Two thousand years ago (Olivelle [2013: 29] argues for "sometime between 50 and 125 C.E."), Kautilya wrote a manual on "wise kingship," the Arthasastra, which we denote by KAS. Among other topics, this book deals with taxation, diplomacy, warfare, and the management of spies (see the surveys by Boesche  and Scharfe ). We concentrate on a small part of book 2 which is about the activities of superintendents. In particular, chapters 21 and 22 treat the superintendent of customs and the operation of customs. Custom authorities collect both "customs duty" (sulka (1)) and the "increase in price" (mulyavrddhi). The latter is called market tax in this article. According to Kautilya, this tax should work as follows:
(1) The Superintendent of Customs should set up the customs house along with the flag facing the east or the north near the main gate ... (7) The traders should announce the quantity and the price of a commodity that has reached the foot of the flag: "Who will buy this commodity at this price for this quantity?" (8) After it has been proclaimed aloud three times, he should give it to the bidders. (9) If there is competition among buyers, the increase in price along with the customs duty goes to the treasury. (KAS 2.21.1, 7-9 in Olivelle 2013: 148) (2)
Olivelle (p. 555) argues that Kautilya has an auction in mind. He interprets "increase in price" as follows: "This must refer to the increase beyond the asking price that was initially announced. Such an increase caused by the bidding process appears to go to the state rather than to the trader." The same interpretation is held by Rangarajan (1992: 239): "... He shall call out for bids three times and sell to anyone who is willing to buy at the price demanded. If there is competition among buyers and a higher price is realised, the difference between the call price and the sale price along with the duty thereon shall go to the Treasury."
An important point concerns the question of whether Kautilya had an ascending or a descending auction in mind. (Auction theory is presented in McAfee and McMillan 1987.) In ascending auctions (also called English auctions), the auctioneer raises the price starting with some minimum price. The last bidder still upholding his wish to buy gets the object. In a descending auction (Dutch auction), the auctioneer lowers the price starting with some maximum price. As soon as one bidder is prepared to pay the price announced, he obtains the object. Of course, "the increase in price" clearly points to the ascending auction. A second reason will be given below.
Since some of the goods were exempt from duty (see KAS 2.21.18 in Olivelle, p. 148), it is not obvious whether Kautilya proposes the market tax for dutiable and non-dutiable goods alike. Be that as it may, we deal with the market tax exclusively. It is, of course, debatable whether "market tax" is a suitable term for Kautilya's tax. Obviously, Kautilya has in mind an indirect tax, i.e., a tax on transactions, in contrast to a direct tax that would affect income or property (see, for example, Schenk and Oldman 2001: 12-17).
For simplicity, we assume that one unit of goods is to be imported and sold. Let us denote the call price by V (the value declared by the trader) and the sale price by p. Also, the trader's cost of buying, or producing, this good is denoted by C. A concrete example might be helpful. The trader may quote a value V-5 panas. Some bidders are interested in the unit of goods at this price and start to outbid each other. Assume a highest bid of p=9 (panas). Then, the tax inspectors will collect a market tax (mulyavrddhi) of 9-5=4.
Our trader may hope to evade the tax by indicating a higher value. For example, V=7 would lead to the tax of p-V=9-7=2, only. However, if the trader overestimates the bidders' eagerness to obtain the object, he may try V=12 and learn that no bidder is prepared to pay as much. Then, we have to imagine what is to happen next. Assume that the trader could try different values during the same market day without additional cost. In our example, he would not find any bidder for V=12, V=11, or V=10. But finally, at V=9, the most eager bidder would be prepared to pay 9. In that case, the trader's market tax is p-V=9-9=0. Thus, it would surely be in the trader's interest to try a relatively high value first and lower the value in successive rounds. In this way, he could practically avoid the market tax.
We argue that Kautilya would not have proposed a tax that can easily be avoided. A similar argument makes clear that Kautilya could not have a descending auction in mind. For that auction type, the trader could quote a very high valuation (for example, V=15) and find out the highest bidder by successively lowering the price. In that case, there would be no danger of not finding a buyer and the market tax p-V=9-15 would be negative (!) or, ruling out negative taxes, zero.
The main idea of the paper is this: on the basis of an ascending auction, we assume that the trader who has not found a bidder (because his value was too high) cannot, without cost, simply try again, with a lower value. In practical terms, the unsuccessful trader may have to pay duty once again or may have to leave the market and incur transportation cost in order to try at another market place. We denote these costs by F. They are not to be confounded with the cost of production C. Then, the market tax presents the trader with an optimization problem. On the one hand, he would like to choose a relatively high valuation V in order to evade the market tax. On the other hand, a high valuation carries the risk of not selling the good and incurring duty and transportation costs F once again.
We spell out the optimization problem in some detail in the next section. We then discuss additional provisions made by Kautilya in section 3. Some remarks on important vocabulary and the setup of the text round out the argument in section 4. Finally, concluding remarks are offered in section 5.
THE TRADER'S OPTIMIZATION PROBLEM
In this section, we explain the optimization problem hinted at in the introduction. Kautilya did not comment on the possibility of V>p (no bidder is prepared to pay V). Since this possibility is central to the understanding of his market tax, we need to distinguish two cases: First, the buyers' competition for one unit of the goods drives up the highest bid p above V. Then, the price to be paid by the winning...