THE ORIGINS OF INEQUALITY: Insiders, Outsiders, Elites, and Commoners Gregory K. Dow (gdow@sfu.ca) Clyde G. Reed (reed@sfu.ca) Department of Economics Simon Fraser University November 2009 1
INTRODUCTION We explore the prehistoric origins of economic inequality. Hereditary inequality is unknown among mobile hunter- gatherers (although some differences in work tasks and food consumption based on age and sex do exist). Sedentary foraging societies are a mixed bag. Some are largely egalitarian, but others have hereditary inequality, both across and within communities. Agriculture is not a necessary condition for inequality, but it often does lead to more pronounced stratification, which is usually based on elite control over land. For evidence, see Kelly (1995), Johnson and Earle (2000), and many others. 2
Our model focuses on food. Inequality means differences across groups and individuals in food consumption. More generally: quantity, quality, variety, reliability. More generally still: the material standard of living. We do not address political power or social status, but in early societies these dimensions of inequality were clearly correlated with economic inequality. The key exogenous variable: Productivity of labor in food acquisition (determined by nature and technology). The key endogenous variables: Population, property rights, and inequality. 3
Our Story in Brief Rising productivity increases regional population density in the long run for Malthusian reasons. The highest local population densities are at the best sites in a region. When the population at a site becomes large enough, the insiders can prevent further entry by outsiders. This leads to insider-outsider inequality across sites (which occurs first at the best sites and then spreads). Further productivity growth eventually makes it profitable for insiders to hire outsiders as food producers. This leads to elite-commoner inequality within sites (which occurs first at the best sites and then spreads). Over time, inequality of both types increases. 4
We argue that these predictions are consistent with data from archaeology and anthropology. At the most general level, our theory is consistent with two stylized facts about early societies: (a) Productivity is correlated with population density, both over time and cross-sectionally. (b) Population density is correlated with inequality, both over time and cross-sectionally. We also argue that our theory is consistent with specific cases: the Channel Islands, the northwest coast of North America, southwest Asia, and Polynesia. 5
Outline Introduction The Theoretical Model (part one) The Theoretical Model (part two) Summary of Empirical Implications Four Cases from Archaeology and Anthropology Conclusion 6
THE THEORETICAL MODEL (part one) A Production Site With An Exogenous Outside Option At a production site, food output is θ sf(L) where θ > 0 reflects regional natural resources/technology; s > 0 reflects the quality of the individual site; and L ≥ 0 is labor time used for food production. The input of land is normalized at unity. A1 The function f is twice continuously differentiable with f(0) = 0; f ′ (L) > 0 for all L > 0; f ′′ (L) < 0 for all L > 0; f ′ (0) = ∞ ; and f ′ ( ∞ ) = 0. Individual agents are negligible relative to total labor at the site (L). Each agent is endowed with one unit of time. These endowments are used for food production, exclusion of outsiders, or some combination of the two (no leisure). The outside option of an individual agent is w > 0, which is the food available by migration to another site. There is an infinitely elastic supply of outsiders who will enter the site if they are not excluded and can obtain more than w by doing so. 7
Insiders who cooperate to prevent land appropriation by outsiders are called an elite . An elite of size e allocates its time between food labor (e f ) and guard labor (e g ) subject to e f ≥ 0, e g ≥ 0, and e f + e g = e. A2 Given elite food labor e f ≥ 0, the minimum guard labor needed to exclude outsiders is e g = g(e f ), where g(0) ≡ 0 ∈ (0, ∞ ). There is some e f 0 ∈ (0, ∞ ) such that g(e f ) e g 0 . The function g is twice = 0 for all e f ≥ e f 0 ) with g ′ (e f ) < continuously differentiable on e f ∈ [0, e f 0 and g ′′ (e f ) > 0. See Figure 1. Now consider any time allocation (e f , e g ) ∈ E. Available food is shared equally among the members of the elite. Each member receives (1) y(e f , e g ) = [max c ≥ 0 θ sf(e f + c) - wc]/(e f + e g ) where c is the number of commoners admitted to the site. Each member of the elite enjoys the surplus (2) v(e f , e g ) = y(e f , e g ) - w 8
An elite forms at a production site if and only if v(e f , e g ) ≥ 0 for some (e f , e g ) ∈ E. In this case we say the site is closed . Otherwise it is open . If the elite at a closed site chooses c > 0, we say that the site is stratified . We denote the total population at a site (elite and commoners together) by n = e + c. A3 When a site is closed, the time allocation (e f , e g ) maximizes v(e f , e g ) subject to (e f , e g ) ∈ E. The commoner population is determined as in (1). When a site is open, there is no elite and the commoner population satisfies θ sf(c)/c = w. At open sites, no set of agents can gain by excluding others. There is entry into the site if food per capita is above w and exit if food per capita is below w. 9
Proposition 1 (existence and uniqueness). Define z = θ s/w > 0. For a closed site there is a unique elite and commoner 0 ], e g (z) = g[e f (z)], and c(z) time allocation e f (z) ∈ [0, e f ≥ 0. Time allocation at a closed site depends only on the ratio of productivity ( θ s) to the outside option (w) at that site. 10
Proposition 2 (open sites). There is an A > 0 such that the site is open for z ∈ (0, A) and closed for z ∈ [A, ∞ ). For an open site there is a unique c(z) ≡ n(z) > 0 that is continuous and increasing on (0, A). We have c(z) → 0 as z → 0 and define c(0) ≡ 0. We also have c(z) → c - (A) as z → A from below, where c - (A) uniquely satisfies Af[c - (A)]/c - (A) ≡ 1. Proposition 2 shows that for low values of z ≡ θ s/w, the site is in the commons. As site quality rises, population rises. The site becomes closed at z = A. 11
Proposition 3 (closed and unstratified sites). The functions e f (z), e g (z), e(z), c(z), and n(z) are continuous on (A, ∞ ). These functions are right continuous at z = A. There is a B > A such that the site is closed and unstratified for z ∈ [A, B], and stratified for z ∈ (B, ∞ ). Thus c(z) = 0 on [A, B] and c(z) > 0 on (B, ∞ ). A > 0 such that e f (z) = e f A on There is some constant e f [A, B]. 0 f ′ (e f 0 )/f(e f 0 ) be the output elasticity at e f 0 , Let η ≡ e f where η ∈ (0, 1). 0 ) ≤ η then e f A = e f 0 and c - (A) = e(A) so that (a) If 1 + g ′ (e f n(z) is continuous at the boundary z = A (see Figure 2a). 0 ) then e f A < e f 0 and c - (A) > e(A) so that (b) If η < 1 + g ′ (e f n(z) drops discontinuously at the boundary z = A (see Figure 2b). For intermediate values of z ∈ [A, B] a site is closed but not yet stratified. A commoner class arises for B < z. 12
Proposition 4 (closed and stratified sites). 0 ) ≤ 0 then e f (z) = e f 0 for all z ∈ [B, ∞ ). (a) If 1 + g ′ (e f 0 ) < η there are C, D with B < C < D ≤ (b) If 0 < 1 + g ′ (e f 0 for z ∈ [B, C] and e f (z) is ∞ such that e f (z) = e f decreasing on [C, D]. If g ′ (0) ≤ -1 then D = ∞ . If -1 < g ′ (0) then D < ∞ and e f (z) = 0 for all z ∈ [D, ∞ ). 0 ) = η then C = B with e f (C) = e f 0 . All other (c) If 1 + g ′ (e f results are as in (b). 0 ) then C = B with e f (C) = e f A < e f 0 . All (d) If η < 1 + g ′ (e f other results are as in (b). (e) In (b), (c), and (d), e g (z) is increasing on [C, D] and e(z) is decreasing on [C, D]. In all cases, c(z) and n(z) are increasing on [B, ∞ ). In (a), the site never moves away from the corner solution 0 , 0) for any value of z because the cost of guard labor (in (e f foregone food output) is always too large. In the other cases, as z increases the elite begins to contract for C < z. This is accompanied by a gradual decline in elite food labor and a rise in guard labor. Total population rises due to a more than compensating increase in commoners. Eventually the elite may specialize in guard labor and rely entirely on food produced by commoners. 13
THE THEORETICAL MODEL (part two) Regional Inequality With An Endogenous Outside Option This section studies inequality in a region with a continuum of production sites. Site quality is s ∈ [0,1] where the number of sites of quality s is given by the density function q(s) > 0. Mobility is costless within the region, but agents cannot leave the region (deserts, mountains, ocean). The outside option (w) at one site depends on the food that can be obtained from migration to another site. 14
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