use the benchmark profit-tax rate x* (defined in Eq. (1)) to express

the contribution made by firm i (which, in this case, is the same in the interim and ex post

stages) under the revenue tax scheme, denoted by qREV(hi), as:

qREVðhiÞ ¼ x*pðhi j NÞ þ rREVðhiÞ; where rREVðhiÞ ¼ x*ðhi � EhÞð1=NÞc: ð4Þ

Under the revenue tax scheme, each firm i is taxed x* fraction of its realized profits less

a tax credit of [� rREV(hi)]. The tax credit is decreasing in h with it being zero for the

‘‘mean type’’ Eh. The higher-than-average cost firms (respectively, lower-than-average

cost firms) pay more (respectively, less) than x* fraction of their realized profits. Thus,

compared to the hypothetical situation of an x* profit tax, the revenue tax is regressive and

involves higher-than-average cost firms ‘‘cross-subsidizing’’ low-cost firms. This feature

of revenue taxation will play an important role in our subsequent analysis.

In the next section, we compare the auction tax and the revenue tax in terms of

‘‘majority preference’’ and ‘‘equity’’. We emphasize that our methodology can be used to

compare the auction scheme to other forms of taxation. Specifically, a unit tax on output

that collects R in the aggregate will be identical to the revenue tax described above, and so

our analysis will be valid in comparing the auction tax to an output tax. Regarding input

taxation, we show at the end for Section 4 how our methodology of comparing the auction

16 Note that Prob[h= h(1)]=[1�F(h)]N� 1. Further, from the theory of order statistics we have: Eð2Þ½hð2Þ jhð1Þ ¼ h� ¼ fðN � 1Þ=½1� FðhÞ�N�1g mhþ

h y½1� FðyÞ�N�2f ðyÞdy. Then it is easy to calculate the explicit expression

for b(h) and establish that bV(h) =� [1�F(h)]N� 1 < 0 and bW(h)=(N� 1)[1�F(h)]N� 2f(h)>0.


and revenue taxation, and our qualitative results, carry over to the case of comparing the

auction to a ‘‘uniform input tax’’.

4. Taxation by auction vs. conventional taxes

This section addresses the central questions of this paper: when will a majority of the

guild members prefer the auction tax to revenue taxation, and when will the former be

more equitable than the latter?

4.1. Majority preference

The issue of majority preference is addressed both at the ‘‘ex ante stage’’—before each

firm learns about its own efficiency parameter h, and at the ‘‘interim stage’’—when each

firm knows its own h but not that of others. The ex ante analysis is appropriate to

determine the guild’s mechanism of choice at its inception. In contrast, the interim analysis

addresses the question: given an initial mechanism choice, will there be subsequent

pressure on the guild by a majority of its members to change it? This issue will be all the

more relevant in an intertemporal setting, and we will subsequently discuss how our

analysis clarifies choices in a dynamic environment.

The difference in firm i’s (expected) payments under revenue taxation and the auction

is:

DðhiÞuqREVðhiÞ � qAUCðhiÞ ¼ ðx*� t*Þpðhi j NÞ þ rREVðhiÞ þ t*bðhiÞ: ð5Þ

At the interim stage, firm i will prefer the auction if and only if D(hi) is positive. We will

say that there is interim majority preference for the auction if the measure of firm types hfor which D(h)>0 is greater than half. If D(h)>0 for all h, the auction will interim Pareto

dominate revenue taxation.

Ex ante, all firms will have the same preference over the two schemes, and each firm

will prefer the auction if and only if the unconditional expectation of D(h) is positive. So,at the ex ante stage, the notions of majority preference and Pareto dominance coincide, and

the auction tax will ex ante Pareto dominate the revenue tax if and only if ED(h)>0.An important factor in determining the sign of D(h) is the relative magnitudes of the

two ‘‘tax rates’’ x* and t*. In comparing these two rates, the basic question is the

following: given the fixed price P0, are the aggregate industry profits bigger when one firm

operates (as in the case of an auction) or when all N firms operate (as in the case of a

revenue tax)? That is, does the auction have an ‘‘efficiency effect’’?17 Note that if all firms

had the same costs, the answer would be negative under decreasing returns to scale (c>1).But when firms are heterogeneous, and the issue is of letting one low-cost firm operate vs.

letting all N firms operate, the answer depends on the relative magnitudes of the returns-to-

scale parameter c and the efficiency parameter of the low-cost firm.

17 In the Industrial Organization literature, the ‘‘efficiency effect’’ refers to the fact that when firms are

strategic competitors, the aggregate industry profits are decreasing in the number of operating firms.


Note that (x*� t*) has the same sign as the profit difference: {p(E(2)[h(2)] | 1)�Np(EhjN)}. Given that this profit difference equals {NEh(1/N)c�E(2) [h(2)]}, and given

our assumption that N>3 (so that that E(2)[h(2)] <Eh), it is easy to see that (x*� t*)>0 for

c = 1. Further, since x* falls in c while t* is independent of c, (x*� t*) falls

monotonically as c increases. Thus, there exists a critical c*>1 for which x* equals t*

(i.e., at c = c*, p(E(2)[h(2)] | 1) =Np(EhjN)). The auction tax mechanism has a positive

efficiency effect relative to revenue taxation if and only if c < c*.We are now in a position to make the ex ante comparison between the two schemes.

From Eq. (5), note that E[D(h)]=(x*� t*)p(Eh |N) + t*E[b(h)] (since E[rREV(h)] = 0).While the first term is positive if and only if the auction has a positive efficiency effect,

the second term is always positive since the expected information rents for any firm

from participating in the auction is positive. Further, E[D(h)] falls monotonically in c.Thus, there exists a unique cANT>c* for which E[D(h)] = 0; at c = cANT, p(E(2)[h(2)] | 1) =Np(Eh |N)�NE[b(h)]. We thus have the following result:

Proposition 1 . There exists cANT>c* such that the auction ‘‘ex ante Pareto dominates’’ the

revenue tax if and only if the returns-to-scale parameter c is smaller than cANT.18

Note that E[D(h)] is the expected net surplus generated by the auction relative to

revenue taxation, this surplus arising due to the efficiency effect and the information rent

effect.19 Proposition 1 asserts that for all guild members, their ex ante choices are identical,

and depend only on whether this surplus is positive or not. In contrast, there can be a

conflict in the ‘‘interim choices’’ of firms with different efficiency levels. For a firm that

knows its ‘‘type’’ h, three effects operate in determining its interim preference. First, by the

last term in the RHS of Eq. (5), since every firm expects information rents from the

auction, all firms prefer it ceteris paribus. Second, the revenue tax involves cross-

subsidization by high-cost firms as reflected in the middle term in the RHS of Eq. (5),

and that, ceteris paribus, makes low-cost firms prefer revenue taxation and high-cost firms

the auction. Finally, every firm will have an additional reason to prefer the auction if it has

a positive efficiency effect, in which case the first term in the RHS of Eq. (5) will be

positive.

Recognize that when the efficiency effect is zero, all higher-than-average cost firms will

strictly prefer the auction, both for the information rent effect and the cross-subsidization

effect. So, when c= c*, there exists (by continuity) a cut-off efficiency level h0 <Eh, suchthat firms with types h>h0 will prefer the auction; see Fig. 1. This, given our assumption

that the distribution function F is symmetric, implies that a strict majority of firm types

will prefer the auction when c = c*. Fig. 1 also depicts the following facts (which are easily

18 This result holds under the assumption that the winning firm is constrained to charge P0. In contrast,

suppose that the winner is free to charge a monopoly price Pm>P0 during the holiday. Then the efficiency effect

will be bigger for every value of c. This will make the auction more attractive to firms, both ex ante and at the

interim stage.19 The information rents arise due to the auctioneer’s inability to extract the winning firm’s full surplus.

If an auction could be so designed where a winning firm had to pay its full value, the guild would collect

p(E(1)[h(1)] | 1), and so set the ‘‘holiday’’ at tV=R/p(E(1)[h(1)] | 1). Then the surplus would arise only due to

the efficiency effect, and the auction would be preferred ex ante if and only if c< cV, where cV is such

that p(E(1)[h(1)] | 1) =Np(Eh |N).

Fig. 1. D(h) measures the extent (positive or negative) to which a type h firm prefers the auction; at c= c*, a strictmajority of firm types, all h< hV and all h> h0, interim prefer the auction.


proved): D(h) is monotonically falling in c, and is a strictly convex function of h attaining

an interior minimum. Thus, there exists a unique cINT>c* for which the measure of the set

of firm types h (under F) for whom D(h)>0 is half.

Proposition 2 . There exists cINT>c* such that in the interim stage, a ‘‘majority of the firm

types’’ (all higher-than-average cost firms, and some low-cost firms) will prefer the

auction to revenue taxation if and only if the returns-to-scale parameter c is smaller than

cINT.20

D(h) is the net surplus generated by the auction relative to revenue taxation for a

particular firm of type h. Proposition 2 states that when c < cINT, this surplus is positive for amajority of the firm types.21 Recognize that for c close to cINT, a subset of firm types will

indeed prefer revenue taxation to the auction, and this subset will include some low-cost firm

types. While a low-cost firm is certainly more likely to win the auction, it will be heavily

cross-subsidized under the revenue tax and that is why it might prefer the revenue tax. The

set of firm types h for which D(h) < 0 will obviously shrink as c falls, and for c close to onethis set may vanish. If that is the case, then for these small values of c, the auction will interimPareto dominate the revenue tax. However, whether that happens or not depends intricately

20 Of course, for a finite N, this does not necessarily mean that once the h’s are realized, there will ex post be

a majority of firms who prefer the auction when c < cINT. However, this event is more likely than its complement.

If we had considered a guild with a continuum of firms (which is certainly unrealistic), then by the law of large

numbers, we could assert that ex post a majority of the firms would indeed prefer the auction when c< cINT.21 Is there a systematic relation between cANT and cINT? It can be shown that when c= cANT,

D(Eh) = t*{b(Eh)�E[(b(h)]}, which is negative since b(�) is a strictly convex function. Thus, when the

expected net surplus is zero (c= cANT), the ‘‘median’’ (i.e., the average-cost) firm prefers the revenue tax. If

preferences were ‘‘single peaked’’ this would imply that cANT>cINT, but preferences are not ‘‘single peaked’’ in

the type space in the current model. Specifically, since D(�) is convex, at c = cANT there may be enough low-cost

firms who prefer the auction so that a majority of types prefer it, implying that cANT < cINT. Consequently, nogeneral result can be stated in this regard without more precise information about firm profit functions.


on the parameters of the model.22 While the auction both ex ante Pareto dominates and is

interim majority preferred to the revenue tax for c close to one, the conflict in interim

preferences between some low cost firms and others might persist for all c>1.What does the above analysis imply about the guild’s preferred fund-raising mechanism

in a dynamic environment when the firms do business over successive time periods?

Suppose that the firms’ cost parameters are generated by the following process:

hit = kgi+(1� k)eit, with ka[0, 1], where g is a ‘‘permanent’’ firm-specific efficiency

parameter and eit is a period and firm specific cost shock. Each firm is privately informed

about its g (which is drawn from a symmetric distribution) at the beginning of time. Then

in every period each firm privately observes its eit and thus its hit. The eit are i.i.d. across

firms and over time and drawn from a symmetric distribution. What tax scheme will be

chosen at the beginning of time, when each firm is privately informed about its g?In the extreme case when k = 0, the ex-ante analysis of our single period model applies.

In the other extreme when k = 1, the interim analysis applies. Of course, the realistic case is

where firms are partially (and privately) informed about the future (0 < k < 1). In that case,

our interim analysis case suggests that, after privately observing their g, there can be a

conflict among members’ preferences, with some firms with ‘‘good’’ signals (i.e., that they

will be efficient) preferring revenue taxation, and all others preferring the auction. As long

as the extent of scale diseconomies is not very large, a majority of the guild members will

prefer the auction scheme. Further, it can also be that once the auction scheme has been

adopted by the guild, it will be a ‘‘stable’’ institution in the sense that in every subsequent

period, a majority of the firms, after observing their efficiency parameters for the period,

will indeed want to be taxed via the auction.23

4.2. Equity

As we have pointed out earlier, equity was an important consideration for Gujarati

guilds in the 19th century. We now compare the equity properties of the auction tax vis-a-

vis revenue taxation in the following simple manner.

We start by noting that a proportional tax on the realized profits of member firms would

be an equitable tax scheme in that it would be neither progressive nor regressive. In

contrast, the revenue tax scheme is definitely regressive. This is shown in Eq. (4), which

expresses a firm’s expected (and ex post) payment under revenue taxation as a

proportional tax on realized profits (at the rate x*) plus a ‘‘deviation payment’’ rREV(�),with the property that the latter is zero for the ‘‘mean type’’ Eh. It is the fact that rREV(�) ispositive for all h>Eh and negative for all h <Eh (i.e., the feature of cross-subsidization

discussed earlier) that makes the revenue tax regressive.

22 When c= 1, D(h) is of the same sign as {Nb(h)� (E(2)[h(2)])� h)}. Note that for any h<E(2)[h(2)], whetherthe difference is positive or not depends on the magnitude of N and the precise functional form of F(�).

23 The dynamic model brings forth the following commitment issue. Suppose that a guild holds an auction at

the beginning of each time period (and we have no evidence to suggest that guilds held multiple auctions at the

same point in time for successive future periods). Then the winner at any point in time reveals something about

his ‘‘permanent’’ parameter g, and in principle the guild can take this information into account when designing the

next period auction. While this is certainly a theoretical possibility, we have found no evidence of guilds using

‘‘discriminating auctions’’ over time where the ‘‘rules of the game’’ differed between past winners and past losers.


We now perform a similar ‘‘decomposition’’ for a firm’s expected payment under the

auction. From Eq. (4), note that we can express qAUC(hi) uniquely as:

qAUCðhiÞ ¼ s*pðhi j NÞ þ rAUCðhiÞ; where s* ¼ t*½1� fbðEhÞ=pðEh j NÞg� andrAUCðhÞ ¼ t*½bðEhÞfpðh j NÞ=pðEh j NÞg � bðhÞ�: ð6Þ

Eq. (6) expresses a firm’s expected payment under the auction as a proportional tax (at the

rate s*) on realized profits plus a deviation payment rAUC(h), where rAUC(Eh) = 0. Giventhat, we will say that the auction tax is ‘‘more equitable’’ than the revenue tax if and only if

for all higher-than-average cost firms the deviation payment is bigger under the latter tax,

i.e., if and only if rREV(h)>rAUC(h) for all h>Eh. Intuitively, we require the amount of

cross-subsidies paid by the higher-than-average cost firms to be smaller under the auction

for it to be more equitable than revenue taxation.24

Recognize that the above definition is concerned with equity in terms of ‘‘interim

payoffs’’ of the guild members. Note that ex post, all firms except the winner pay t*

fraction of their realized profits in the auction. So, in ex post terms, by an analogous

criterion as used in the above definition, the auction is certainly more equitable than a

revenue tax. And since all firms are symmetric ex ante, there is no issue of inequity at the

ex ante stage.

From the definitions in Eqs. (4) and (6), note that the ‘‘deviation payment functions’’

have the following properties: rREV(�) is a strictly increasing, linear function of h with

BrREV(h)/Bh = x*(1/N)c, and rAUC(�) is a strictly concave function of h with BrAUC(h)/Bh =� t*[b(Eh){(1/N)c/p(Eh |N)} + bV(h)]. Then it is easy to see that for any particular

value of c, the auction tax will be ‘‘more equitable’’ than the revenue tax if and only if the

rREV(�) function is steeper than the rAUC(�) function at the ‘‘mean type’’ Eh, i.e., if andonly if BrREV(Eh)/Bh>BrAUC(Eh)/Bh; see Fig. 2.

When c = 1, it is easy to show that for a symmetric F(�) function (implying that

F(Eh) =1/2), BrREV(Eh)/Bh =R /Np (Eh | 1)>[R(1�F(Eh))N� 1] / [p(E (2)(h (2)) | 1) =� t*bV(Eh)>BrAUC(Eh)/Bh for all N>3. Then given that BrREV(�)/Bh and BrAUC(�)/Bhare continuous in c, we have the following result:

Proposition 3 . There exists a critical value cEQ>1 such that when the cV cEQ, the auctionis more equitable than the revenue tax.25

24 Formally, our definition of ‘‘more equitable’’ can be presented as follows. Consider two tax schedules, T(1)

and T(2), both of which collect the same aggregate revenue in expected terms. Let the expected payment by firm hunder T(i) (for i = 1, 2) be expressed as q(i) = s(i)p(h |N) +r(i)(h) where r(i)(Eh) = 0. Suppose that T(1) is regressivein that r(1)(h)>(respectively, < ) 0 as h> (respectively, < ) Eh.Then T(2) is ‘‘more equitable’’ than T(1) if and

only if r(1)(h)>r(2)(h) for all h>Eh. This is the definition that we use above. We could strengthen this definition

and say that T(2) is ‘‘strictly more equitable’’ than T(1) if and only if r(1)(h)>(respectively, < ) r(2)(h) for all h>(respectively, < ) Eh.

25 We emphasize two points. First, whether the slope difference {BrREV(Eh)/Bh�BrAUC(Eh)/Bh} increases

or decreases in c depends on specific functional forms. If it does increase in c then the auction will be more

equitable than the revenue tax for all c>1. Second, recalling the definition of ‘‘strictly more equitable’’ in footnote

24, we have no general result as to when the auction will be strictly more equitable than the revenue tax. Note that

when BrREV(Eh)/Bh>BrAUC(Eh)/Bh, it is certainly the case that rREV(h) <rAUC(h) for some h<Eh, but giventhat rAUC is a strictly concave function of h, some highly efficient firms can be getting a larger tax break under the

auction vis-a-vis revenue taxation; see Fig. 2.

Fig. 2. Here, for a particular value of c>1: rREV>rAUC>0 for all h>Eh, rREV < rAUC < 0 for all ha(hW, Eh), andrAUC <rREV < 0 for all h< h’’.


The above proposition holds for any guild size N>3. We would also like to note that for

‘‘large enough’’ guilds, a higher-than-average-cost firm’s expected payment under the

auction will ‘‘almost’’ be a proportional tax, and so the auction will certainly be more

equitable than the revenue tax. To see this, note from Eq. (6) that for all h>Eh,rAUC(h) < t*b(Eh), the RHS being the expected information rent for the average-cost

firm. For a large enough guild size, this information rent will be extremely small (e.g., for

N = 30, the probability that the average-cost firm wins the auction is 2 in a billion), and so

for all firms with h>Eh, rAUC(h) will be arbitrarily close to zero.

Propositions 1–3 delineate conditions under which (a) guild members prefer the

auction over a revenue tax both ex ante and in the interim, and (b) the auction is more

equitable than revenue taxation in terms of interim payoffs. The results indicate the central

role of the returns-to-scale parameter c in generating an ‘‘efficiency effect’’ for the auction.This effect is positive for small values of c, and then the auction is the preferred fund-

raising mechanism for the guilds.26 We conclude this section by demonstrating that a

similar comparison, which generates an analogous set of conclusions, can be made

between the auction tax and an input tax scheme.

Consider the case where the guild can observe all inputs used by a firm, and imposes a

‘‘uniform input tax’’ z* =R/(Eh)(1/N)c � 1 on all inputs. Then each firm i pays (R/N)(hi/Eh)and the expected collection is R. As in Eq. (4), the contribution made by firm i under the

uniform input tax can be expressed as {x*p(hijN) + rINP(hi)}, where rINP(hi) = x*(hi�Eh){(1/N)c+(p(EhjN)/Eh)}. Given that, the auction scheme can be compared to such input

taxation by a similar analysis as is presented above. First, the ex ante comparison between

the auction and the input tax will be identical to the preceding analysis and Proposition 1

26 In this context, the following question naturally arises: if there is indeed a positive efficiency effect from

letting only the most efficient firm operate, why did the guilds not exploit it more to increase the aggregate

earnings of all members? Recognize that in order to do that, a guild would have to (a) identify the most efficient

firm in each period, and (b) coerce it to share profits with the ‘‘sleeping’’ guild members. We have no evidence to

suggest that the Indian guilds could achieve that amount of collusion, or wield that kind of power.


will be obtained. Second, an interim comparison as in Proposition 2 can be carried out

between the auction and the input tax scheme, and by analogous arguments as above it can

be shown that there exists a cW>c* such that the former is interim majority preferred to the

latter if and only if c < cW. Finally, following our definition of equity comparisons between

tax schedules, it is easily established that the input tax is even less equitable than the

revenue tax. This is because high cost firms use greater quantities of the inputs to produce

the same output. So the import of Proposition 3 carries over when the auction is compared

to an input tax.

5. Concluding remarks

In this paper, we have documented a novel mechanism used by 19th century Gujarati

guilds to raise funds. They implicitly taxed their members by auctioning off the right to

remain in business on a holiday to a single firm. Such auctions have been described as a

‘‘prime source’’ of funds for ‘‘most guilds’’. At the same time, some guilds did use con-

ventional forms of taxation (like sales and input taxes) to raise a part of their funds. Recog-

nizing this, we have compared these different forms of taxation in a formal model of a guild.

Our analysis has identified some of the conditions that make an auction scheme a

‘‘better’’ mechanism for fund raising, as compared to conventional taxes. The latter are

regressive—they involve high-cost firms cross-subsidizing low-cost ones. The extent of

regressivity is much less in an ‘‘auction tax’’. This makes the auction scheme more

equitable; it comes closer to allocating taxes in proportion to profits. In addition, the auction

can generate a surplus vis-a-vis conventional taxation, in part because it shifts production to

the most efficient firm—an ‘‘efficiency effect’’. The smaller is the extent of scale

diseconomies in production, the bigger is this effect. Whenever the auction generates a

positive expected surplus, all guild members prefer it ex ante. Further, the bigger the

surplus, the more likely is it that once the firms know their ‘‘types’’, a majority of them (all

higher-than-average cost firms and some low-cost firms) will continue to prefer the auction.

Of course, there could be other reasons, which make the auction scheme desirable, that

we have not considered. One reason could be that even though a guild implicitly taxed all

its members via the auction, ex post, only one firm (the auction winner) made the entire

contribution to the guild funds. If guild members derived utility from such overt and

visible acts of altruism that would tend to make the auction scheme more popular.27

Another reason could be that while conventional taxes can cause quantity distortions in

firm decisions, the auction tax does not create any such distortion. This may lead to the

auction generating a bigger surplus than conventional tax schemes.28

Our study has highlighted the features that need to be present for the auction scheme

‘‘to work well’’, and thus indicated why it may not be the mechanism of choice in all

27 Though if guild members wanted to demonstrate altruism, they could surely have done so without

resorting to such a complicated auction scheme.28 If guilds fixed quantities, conventional taxes would not have a distortionary effect. Moreover, given that

the guild’s collections were small in relation to member earnings, even if conventional taxes distorted choices,

these distortions would be small. That is why we have ignored this issue in our formal analysis.


cases. First, we have emphasized that a crucial issue is whether a single firm can replicate

the earnings of all guild firms operating together. The extent of scale diseconomies plays

an important role in determining this (as do factors like the spatial dispersion of

customers, the extent of their ‘‘brand loyalty’’, etc.). Thus, the auction scheme might

be more suitable for traders than for certain kinds of craftsmen; scale diseconomies are

likely to set in much quicker for a barber than for a grain-dealer. Second, the auction

scheme requires that the guild members collectively create a monopoly position which can

then be auctioned off. The Gujarati guilds could create such a position, but this may not

have been feasible in other associations.29 Guilds in larger cities with geographically

dispersed members would find it harder to monitor whether a firm stayed open on a

holiday in violation of guild rules. The monitoring problem, along with the fact that a

single firm could possibly serve only a small portion of a large market, would limit the

desirability of the auction. Not surprisingly, Hopkins (1902, p. 190) found that ‘‘this

custom of auctioning off the right of not keeping a holiday is more common in the smaller

towns’’.

In conclusion, we note that that the scheme of auctioning off the rights to stay open on a

holiday to a single firm may not have been the ‘‘optimal’’ fund-raising mechanism for the

Gujarati guilds. If diseconomies of scale were indeed a primary reason to not use the

auction, then it might have been better to have more than one firm win such an auction

(especially in large markets). While the Gujarati guilds might not have been ingenious to

such an extent, there is no denying that the idea of collecting funds by ‘‘selling’’ a

collectively created monopoly right to work was a very clever one.30

Acknowledgements

We thank Jonathan Conning, Karla Hoff, and participants at the 2000 North Eastern

Universities Development Conference, and at seminars at Williams College and the

University of Windsor for helpful comments. We are especially grateful to Omar Azfar,

Rachel Kranton, and two anonymous referees for detailed suggestions on earlier drafts. We

are responsible for all remaining errors.

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collectively, may not have a monopoly in any occupation. Then an income tax will be more feasible than an

auction/holiday scheme. Indeed, as is well known, many religious institutions use tithes (a 10% income tax).30 And some guilds ‘‘sold’’ this right more cleverly than others. While we have focused on the guilds that

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Documents

Taxation by auction: fund raising by 19th century Indian guilds