The “Value Principle” in Management Practices, Organizational Design, and Industrial Organization ^†

Abstract

The value principle in organizational economics states that the net market value of the goods that a firm sells is a key determinant of its organizational design. We survey and extend some recent developments in the theoretical literature at the nexus of organizational and industrial economics, focusing on this precept as the unifying theme. Under perfect competition, we study how market price influences the use of scarce professional management and the degree of organizational heterogeneity in an industry. In a more general setting, we show how changes in demand influence not only the use of professional management, but also the size and the market power of firms. And we show how prices can affect the internal control structure of firms, sometimes in highly distorted ways. We discuss applications to comparative industrial organization and to technological diffusion.

1. Introduction

A large and growing body of theory and evidence is showing that many elements of organizational design—ownership structure, the use of professional management, and internal control structures, to name a few—affect what firms do and how they perform. Thus, our understanding of how organizations arise has implications for many fields of economics, the foremost of which is industrial organization.

In practice, organizational economics tends to focus on how the terms of trade-offs among various incentive problems are governed by aspects of “technology”: the complementarity or substitutability of assets; product complexity or relationship specificity; costs of communication; or degrees of contractibility, among many. Undoubtedly these are central. But confining attention to technology also has shortcomings. First, it presents empirical and policy challenges because of the difficulty in measuring these aspects of technology or theorizing about how they might change. Second, it may lend to the impression shared by many economists outside the field that organization is just “part of the technology”, and, in particular, exogenous to their concerns. Finally, a positive economic theory of organizational design that relies solely on technology for its predictions is simply incomplete.

Over the years, a strand of theoretical work (e.g., Banerjee & Newman, 1993; G. Grossman & Helpman, 2002; Legros & Newman, 1996, 2013) along with some supportive empirical work (Alfaro et al., 2024, 2016; Forbes & Lederman, 2009, 2010; McGowan, 2017) have emerged, showing that the market values of the goods that a firm sells (or buys) are key determinants of its organizational design, a precept we designate the “value principle”. While simple, if not obvious, it has arguably been underexploited in the analysis of how organizations are designed. This is unfortunate, for predicated as it is on the effects of observables such as prices and productivity, it has an advantage in generating operationally testable predictions. Furthermore, because value is determined in the market, a firm’s organization can hardly be considered exogenous to many economic problems, especially those in industrial organization, a field chartered to elucidate how prices are formed. Last, but hardly least, policymakers ignore the value principle at their peril; indeed, that practice has already led to policy blunders, as argued in Legros and Newman (2017) for the case of divorcement in the British beer industry.

In this paper, we review and extend recent results in the theoretical “Organizational Industrial Organization” literature with the value principle as a unifying theme. We study three distinct kinds of organizational design problems: (1) the use of scarce professional management, along with its span of control, in competitive product and managerial markets; (2) horizontal integration motivated by the acquisition of market power in the absence of increasing returns to scale; and (3) internal control structures via informal delegation of authority. In each case, market value is a key driver of the organizational outcome, which then feeds back to industrial performance.

A recurrent pattern is the non-monotonicity of organizational design or productivity in the level of demand. The model suggests that the use of professional management in competitive environments follows an inverted-U pattern: at low product value its enhanced productivity does not cover its cost, while at very high values members of the enterprise have strong enough incentives to perform well without it. Where horizontal integration is a possibility, firm size and the degree of competition also follow non-monotonic patterns as demand increases, from completely fragmented, straight through to monopoly, and then on through decreasing concentrations of oligopoly. Nor do firms perform monotonically in the degree of decentralization: in particular, partial decentralization may be less efficient than either full centralization or complete decentralization.

We suggest that these results may help to explain some documented patterns in developing countries such as the “missing middle” phenomenon; the relative rarity of professional management; and predominance of tiny firms alongside very large ones. For the wealthier nations, the results on internal control may help our understanding of the information technology (IT) “productivity paradox” of the 1980s and 1990s. They also suggest some empirical cross-country or cross-industry patterns of internal control structures that, as far as we know, have yet to be investigated.

In the next section we set up the basic organizational building block. Section 3 examines ownership structure, focusing on the distinct productivity enhancement and market power acquisition roles of professional management. Section 4 turns to internal control structures, and Section 5 summarizes and concludes with some further discussion of empirical implications.

2. Model

The basic organizational building block is adapted from Legros and Newman (2013). It shares with the incomplete contracts/property rights tradition (S. Grossman & Hart, 1986; Hart & Moore, 1990) a focus on ownership and other mechanisms for assigning control rights, but assumes that production/investment decisions are never contractible, rather than ex-post contractible, as in the hold-up models that are more common in that literature. Following Hart and Holmström (2010), “professional” managers are motivated solely by profit, unlike other productive actors in the economy. In the presence of incomplete contracting, they require authority to implement production decisions, which they acquire through asset ownership. The act of acquiring these assets from the original owners, who then engage in production under the professional manager’s authority, is what we refer to as integration.

2.1. Technology, Preferences, Demographics

The industry is populated by a unit-measure continuum of “enterprises”, each consisting of two assets, $A_E$ and $A_S$, that are owned, respectively, by decisionmakers of type E and S (many interpretations possible: engineering and sales managers, entrepreneur and supplier, endocrinologist and surgeon, to name a few). The two assets, and the associated decisionmakers’ investments, must be combined to produce output. Specifically, output is 1 with probability $f(e_E,e_S),$ and 0 otherwise; $f(·,·)$ is strictly increasing in the non-contractible investments $e_E,e_S\in [0,1]$. To facilitate focusing on the role of enterprise value rather than surplus distribution in determining organizational and performance outcomes, we assume that $f(·,·)$ is symmetric. The decisionmakers have quasilinear payoffs $y_E-c(e_E)$ and $y_S-c(e_S),$ where y is income derived from production, and $c(·)$, which is increasing and strictly convex, represents the private cost of supplying the input. Again, for the sake of symmetry, we assume identical cost functions.1 We assume that there are no other (marketed) inputs such as materials and commodity labor, or at least that their cost is zero. We return to this point at the end of the section.

In addition to the E’s and S’s, there is a measure $m<1$ of profit-oriented professional managers ($PM$s). A $PM$ is also capable of making the decisions $e_E,e_S$, but has no direct interest in them: she only chooses $e_E$ or $e_S$ to maximize income $y_P$ garnered from an enterprise she owns (in which case the E and S are her subordinates). Only if there are several ways to choose $e_E,e_S$ that all yield the same profit will she consider the interests of her subordinates, in which case she picks the (generically) unique allocation that minimizes their joint cost $c(e_E)+c(e_S)$ (a “minimum blowback” assumption).2

All actors have zero opportunity costs of participation in the industry. One $PM$ can own and operate multiple enterprises.3 This (potentially) comes at a cost for the $PM$: to operate $s\ge 0$ enterprises, she incurs the non-decreasing, convex cost cost $C(s),$ for which $C(0)=0.$4

2.2. Timing and Contractibility

We assume that all parties in the model have sufficient cash or other liquid assets on hand to make side payments (full transferability), again to be able to set aside distributional concerns in favor of a focus on the effects of enterprise value. This implies that all contracting arrangements will maximize the surplus generated by the negotiating parties, subject only to contractibility constraints.5

As mentioned above, neither of the inputs $e_E,e_S$ are contractible. Revenue shares are contractible. Ownership of assets, which, à la S. Grossman and Hart (1986), confer control rights over the decisions to the owner (including the possibility of reassigning control informally to someone else) is contractible, as are side payments either between E and S or among those two and the $PM$.

Sometimes it will be convenient to use a simplified, aggregated (or “representative agent”) version of the building block; symmetry and surplus maximization implied by full transferability facilitate this. Define $a=e_E+e_S$, and restrict attention to symmetric ($e_E=e_S$) allocation of these inputs—given the fundamentals, they are characteristic of the first-best, equal (and surplus–optimal) profit-sharing, and optimal professionally managed outcomes. In addition to analytical convenience, this representative-agent formulation highlights an alternative interpretation, namely, a single individual proprietor who is subject to family or network obligations (or “taxes”), which may be especially salient for developing economies.

2.3. Functional Forms

To minimize mathematical distractions, from now on we specialize to the following functional forms. The success probability $f(e_E,e_S)=\min \{1,e_E+e_S\}$. The private cost function is $c(e)=\frac{1}{2}\psi e^2$, and managerial cost $C(s)=\frac{1}{2}\sigma s^2$ (in Section 3.2, $\sigma =0$). Now, with $a=e_E+e_S$, the total private cost in symmetric allocations is $\frac{1}{2}\varphi a^2$, where $\varphi \equiv \psi /2.$6

Most economic results do not depend on this functional form; the main effects of generalization are the possibility of multiple competitive equilibria brought on by a loss of monotonicity that may be difficult to characterize precisely. Those possibilities arise even with our functional forms, but the closed forms we obtain allow for simple parametric characterization of when they occur.

2.4. Demand

Demand is represented by a strictly decreasing function $Q=D(p)$, where p is the industry price. For the competitive analysis in Section 3.1, no other restrictions need be imposed; in Section 3.2 we require that the inverse demand $p=P(Q)$ be log-concave. So that we can compare salient differences in demand across developed and developing economies, it will be convenient to focus attention on a representative of this class, namely, the linear case $P(Q)=A(1-Q)$, where low A is likely to be characteristic of poor economies.

2.5. On Interpreting (Market) “Value”

We have ignored any marketed inputs (or normalized their price to zero), but if, instead, they are costly, p can be interpreted as the price-cost margin or net value. That is, if the product price is P and the potential unit of output also requires a unit of input paid c contingently on success, let $p=P-c$, and expected revenue is $a(P-c)=ap$. For purposes of interpretation, when considering price movements within an industry in one country, P is changing and c is fixed, as in the usual interpretation. When comparing across countries, especially ones with significantly different wealth levels, P and c vary roughly in proportion, so that the net value p is higher in the rich country. What is important is that the “private” costs represented by the parameter $\varphi$ need not vary nearly as much across countries, at least not in lock step with the prices of marketed commodities. That, after all, is part of what makes them private, and the problem of development so compelling.

3. Ownership Structures in Industry Equilibrium

We begin with the decision to adopt professional management via vertical (or lateral) integration in perfectly competitive product and managerial markets. The next subsection considers horizontal integration and the acquisition of market power; the authority of professional management becomes the mechanism for eliminating the cartel problem, that it the individual enterprise’s temptation to overproduce.

3.1. A Competitive Industry with Competitive Managerial Market

Consider a single E–S pair who decide ownership structure, correctly anticipating the market price p. If they are non-integrated, the outcomes of the simultaneous choices by each partner are equivalent to the solution of ${\max }_a\frac{1}{2}p\min \{a,1\}-\frac{1}{2}\varphi a^2$, or $a=\min \{\frac{p}{2\varphi },1\}$7 so that expected output solves ${\max }_a\frac{1}{2}p\min \{a,1\}-\frac{1}{2}\varphi a^2$, i.e., $a=\frac{p}{2\varphi }$ for $p\le 2\varphi$, 1 otherwise. This yields a surplus of $\frac{3p^2}{8\varphi }$ when $p\le 2\varphi$ and $p-\varphi /2$ otherwise.

If integrated, they sell their assets to the $PM$, who assumes ownership and control of the decisions. The $PM$ receives a compensation package worth W, which is determined in a competitive managerial market. The compensation may be partly fixed, but at least some of it must be a share of the revenue.8 The $PM$ will, therefore, maximize profit $pa$, setting $a=1$. This only says that $e_E+e_S=1$ under integration, but the minimum-blowback assumption implies that the $PM$ lexicographically chooses the least-cost way to accomplish this, i.e., $e_E=e_S=\frac{1}{2}$, so that surplus is $p-\varphi /2.$ Of course, the E–S pair only accrues $p-\varphi /2-W$ of this, as W goes to $PM.$

On the supply side of the managerial market, one $PM$ can own and operate several enterprises and will offer to buy $\arg {\max }_{s}sW-1/2\sigma s^2$ when the compensation is W. Thus, $s=W/\sigma .$ The supply of $PM$ services to the industry is therefore $mW/\sigma .$

The demand side of the managerial market is slightly more involved. Taking W as given, an enterprise prefers integration to non-integration whenever $p-\varphi /2-W>\frac{3p^2}{8\varphi }$. Note that if $p>2\varphi$, non-integration yields surplus $p-\varphi /2$ and therefore dominates integration for any non-negative W: thus, demand for professional managers is zero for such p unless $W=0$. Similarly, the demand for integration and the $PM$’s will be zero if $p<2\varphi /3$ (the latter being the smaller root of $p-\varphi /2=\frac{3p^2}{8\varphi }$). For $p\in (2\varphi /3,2\varphi )$, demand is 1 (the measure of enterprises) if $W<p-\varphi /2-\frac{3p^2}{8\varphi }$ and $[0,1]$ if $W=p-\varphi /2-\frac{3p^2}{8\varphi }$. Thus, demand for professional management is nonmonotonic in product price.

In the high-price ($p>2\varphi$) regime, despite the “free-riding” incentives inherent to partnerships and non-integration (which are formally identical), the value of the enterprise is high enough that this ownership structure performs reasonably well (in this model it reaches maximum productivity), and is, therefore, not worth any positive managerial compensation W to integrate.

Of particular interest in the case of developing countries, on the low price side ($p<2\varphi /3$), the higher productivity of integration and professional management is undeniable, but the value of higher productivity is low because of the low price, and, thus, integration is avoided in order to avoid the comparatively high private cost. Low demand and, therefore, low enterprise value imply low productivity organization forms. Insofar as these features are characteristic of demand in many developing countries, we have a simple account of the predominance of “small” enterprises that make little use of professional managers and modern management practices that has been noted by many empiricists (e.g., Bloom et al., 2013; McKenzie & Woodruff, 2017): the productivity gains are not worth the cost, given the market value of output. What matters, of course, is the fraction of value that accrues to the enterprise—the prevalence of network taxes already mentioned, or extreme extractive practices of middlemen in many developing-country industries Bardhan et al. (2021), would only exacerbate the problem, making use of professional management even less likely.

Managerial compensation W is determined by market clearing: for $p\in (2\varphi /3,2\varphi )$, the equilibrium compensation $W=\min \{p-\varphi /2-\frac{3p^2}{8\varphi },\frac{\sigma }{m}\}.$ Notice that a typical market clearing outcome is heterogeneity of ownership structures: whenever $W=p-\varphi /2-\frac{3p^2}{8\varphi }$, some enterprises are integrated and the rest are not. In fact there is an “inverted-U” relationship between price and the degree of integration. As price increases from $2\varphi /3$ to $2\varphi$, integration first increases, peaking at $p=4\varphi /3$, where $W=\min \{\frac{\sigma }{m},\frac{\varphi }{6}\}$ and $\min \{1,\frac{m\varphi }{6\sigma }\}$ enterprises are integrated, then decreases to zero as price rises further to $2\varphi .$ Depending on parameters, pure integration may occur in a neighborhood of $p=4\varphi /3$. This can be ruled out with the parametric condition

$$m<\frac{6\sigma }{\varphi },$$

(1)

which ensures that the maximum willingness to pay for integration is too small—or that professional managers are too scarce or costly—to attract excess supply of management.9

Proposition 1. 

Under assumption (1), integration and non-integration co-exist for $p\in (2\varphi /3,2\varphi )$. For $p\notin (2\varphi /3,2\varphi )$, there is pure non-integration.

The span of control s (or size, as measured by the number of enterprises owned by one $PM$) of competitive firms follows the same pattern as the overall degree of integration. If price is low, we have only non-integration; then, as price increases, span begins to increase, reaching a maximum of $\frac{\varphi }{6\sigma }$ at $p=\frac{4\varphi }{3}$, then declines to zero as p approaches $2\varphi$.

We, therefore, have two consequences of the scarcity professional management: (1) endogenous heterogeneity of ownership structures over an interval of prices (rather than at just a single price, as in Legros and Newman (2013), despite all enterprises being identical; and (2) non-monotonicity of ownership structure in industry price. The first result underscores the theoretical genericity of endogenous organizational-cum-performance heterogeneity, something that has been a recurrent theme in empirical organizational economics Gibbons and Henderson (2013). Integrated enterprises produce more output than non-integrated ones, yet their co-existence in competitive equilibrium is endemic, a consequence of the lack of arbitrary scalability in this model (preventing one enterprise from taking over the entire industry) and the scarcity of management. In fact, pure integration is an outcome only if $p-\varphi /2-\frac{3p^2}{8\varphi }>\frac{\sigma }{m}$; the left side of this inequality is bounded above by $\varphi /6$, so endogenous heterogeneity is more likely the fewer $PM$s there are (small m) or the more costly it is to implement managerial practices ($\sigma$).

This is not the first paper to observe non-monotonic responses of ownership structure to price levels. Indeed, Dam and Serfes (2021) study this relationship in an “abundant-management” model similar to Legros and Newman (2013), but with cash-constrained and heterogeneous enterprises. Their results are driven by the interplay of market price and the distribution of surplus within E–S pairs, a mechanism that we have shut down with the assumption of plentiful liquidity for side payments.

Finally, we can derive the “organizationally augmented supply” for the industry. As each integrated enterprise produces expected output of 1, and each non-integrated one produces $\min \{1,p/(2\varphi )\}$, the supply $S(p)$ is $\frac{p}{2\varphi }$ for $p\le 2\varphi /3$; under assumption (1), the supply for $p\in (2\varphi /3,2\varphi )$, given the managerial market has cleared, is

$$S(p)=(1-\frac{mW}{\sigma })\frac{p}{2\varphi }+\frac{mW}{\sigma };$$

(2)

and for $p>2\varphi$, $S(p)=1.$ Noting the equilibrium dependence of W on the product price p and rearranging (2) gives us, for $p\in (2\varphi /3,2\varphi )$,

$$S(p)=\frac{p}{2\varphi }+(1-\frac{p}{2\varphi })\frac{m}{\sigma }(p-\frac{\varphi }{2}-\frac{3p^2}{8\varphi }).$$

(3)

The changing differences in output levels between non-integration and integration, which contribute to the shift from non-integration to integration and back again in this range, raise the possibility that supply could be non-monotonic in price.10 Indeed, without assumption (1), at the price of the product $\frac{4\varphi }{3}$ that maximizes the willingness to pay for management, all enterprises would be integrated and the output is 1. But for prices closer to $2\varphi$, W must be small, as the surplus gap between integration and non-integration is small. If the supply of management declines rapidly enough with respect to the rising output from non-integration, then supply will decline as well.

It turns out that a strengthening of assumption (1) so that management is more scarce or costly, or private costs lower, ensures monotonicity of supply, despite the non-monotonicity of integration:

Proposition 2. 

The supply in (3) is monotonic if, and only if,

$$m\le \frac{9\sigma }{2\varphi }.$$

To see this, differentiate (3) to reveal that $S^{\prime }(p)$ is minimized at $p=14\varphi /9$, where it is non-negative if and only if the condition in Proposition 2 holds.

3.2. Endogenous Market Structure and Imperfect Competition

So far we have considered “small” (i.e., price-taking) firms wherein the chief organizational decisions are whether to employ professional management via vertical integration, and if so, the resulting span of control. Whatever the organization of individual firms, their behavior on the product market has been taken to be competitive.

What of pure horizontal integration, the combination of identical assets into potentially “large” firms with market power?11 It is well known that horizontal integration has the potential to result in increased market prices: a large $PM$’s authority is one means by which the “cartel problem” can be avoided. In contrast to a small producer who would want to cheat on any anti-competitive price-fixing arrangement, a $PM$ who controls many enterprises has not only the wherewithal—authority to determine her enterprises’ output—but also the strict incentive to adhere to it, as she perceives her market power.

Considering the role that demand plays in the determination of market structure in classical IO, it may come as no surprise that the value principle bears the question of horizontal integration. But, here, there are some subtle differences, in particular ones that help shed light on the proclivity for firms in developing countries to be very small, to avoid professional management practices, and to have low productivity. IO cannot explain this with its existing theories of market structure. But organizational IO can, and the value principle is at the core.

We follow Legros et al. (2025) and drop the exogenous internal diseconomies of firm size represented by $C(s)$ by letting $PM$s have zero management costs (i.e., $\sigma =0$). Thus, a $PM$ could, in principle, operate an arbitrary measure of enterprises (E–S pairs).12 This will allow for the possibility that a (small) finite number of $PM$s are controlling the whole industry and, thus, have market power. It is also convenient to assume that $PM$s are abundant (e.g., their measure is at least that of the scarcer of the E’s and S’s), so that along with their zero opportunity cost, we can abstract from their compensation in what follows.

As explained in Legros et al. (2025), what prevents a firm from growing to encompass the entire market is free-riding in the form of a fundamental hold-out problem that was noted by Stigler (1950): no enterprise would want to join an oligopoly unless the purchase price for its assets compensates for the payoff it could obtain by standing alone outside the oligopoly. In Stigler’s (implicitly) perfect-contracting world, where all inputs are priced, the standalone producer can produce any quantity it likes, including mimicking what it would do as a member of the oligopoly, without affecting the market price set by the oligopoly. But then it can do strictly better by choosing some other quantity. This hold-out effect is so powerful that without the organizational contracting frictions (here represented by non-contractible investments and the imperfect remedies in the form of profit sharing or $PM$ authority), only perfect competition could prevail in equilibrium.

But with contracting frictions, it is possible that the payoff obtained inside the oligopoly is not available to a standalone enterprise. As before, given an equilibrium price p, a standalone run by a $PM$ will generate surplus $V^I=p-\varphi /2$, as, given her authority, the $PM$ could not commit to choosing anything but $a=1$; a standalone unmanaged producer would accrue $V^N=\frac{3p^2}{8\varphi }{\mathbb{I}}_{\{p\le 2\varphi \}}(p)+(p-\frac{\varphi }{2}){\mathbb{I}}_{\{p>2\varphi \}}(p)$ (${\mathbb{I}}_{\mathcal{X}}(x)$ is the indicator for $x\in \mathcal{X}$). For any E–S pair to be willing to join a “large” $PM$, the offer price for their assets, less the anticipated effort costs endured within the oligopoly, must weakly exceed the greater of these two amounts. Thus, if the $PM$ of a large oligopolistic firm chooses for each of its subordinate E–S pairs an output level $a_O$, the surplus generated by one of these pairs is $p{a}_O-\frac{1}{2}\varphi a_O^2$. However, $a_O$ need not equal 1 (the level in a professionally managed standalone) nor $p/(2\varphi ),$ the level in a non-integrated one, so it is no longer a priori obvious that standalones outperform the oligipoly as Stigler argued.

The structure of the model is essentially as before, except that after $PM$s have purchased the enterprises, Cournot competition replaces perfect competition in the product market. The large number of $PM$s first compete for ownership of assets by making bilateral offers (a purchase price for each enterprise that is uncontingent on the responses of other enterprises or $PM$s); each enterprise accepts at most one offer. Once this asset market has settled, the $PM$s who have secured a positive measure of assets choose quantities for their firms, taking the quantities of other $PM$s as given, and order each of their acquired subordinates to select an effort level to help effectuate that quantity.13 When deciding which offer to accept, each enterprise not only compares offers among putatively “large” $PM$s, but also forecasts the payoff of remaining a standalone firm, either accepting an offer from a $PM$ that intends to remain small, or as non-integrated entity.

Suppose that $n\ge 1$ $PM$s Cournot compete in the product market. We treat n as continuous for expositional simplicity.14 Suppose further that the consumer side of the market is represented by the linear inverse demand $P=A(1-Q)$.15 Our main concern will be how the ownership and industrial structures, which are co-determined in the model, respond to shifts in demand, specifically the valuation parameter A.

Each $PM$ i chooses quantity $q_i$ to maximize

$$A(1-q_i-\sum _{j\ne i}{q}_j)q_i,$$

yielding $q_i=\frac{1}{n+1}$, all i; thus the industry quantity $Q=\frac{n}{n+1}$, and price $p=\frac{A}{n+1}.$ If each of these n firms comprise an equal measure $1/n$ of enterprises,16 then the intensity a with which any one constituent enterprise works satisfies

$$\frac{1}{n}a=q_i=\frac{1}{n+1},$$

so that $a=\frac{n}{n+1}$ (by the minimum-blowback assumption and the strict convexity of private costs, this will be equal across the identical enterprises inside a firm; by the law of large numbers, $P{M}_i$ achieves her desired $q_i$ almost surely, as she owns a continuum of enterprises). The surplus generated by a single enterprise belonging to a firm in an n-oligopoly is

$$V_n^O=pa-\frac{\varphi }{2}{a}^2=\frac{An}{{(n+1)}^2}-\frac{\varphi }{2}\frac{n^2}{{(n+1)}^2}.$$

Note that this is decreasing for $n\ge 1$. Thus, the more concentrated the industry (the lower the n), the higher the per-enterprise payoff. This is not just because monetary profit is higher, as in standard IO models, but also because of a “quiet life” effect: large $PM$s are in no better position to commit to effort levels than small ones, but because of their incentives to restrict output due to their market power, they adventitiously lower the effort required of their subordinates. This is what potentially offers enterprises something under oligopoly that they cannot accrue as a standalone managed firm (meanwhile, unmanaged standalones suffer from the usual low productivity problems due to internal free-riding, and so are potentially also at a disadvantage relative to oligopoly).

For an n-oligopoly to be viable, in addition to the feasibility requirement $n\ge 1$, two conditions must be satisfied:

$$V_n^O\ge V^N,$$

(4)

and

$$V_n^O\ge V^I,$$

(5)

where $V^N$ and $V^I$ are evaluated at the price the n-oligopoly generates. Conditions (4) and (5) require that the oligopoly deliver at least the surplus that, respectively, non-integrated and professionally managed standalones can deliver, given the price the oligopoly generates.

Using the values derived above, substituting $\frac{A}{n+1}$ for p, and isolating n, (4) becomes

$$\frac{A}{2\varphi }\le n\le \frac{3A}{2\varphi }$$

(6)

and (5) reduces to

$$\frac{2A-\varphi }{2\varphi }\le n.$$

(7)

Condition (7) reflects that if the oligopoly is too concentrated, it delivers prices that are so high that standing alone with with a $PM$ is too tempting; despite the higher effort, the increased output is worthwhile. A similar intuition underlies the first inequality in (6). If, instead, an oligopoly has $n<\frac{A}{2\varphi }$, then the price it generates would induce even a non-managed enterprise to produce more output as well as surplus (it turns out that this constraint never binds: $n=\frac{A}{2\varphi }$ and $n\ge 1$ imply $A\ge 2\varphi$, so the oligopoly price $p=\frac{2\varphi A}{A+2\varphi }\in \left(\frac{2\varphi }{3},2\varphi \right)⟹V_I>V_N$; but then only (5)—equivalently, (7)—is salient). On the other hand, if the oligopoly is not concentrated enough (the second inequality in (6)), then oligopolistic $PM$s overwork their subordinates, albeit less than perfectly competitive $PM$s do, and it is more attractive to stand alone without a manager to enjoy a quiet, if unprofitable, life in the fringe.

It is evident that (6) cannot be satisfied for any $n\ge 1$ if $A<\frac{2\varphi }{3}$. With demand this low, a competitive equilibrium exists with $p<\frac{2\varphi }{3}$; thus, all enterprises are nonintegrated price-takers. Even a monopoly works its members too hard, given the monetary return, for any enterprise to subject itself to professional management.

But for higher values of A, there will typically be many n satisfying these conditions. Thus, with contracting frictions, oligopoly may be viable—resistant to free-riding—even though there are no significant economies of scale in production. For what remains, we focus on the value of $n\ge 1$ satisfying (6) and (7) that maximizes per-enterprise surplus.17

With $A=A_0:=\frac{2\varphi }{3}$, monopoly ($n=1$) becomes viable, with $V_N>V_I$ at the monopoly price $A/2$ (recall $V_N>V_I$ as long as $p<\frac{2\varphi }{3}$). As A rises, the second inequality in (6) becomes slack, and the most concentrated oligopoly remains a monopoly. As A crosses $\frac{4\varphi }{3}$, the monopoly price exceeds $\frac{2\varphi }{3}$, at which point $V_I>V_N$. However, (7) does not bind until $A=A_1:=\frac{3\varphi }{2}$, above which concentration (measured by $1/n$) begins to decline, as $n=\frac{A}{\varphi }-\frac{1}{2}.$ In summary,

Proposition 3.  

(i) 

There exists a valuation level $A_0$ for which $A<A_0$ implies that the industry is perfectly competitive, and no enterprises have professional managers.

(ii) 

There exists $A_1>A_0$ such that $A\in (A_0,A_1)$ implies that the industry is monopolized, with a professional manager ensuring compliance with output restrictions.

(iii) 

For $A>A_1$, industry concentration is decreasing in A; professional management is used by all enterprises.

While it is true that standard endogenous entry models would imply a counterpart to the decreasing concentration result in (iii), they do so by invoking a “large” non-convexity (e.g., entry cost). They are silent about the use of management to accomplish firms’ objectives. Moreover, they have no counterpart to (i). That result is evocative of the situation in poor countries discussed above, in which many enterprises are small and poorly managed, with low productivity. The model suggests a possible origin: low demand (that is, low A) from the impoverished population.

At the same time, the model also suggests that large firms should also be quite prevalent in poorer countries. In fact, there is substantial empirical literature documenting a “missing” (or at least attenuated) middle in the size distribution of firms in developing countries (Hsieh & Olken, 2014). Most explanations focus on regulatory or credit market origins, with mixed empirical success.

The value principle offers a possible alternative. Suppose that there are a large number of industries, each with a linear demand as in the model above, but with the maximum valuation A drawn independently from a distribution $F(A)$. In our rather stylized model, each industry will have a unique firm size corresponding to its draw of A, but aggregating across all industries will lead to a non-generate size distribution (the evidence is much the same, looking at all firms, or all in a broad sector such as manufacturing). The measure of infinitesimal firms is $F(A_0)$, that of the largest (monopolies) $F(A_1)-F(A_0)$, and that of the intermediate sizes ($1/2,1/3,\dots$) $1-F(A_1)$. If we take a richer country to be one with distribution $\widehat{F}(A)$, where $\widehat{F}$ first-order stochastically dominates F, then the richer country will have a smaller measure of infinitesimal firms and a larger measure of intermediate ones (the change in the measure of monopolies $\widehat{F}(A_1)-\widehat{F}(A_0)-[F(A_1)-F(A_0)]$ is ambiguous without further restrictions on the family of distributions; for the uniform family, with support $[0,A]$ for the poor country and $[0,\widehat{A}],\widehat{A}>A,$ for the rich, there are relatively fewer monopolies in the rich country; but for the exponential or Fréchet families the comparison is ambiguous without precise information about the scale/shape parameters and the values of the $A_0$ and $A_1$). More particular quantitive propositions that can be brought to data await further research.

Developing countries typically have less stringent antitrust policy, although there is variation (see Besley et al., 2021). The present model suggests that such policy needs to be designed with care, especially in low-value industries (see Legros et al., 2025 for discussion of the rich-country case). In particular, if $A\in (2\varphi /3,4\varphi /3)$, monopoly is the equilibrium outcome, with $p=A/2$. Note that forcing perfect competition in this range would be counterproductive (at least from the consumers’ point of view). With A in the lower half of this interval, the competitive price would be $\frac{2A\varphi }{A+2\varphi }>\frac{A}{2}$; in the upper half, the competitive price is $\frac{2\varphi }{3}>\frac{A}{2}$. The presence of low-productivity non-managed enterprises results in so little output that even a monopoly that operates solely to exploit market power would improve things for consumers.

In fact, forcing monopoly on a market could improve things for consumers. To see this, consider $\varphi /2<A<2\varphi /3$, which in equilibrium generates perfect competition with non-managed firms. Forcing producers into a profit-maximizing syndicate (in effect ignoring constraint (6)) would result in equilibrium price of $A/2$, which we already noted is smaller than the competitive price $\frac{2A\varphi }{A+2\varphi }$ (consumers would also benefit if $A\le \varphi /2$, but this would generate negative payoffs for the producers who would need to be subsidized—or conscripted—to participate).

4. Other Management Practices: Centralization, Decentralization, and Favoritism

Thus far, we have focused on the value principle’s role on the determination of ownership structure, i.e., vertical and horizontal integration, as well as managerial span. But its influence reaches beyond those. Here, we discuss how it may be reflected in other management practices, namely, the determination of internal control structure, specifically how decentralized decision making is within the firm. On the empirical side, high degrees of decentralization have been associated with high productivity, making this aspect of the internal organization of firms immediately relevant to IO.

We maintain the assumption that decisions $(e_E,e_S)$ are never contractible; thus, the allocation of control continues to influence firm performance. We confine attention to integrated enterprises, that is, where there is a $PM$ who has formal title to the productive assets, and the question is whether control of $(e_E,e_S)$ might be reallocated to one or more of the subordinates $E,S$ (possibly integration has already occurred for reasons orthogonal to our model; for an explicit treatment of how (vertical) integration and internal control structure are jointly determined, see Alfaro et al., 2024). We focus on the relationship between a $PM$ and a single E–S pair, even if she happens to own several enterprises (i.e., apart from the effects on $PM$s administration cost which in turn is not dependent on the internal control decisions that will be made, there are no externalities across enterprises owned by a single $PM$). We also return to the competitive (price-taking) behavior of $PM$s of Section 3.1.

4.1. Delegation

We first consider the chief mechanism by which this reallocation (that is, transfer of control from the $PM$ to her subordinates) is accomplished, namely, delegation by the $PM$—a non-contractible act that is among the $PM$’s rights as owner of the assets. We shall compare it with an efficient control benchmark that might be achieved via contract or efficient renegotiation.18 As in the previous section, the $PM$ takes into account only monetary profit, neglecting the private costs of her subordinates except to break ties. Despite her indifference among subordinates, the outcome of her delegation decision will sometimes take an inefficient form that we refer to as favoritism.

The $PM$ can choose three control structures: (1) centralization, wherein she makes all decisions; (2) partial decentralization, wherein only one of the two subordinates is awarded control, while the rest of the decisions are made by the $PM$; and (3) full decentralization, in which all decision rights are kicked back to the subordinates E and S.

The $PM$ makes the delegation choice in the wake of a “problem” that arises randomly during the production process (e.g., Alfaro et al., 2024; Garicano, 2000).19 We suppose that problems are indexed by elements of the unit interval, and that they can be solved by whoever makes the production decision(s) $e_E$ or $e_S$ (problem solution and production decision are, thus, not completely separable). Parties differ in their competence at solving any particular problem, and each party’s competence may vary across problems. Specifically, we assume that the $PM$ is a generalist who solves all problems equally well: this is represented by recasting the success probability used earlier to $z\min \{1,e_E+e_S\}$, where $z\in (0,1)$ is a constant.

The subordinates are specialists, better than the $PM$ at some problems, worse at others. We represent this situation by supposing that the success probability if controlled by one or both of the subordinates is $x\min \{1,e_E+e_S\}$, where x is mean-preserving spread of z, i.e., a random variable with continuous c.d.f. $G(x)$ supported on $[0,1]$ with $\mathbb{E}x=z$ (as we can always reorder the index identifying problems by the subordinates’ productivity in solving them, we shall refer to individual problems by x). We consider both E’s and S’s competence at each problem relative to the $PM$ as the same, hence we do not index x by the identity of the subordinate, though it would be straightforward to generalize to that case, say by letting x represent an average, or the maximum, of the two subordinates’ competences. If $z=1$ (so the MPS and support assumptions imply that $G(x)$ is degenerate), then this model reduces to the one considered in the earlier sections.

We assume that the control structure is determined after the realization of the problem. Thus faced with a production problem, the $PM$ now must decide who will solve it, recognizing that said party will also choose the relevant $e_E$ (or $e_S$). As no additional information is learned after the control assignment (beyond success or failure of the project, upon which no action can be taken), the $PM$ will never be tempted to revoke control once she has assigned it.

Suppose that at the time of asset purchase, the $PM$ has negotiated a profit shares $1-\pi \in (0,1)$ for herself, with the remaining $\pi$ split equally between E and S (any other split between them is less efficient), and we assume that these shares are not renegotiated.20 If she centralizes, retaining control over $(e_E,e_S)$ for herself, then, as before, she selects $e_E=e_S=1/2$, but now the expected revenue is $pz.$ If she decentralizes, while retaining her share $1-\pi$ of the profits, then the two subordinates will act as they do when non-integrated, except that in place of p we have $\pi xp$, so that the joint outcome $a=e_E+e_S$ of their choices will be $a=\min \{\frac{\pi px}{2\varphi },1\}$, resulting in an expected output $\min \{\frac{\pi p{x}^2}{2\varphi },x\}$, and an expected revenue $\min \{\frac{\pi p^2{x}^2}{2\varphi },px\}$. Finally, if she assigns control to just one subordinate, say E, she chooses after observing his choice; knowing this, he will choose $e_E=0$ (regardless of his share of revenue), and the $PM$ will consequently set $e_S=1$.21 Expected revenue is $py$, where $y=\lambda z+(1-\lambda )x$ for some fixed $\lambda \in (0,1)$, i.e., an average of the competencies of the $PM$ and the controlling subordinate.

Notice that the private cost of centralization is $\varphi /2$, divided between subordinates. But, while partial decentralization does not impose a private cost on the controlling party (E in our example), it imposes the maximum cost $\psi /2=\varphi$ on the other (S), regardless of how small the productive advantage $y-z$ could be. Consequently, it may have the appearance of favoritism, and we shall refer to it as such from now on.22

The $PM$ chooses the control structure that generates the largest revenue among $pz,py,$ and $\min \{\frac{\pi p^2{x}^2}{2\varphi },px\}.$ A little algebraic manipulation, along with the $PM$’s tie-breaking rule, leads to a characterization of the values of x for which each control structure is $PM$-optimal:

Lemma 1. 

Define $\widehat{x}(p):=\frac{2\varphi }{\pi p}$ and $\tilde{x}(p):=\frac{\varphi }{\pi p}\left(1-\lambda +\sqrt{{(1-\lambda )}^2+2\pi \lambda pz/\varphi }\right)$. Then under delegation:

If $z<\widehat{x}(p)$ ($\iff z<\tilde{x}(p)<\widehat{x}(p)$), there is

• Centralization when $x\le z$;
• Favoritism when $z<x<\tilde{x}(p)$;
• Decentralization when $\tilde{x}(p)\le x$.

If $z\ge \widehat{x}(p)$ ($\iff z\ge \tilde{x}(p)\ge \widehat{x}(p)$), there is

• Centralization when $x\le z$;
• Decentralization when $z<x$.

The $PM$ trades off the free-riding/coordination problem present under decentralization against the competence of all parties to solve problems. For low x, this always favors centralization. For middling x, the improved competence of the subordinate merits their involvement, but not enough to give them free reign, so the $PM$ retains some control in order to ensure high effort/coordination, even though her relative incompetence implies that she has to compromise somewhat on the quality of problem solving. When subordinates are sufficiently more competent than $PM,$ it pays to decentralize, as problem solving is much better and incentive problems are mitigated.

Figure 1 illustrates. The cutoffs $\widehat{x}(p)$ and $\tilde{x}(p)$, both decreasing, are, respectively, the lowest value of x for which $a=1$, and the value of x for which expected revenues under favoritism and decentralization are equal. The firm supplies $\max \{z,y,\min \{\frac{\pi p{x}^2}{2\varphi },x\}\}$ to the market ex-post; with problems drawn independently across firms, the competitive industry supply is

$$S(p)=\mathbb{E}\max \{z,y,\min \{\frac{\pi p{x}^2}{2\varphi },x\}\},$$

non-decreasing in p (in the case $z\ge \widehat{x}(p)$, this expression reduces to $S(p)=\mathbb{E}\max \{z,x\}.$ The same is true if $\lambda =0$, that is, the $PM$’s participation under favoritism does not dilute the efficacy of the problem solution at all, despite her relative incompetence).

The likelihood of centralization, favoritism, and decentralization in any firm and, by independence, the prevalence of them in the industry as a whole, are, respectively, $G(z)$, $\max \{G(\tilde{x}(p))-G(z),0\}$, and $\min \{1-G(\tilde{x}(p)),1-G(z)\}$. We are led immediately to the following conclusion about the effects of firm value on the internal structure of control.

Proposition 4. 

Under delegation,

(i) 

Centralization is independent of industry price p;

(ii) 

Favoritism is non-increasing in p;

(iii) 

Decentralization is non-decreasing in p.

The terms of the $PM$’s trade-off between coordination and competence are affected by the price in a manner similar to that of integration, except that now it is the $PM$, rather than E and S, who are designing the control structure. At low prices, the incentive problems of decentralization are most severe and the $PM$ will cede complete control only under exceptional circumstances (high x), if at all. As price increases, decentralization’s incentive problems decrease for each x, increasing the range of x over which its superior use of subordinate competence outweighs the incentive costs, resulting in less favoritism. For high enough p, decentralization’s costs vanish, and with that, favoritism.

There is evidence of a lower presence of decentralization in poor countries than in the wealthier ones (Bloom & Van Reenen, 2006). This model offers a simple explanation: poor countries have lower firm values (p) than rich ones. We are not aware of evidence on the extent of within-firm favoritism, but, again, the model would suggest that this should be more prevalent in poorer countries, for the same low-firm-value reason: favoritism is not personal, it is strictly business (Coppola, 1972), the rational choice of a profit-maximizing professional manager balancing the incentives and competence of her subordinates in a low-value environment.

4.2. Efficient Control

If we consider, instead, efficient control allocations (under the supposition that control could be assigned through a contract, either contingently or through negotiation once the problem is revealed), then the relevant quantities to compare include the private costs: $pz-\varphi /2$ under centralization, $py-\varphi$ under favoritism, and $\frac{3p^2{x}^2}{8\varphi }{\mathbb{I}}_{\{px\le 2\varphi \}}(x)+(px-\frac{\varphi }{2}){\mathbb{I}}_{\{px>2\varphi \}}(x)$, under decentralization (if the parties can renegotiate control, they might as well renegotiate profit shares under decentralization to $\pi =1$, making compensating side payments to the $PM$, as this maximizes total surplus by creating the strongest possible incentives for E and S). Due to its high private costs, favoritism never occurs: for $x\ge z$, $x\ge y,$ so $px-\frac{\varphi }{2}>py-\varphi ,$ and $\frac{3p^2{x}^2}{8\varphi }\ge \frac{3p^2{y}^2}{8\varphi }>py-\varphi$, so decentralization dominates; for $x<z$, $y<z$, so $py-\varphi <pz-\frac{\varphi }{2}$), and centralization is preferred.23

Meanwhile, efficient decentralization is also responsive to price, but in contrast to delegated decentralization, non-monotonically: decentralization occurs whenever $x>x^{*}(p):=\sqrt{\frac{8\varphi (zp-\varphi /2)}{3p^2}}$ (assuming $zp-\frac{\varphi }{2}>0$, which is necessary for integration to occur at all). This expression decreases with p, so decentralization is more likely if, and only if, $p>\varphi /z$. The non-monotonicity in price response in this case parallels the one for integration in Section 3.1. At low prices, decentralization is low cost but also low productivity, and increasing price favors centralization because its considerable productivity advantage becomes all the more salient when output value increases; at higher prices, decentralization’s productivity catches up enough to centralization’s that further increases in price benefit decentralization more because its productivity is increasing, while centralization’s is constant.

Along with the presence/absence of favoritism, the contrast between monotonic decentralization in the delegation case and the non-monotonic response here could offer another possible way to distinguish delegation from efficient control allocation.

4.3. Productivity of Different Internal Control Structures

For IO, a principal reason to be concerned with organizational design is its implications for productivity (i.e., average net output per production unit, which often does not take into account private costs). In this regard, as has been argued elsewhere (Alfaro et al., 2024), one of the main benefits of integrating is the option value that accrues to the new owner: she has flexibility to redeploy control to those who can most benefit her when using it (of course, in the case of favoritism, this may be a disadvantage to the enterprise as a whole, as small productivity advantages may result in large and inefficient reallocations of private cost burdens). Thus, integration may have additional productivity benefits beyond those cited in Section 3.1.

Moreover, it has often been contended that among integrated firms, those that are more decentralized may also be more productive. Our analysis here should suggest interpreting this pattern with caution, as the measured effect could be a result of selection. Specifically, the average output per enterprise under centralization, favoritism, and decentralization are $z{a}_C=z$, $y{a}_F=y$, and $x{a}_D=x\min \{\frac{\pi px}{2\varphi },1\}$. According to Lemma 1, favoritism occurs only when the realized $x$, and therefore y, exceed z, so it is more productive than centralization whenever it is chosen (thus providing an ostensible justification for favoritism, despite the high costs it imposes on the unfavored). Whenever there is decentralization, the realized x must exceed any that would induce favoritism or centralization. This implies that output is also higher than any generated by equilibrium favoritism or centralization: from the definition of $\tilde{x}(p),$ which is weakly larger than any favoritism output y, $x\min \{\frac{\pi px}{2\varphi },1\}\ge \tilde{x}(p),$ whenever $x\ge \tilde{x}(p)$ (if there is no favoritism, then decentralization’s output x exceeds centralization’s by the second part of the lemma).24 Yet by revealed preference, as the $PM$’s objective differs from output only by the factor p, if a centralized or partially decentralized firm were forced to decentralize, then productivity would fall.25

4.4. Delegation and the Diffusion of Productivity Shocks

The value principle applies not only to price and similar notions of value, but also to (total factor) productivity. If, instead of producing a unit of output worth p, the enterprise produces R units worth $Rp$, the analysis proceeds straightforwardly with $Rp$ in place of p: the larger the R, the more likely the firm is decentralized, just as it is with higher p. If firms are heterogeneous in their R’s, then for a fixed demand, a higher industry productivity (average R) would tend to drive down the competitive price p, and we are led to the following.

Proposition 5. 

A firm’s degree of decentralization is increasing in own productivity and decreasing in industry average productivity.

Propositions 4 and 5 may help illuminate the famous “IT productivity paradox” of the 1980s and 1990s, in which one could “see the computer age everywhere, except in the productivity statistics” (Solow, 1987). We shall keep the discussion somewhat informal. Several writers have suggested that this phenomenon may have at least partly organizational origins. For instance, Bresnahan et al. (2002) shows that firms with higher productivity growth from IT investment were more decentralized, and Brynjolfsson (1993) suggests that low-growth firms were “mismanaged”. This cross-sectional nature of the evidence suggests a heterogeneous firm framework, which may be useful for studying propagation more generally.

Consider a competitive industry in which firms are (exogenously) heterogeneous in their ability to extract the benefits of a new technology (such as IT), or at least in their ability to learn how to do so. Before introduction, all successful firms produced one unit and the equilibrium price was p. Now, a fraction $\alpha$ can produce $\overline{R}$ with the new technology, while the rest produce $\underline{R}$, where $1^{+}\approx \underline{R}<\overline{R}$. Think of the cost of adoption as small, so that all firms adopt. Average productivity is increasing in $\alpha$.26

After adoption, if the demand function is fixed, the price must fall, as average productivity at the original price has increased. But the response of the two performance classes of firms could be very different. If the price falls to $p^{\prime }$ such that $\underline{R}{p}^{\prime }<p$, with $\widehat{x}(\underline{R}{p}^{\prime })>z$, then the low-performing firms will decentralize less, resorting to favoritism more, as $\tilde{x}(\underline{R}{p}^{\prime })>\tilde{x}(p)$, which could certainly be interpreted as a form of mismanagement. They may even produce less than before the shock. Meanwhile, as $\overline{R}{p}^{\prime }>p$ (otherwise the price could not have fallen), the high-performing firms will be at least as decentralized as before, and more decentralized than the low performers, and will see their productivity rise. The aggregate effects would be to increase overall production, as the price fell, but could be considerably dampened by the induced reorganizations of the low performers, and considered disappointing compared to what would be expected of homogeneous firms.

In this scenario, the low performers decentralize less not because of (indeed, despite) their own technological shock, but because of the pecuniary externality transmitted from the high performers via the market price. The effect is to drive larger performance and decentralization wedges between the two types of firms than would be there if the internal control structure were exogenously fixed. Over time, as firms figure out how to harness new technology ($\alpha$ increases), the price falls further to $p^{″}$, possibly making high performers somewhat less productive than at the beginning (if $\widehat{x}(\overline{R}{p}^{″})>z$), and the now smaller number of laggards even less so. This likely would make correlations such as those found in Bresnahan et al. (2002) less pronounced at the end of the diffusion than at the beginning.

Importantly for management policy, this application of the value principle tells us that less decentralization among low performers may be a symptom, not a cause, of low ability to use the new technology.

5. Discussion

In this paper, we have applied the value principle to study three distinct kinds of organizational design problems: (1) the use of professional management, along with its span of control, in competitive product and managerial markets; (2) horizontal integration to achieve market power; and (3) internal control structures via informal delegation of authority. In each case, product demand is a key driver of outcomes.

A recurrent theme that contrasts with much (but not all) earlier work is non-monotonicity in value of organizational design and practice. In a world of scarce management and competitive markets, the use and span of professional managerial control is an inverted U in the product price. This may lead to non-monotonic product supply, and we provide precise conditions under which it does. In the context of horizontal integration, firm size and the degree concentration are likely to jump from tiny to very large and then down again through more moderate levels, as consumer willingness-to-pay increases. With internal control structures, organizational performance (for its members) is non-monotonic in the degree of decentralization, with partial decentralization—or “favoritism”—likely to be the poorest performing, but also likely to disappear in high-value environments.

We have also discussed how these patterns are likely to manifest themselves in poor- and high-income countries, by taking the view that in the first order, widespread poverty leads to low demand and therefore low market value. The relatively large fraction of tiny, low-performance firms in poor countries and the so-called missing middle in the size distribution turn out to be fairly easy consequences of the value principle. It also has implications, which to our knowledge have not (yet) been investigated empirically, about differences in the internal control structure of firms in poor and rich countries, with favoritism likely to be more prevalent in the former, not because of some inherent cultural flaw, but as a rational outcome of the trade-off between coordination losses and gains from specialization in low-value environments.

In Section 3.1, we treated managers as a scarce, fixed resource. Of course, management is an occupation that can be entered at some cost. In a low-price environment (poor country), there will be little payoff to being a manager, and, consequently, little entry into management, exacerbating the scarcity problem. In earlier work Legros and Newman (2013), we have shown that this state of affairs may be inefficient: society would benefit from more professionally managed firms than the equilibrium number.27 A possible policy remedy is to subsidize managerial training, though that is not unproblematic.

In fact, the authors of Bloom et al. (2013) implemented a version of such subsidies in a randomized control trial of management interventions. They report that at baseline, firms made very little use of good practices, particularly in comparison with similar firms in richer countries, but that take-up was high once free training was provided, with concomitant increases in productivity. A follow-up paper Bloom et al. (2020) reports that treated firms had partially backslid on good practices, though some had spread throughout multi-plant firms.

These findings are readily reconciled with the aid of the value principle. Investment in hiring and costly training mangers does not pay off if the returns in terms of value, rather than quantity, are low. But once acquired at low cost, it may be relatively easy to convey to the rest of the firm. However, management practices are likely to have significant pecuniary and private marginal costs in addition to the fixed costs of hiring and training; with low product value, these are not worth incurring either, and the observed backsliding is a rational consequence.