* Earlier versions of this paper were delivered in 1986 at the Newberry Library and the American Historical Association meeting. My thanks to James Sandos for brainstorming through an early formulation of the problem. The advice and criticism of colleagues in economics and mathematics - Richard Carson, Carlo M. Cipolla, Alfred Manaster and David Weir – have saved me from making the same errors as the Castilian accountants. Suggestions from Michael Bernstein, Jack Greenstein, David Luft and Robert Westman have helped refine my arguments.

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¹¹ Burke, Peter, ‘Southern Italy in the 1590s: hard times or crisis?’, in The European crisis of the 1590s. Essays in comparative history, ed. Clark, Peter (London, 1985), pp. 177–208Google Scholar.

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¹⁴ Ibid. pp. 87–8 documents naval and military demobilization after Lepanto. See Aymard, Maurice, ‘Chiourmes et galères dans la Méditerranèe du XVI^e siècle’, in Mélanges en l'honneur de Fernand Braudel. Histoire économique du monde méditerranéen 1450–1650 (Toulouse, 1973), pp. 49–64Google Scholar and for information on the state of the Neapolitan galleys from 1574, Archive General de Simancas [AGS], Visitas d'Italia, leg. 71, 72, 74.

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¹⁸ Biblioteca Nazionale, Napoli [BNN], MS XV.B.11, ‘Lettere Regie’, cc. 293–294 (24 vi 1573).

¹⁹ On the theory and practice of hearth tax injustices, Calabria, Antonio, Cost of empire, pp. 39–40Google Scholar with a fuller account in Calabria, Antonio, ‘State finance in the Kingdom of Naples in the age of Philip II’ (unpublished Ph.D. dissertation, University of California, Berkeley, 1977), p. 40Google Scholar. On the question of frauds in early modern public life, see Waquet, Jean-Claude, De la corruption. Morale et pouvoir à Florence aux XVII^e et XVIII^e siècles (Paris, 1984)Google Scholar.

²⁰ Parker, Geoffrey, Philip II (Boston–Toronto, 1978), p. 58Google Scholar remarks upon biographers' anecdotes emphasizing the ‘king's anxiety not to wrong anyone’ and his legendary devotion to fairness and justice popularized after his death. , Lovett, Early Habsburg Spain, p. 121Google Scholar demonstrates this ‘commendable’ quality by citing an attributed quotation: ‘Law courts should not be like spider's webs which [catch] the fly while allowing the lizard to pass through’.

²¹ AGS, Estado, Ndpoles, leg. 1066, f. 88 and f. 89 (1575).

²² See , Lovett, ‘Juan de Ovando’, pp. 13–14Google Scholar for details on the personnel in the finance ministry.

²³ BNN, MS Branc. V.B.5, ‘Parlamenti e gratie della Città di Napoli’, cc. 190r–113r (22 iv '575)

²⁴ Ibid. pp. 8–17 summarizes two important reform documents prepared by Ovando for Phillip II: ‘an enormous relatíon’ dated 16 January 1574, and the ‘great memorial on the state of royal finance’ dated 11 April 1574.

²⁵ , Calabria, Cost of empire, p. 78Google Scholar gives actual expenses for conducting the delayed census in 1595 as 120,000 ducats.

²⁶ See n. 23. On the Neapolitan parliament, D'Agostino, Guido, Parlamento e società nel Regno di Napoli (Naples, 1979)Google Scholar.

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²⁹ AGS, Estado, Nápoles, leg. 1079, f. 32 (11 ii 1579). This consulta describes the Neapolitan state budget of 1575: ‘said balance of the referred to year remain to be paid by merchants, and the money is consigned to them above and beyond the donativo of 1575’.

³⁰ AGS, Estado, Nápoles, leg. 1066, f. 98 (8 xi 1575).

³¹ BNN, MS XV.B.11, c. 367 (18 xi 1575).

³² , Lovett, ‘Juan de Ovando’, p. 13Google Scholar.

³³ AGS, Estado, Nápoles, leg. 1072, f. 145 (1576), transcribed, but misdated, in , Coniglio, Il Viceregno, II, 519–21Google Scholar.

³⁴ BNN, MS XV.B.II, c. 374 (24 iii 1576).

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³⁹ AGS, Visitas d'Italia, Nápoles, leg. 23:3, cc. 61v–62V.

⁴⁰ Braudel, Fernand, The Mediterranean and the Mediterranean world in the age of Philip II, trans. Reynolds, Siâ;n (New York, 1972), I, 584–5Google Scholar cites Bibliothèque Nationale, Paris, MS Esp. 127, fo. 52.

⁴¹ Ruiz Marín, pp. 6–7, 13–14 gives interest rates of 12–15 per cent between 1525 and 1530, 7–12 per cent between 1535 and 1540, 10–13 per cent between 1528 and 1548, 43 per cent in 1554; and for juros, rates of 6·25 per cent between 1545 and 1550, 6·09 per cent in 1552, 6·78 per cent in 1560, 5·81 per cent in 1594, and 5·79 per cent in 1598.

⁴² , Calabria, ‘State finances’, pp. 197–9, 299–300Google Scholar. The mode rate in four sample years was 10 per cent in 1560, 9 per cent in 1574, 8 per cent in 1583, and 7 per cent in 1600.

⁴³ From the inflation information in note 9, nominal interest rates in Naples would have been about 9 per cent in the 1560s, 7 per cent in the 1570s, 4 per cent in the 1580s, and just below zero by 1600 – albeit prices would still have remained at the high levels of the 1590s.

⁴⁴ Cipolla, Carlo M., ‘Note sulla storia del saggio d'interesse. Corso, dividendi e sconto dei dividendi del banco di S. Giorgio nel sec. XVI’, Economia Internationale, V, 1 (1952), 255–74Google Scholar.

⁴⁵ , Calabria, Cost of empire, p. 106Google Scholar cites Tracy, James D., A financial revolution in the Habsburg Netherlands. Renten and Renteniers in the county of Holland, 1515–1565 (Berkeley, 1985), pp. 60, 92, 207Google Scholar.

⁴⁶ , Lovett, ‘The Castilian bankruptcy’, pp. 904–5Google Scholar. de Roover, Raymond, ‘Monopoly theory prior to Adam Smith: a revision’, in Business, banking, and economic thought in late medieval and early modern Europe, ed. Kirshner, Julius (Chicago, 1974), pp. 273–305, esp. 277–8Google Scholar, traces the long-enduring scholastic understanding of the ‘just price’. The ‘just price’ was either the legal (fixed) price set by public authorities or the market (competitive) price agreed upon through the ‘common estimation’ of buyers and sellers who were sensitive to ‘the interplay of the forces of demand and supply’. See also de Roover's, classic article, ‘The concept of the just price: theory and economic policy’, Journal of Economic History, XVIII (1958), 418–34CrossRefGoogle Scholar.

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⁴⁸ Trenchant, Jean, L'Arithmetique, departie en trois livres (3rd edn, Lyons, 1571), pp. 292–311Google Scholar defines and demonstrates merite simple and merite à chef de terme, and disconte simple and disconte à chef de terme.

⁴⁹ Smith, D. E., History of mathematics (2 vols., New York, 1958), II, 565–6Google Scholar. On Trenchant, see Davis, Natalie Zemon, ‘Sixteenth-century French arithmetics on the business life’, Journal of the History of Ideas, XXI, (01–03 1960), 37Google Scholar. On the teaching of business math, see Swetz, Frank J., Capitalism and arithmetic. The new math of the 15th century (La Salle, Ill., 1987)Google Scholar and Grendler, Paul F., Schooling in Renaissance Italy: literacy and leaning, 1300–1600 (Baltimore, 1989)Google Scholar.

⁵⁰ For a similar inversion from contemporary economic notation in Naples, see the language employed in the ‘free-bidding’ of pasture (the system used to replace the direct numeration of sheep) in the Foggian sheep customhouse. See, Marino, John A., ‘Professazione voluntaria e pecore in aerea: ragione economica e meccanismi di mercato nella dogana di Foggia nel secolo sedicesimo’, Rivista Storica Italiana, XCIV, 1 (1982), 30–2Google Scholar: ‘In our contemporary market language, price quotations are expressed in changing monetary values while the quantity of the commodity remains constant. We sell land, for example, for an amount of money per acre because “selling price” (we don't call it “buying price”) is expressed in seller, not buyer notation. Doganal logic operated inversely. It was a system based upon a buyer's budget. Because of the inelasticity of the sheepowner's profit margin, the monetary value (1000 sheep at 132 ducats) remained constant and the commodity (10 to 14 carra of pasture) fluctuated. The principles of economic reasoning are not overturned in the least. But such a different verbalization of the processes of economic thought reflected the official relationship between shepherd buyers and state middlemen in the establishment of a fixed price for fodder expenditures.’

⁵¹ Febvre, Lucien, Le problème de l'incroyance au XVI^e siècle. La religion de Rabelais (Paris, 1942)Google Scholar. For a recent review, Wootton, David, ‘Lucien Febvre and the problem of unbelief in the early modern period’, Journal of Modern History, LX, 4 (12 1988), 695–730CrossRefGoogle Scholar.

⁵² Cipolla, Carlo M., Before the Industrial Revolution. European society and economy, 1000–1700 (2nd edn, New York, 1980)Google Scholar.

⁵³ Wilcox, Donald J., The measure of times past: pre-Newtonian chronologies and the rhetoric of relative time (Chicago, 1987), pp. 222–3Google Scholar summarizes his distinction between relative and absolute time, which is roughly analogous to the distinctions I see between the sixteenth-century accountants' simple discount and the modern compound discount equation.

⁵⁴ , Lovett, ‘Juan de Ovando’, p. 7, n. 31Google Scholar cites Instituto Valencia de Don Juan, Madrid [IVDJ], Envío 53, fo. 97 (12-ix-1574).

⁵⁵ , Lovett, Philip II and Mateo Vázquez de Leca, p. 89Google Scholar for information on factional rivalries and an opinion on the financial manipulations of Auñon and Garnica by Juan Fernández de Espinosa, a rival in the Spanish financial councils: ‘I think that Auñon uses Garnica…and that the former has the same intention of confounding and obscuring all items of business’.

⁵⁶ During the second half of the sixteenth century, neo-Thomistic moral theologians grappled with these problems. See, Schumpeter, Joseph A., History of economic analysis, ed. Schumpeter, Elizabeth Boody (New York, 1954), pp. 103–7 and 327–9Google Scholar. See also, Grice-Hutchinson, Marjorie, The School of Salamanca. Readings in Spanish monetary theory, 1544–1601) (Oxford, 1952)Google Scholar and Early economic thought in Spain, 1177–1740 (London, 1978)Google Scholar.

⁵⁷ In a similar discussion over royal defaults in the seventeenth century, Elliott, J. H., The Count-Duke of Olivares (New Haven, 1986), p. 77Google Scholar cites a 1621 argument that ‘for the Crown to tamper with interest rates was to default on its moral obligation’.

⁵⁸ , Lovett, Philip II and Mateo Vázquez de Leca, p. 66, n. 35Google Scholar cites, IVDJ, Envío 51, fo. 32 (1574).

⁵⁹ , Lovett, ‘The general settlement’, pp. 3–6Google Scholar.

⁶⁰ Braudel, Fernand, Civilization and capitalism, 15th–18th century, Vol III, The perspective of the world, trans. Reynolds, Siân (New York, 1984), p. 168Google Scholar.

⁶¹ , Lovett, ‘Juan de Ovando’, p. 12Google Scholar. See also, , Calabria, Cost of empire, App. II, pp. 56–69Google Scholar discusses an accounting dispute between Naples and Madrid over state budgets in the 1590s, which clearly demonstrates Neapolitan sophistication over their Spanish auditors.

⁶² Trenchant, pp. 299–300 gives the example of a 1555 loan of Henry III at compound interest in favour of the merchants, ‘4 per cent per fair, i.e., 16 per cent per year.’

⁶³ For an examination of the power of rhetoric in economics, McCloskey, Donald, The rhetoric of economics (Madison, Wis., 1985)Google Scholar.

⁶⁴ , Marino, ‘Professazione voluntaria e Pecore in aerea’, pp. 5–43Google Scholar.

⁶⁵ AGS, Visitas d'Italia, Náoles. leg. 23:3, cc. 285r–289V.

⁶⁶ , Lovett, ‘The Castilian bankruptcy’, p. 911Google Scholar summarizes the debate.

⁶⁷ Elliott, J. H., Spain and its world, 1500–1700: selected essays (New Haven, 1989)Google Scholar.