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Are Workers' Enterprises entry policies conventional? Gianpaolo Rossini University of Bologna Michele Moretto University of Padova EARIE Annual Conference, Valencia 6-9 September 2007. Introduction.
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Are Workers' Enterprises entry policies conventional?Gianpaolo RossiniUniversity of BolognaMichele MorettoUniversity of PadovaEARIE Annual Conference, Valencia 6-9 September 2007
Introduction • LMFs exist in most countries and industries (Craig and Pencavel, 1992, 1995; Moretto and Rossini, 2003). • LM banks in developed and emerging countries contribute to equity and financial stability (Hesse and Cihàk, 2007): market share of some 10%. • LMF close to (US Census) Nonemployer (Moretto and Rossini, 2007 - SEJ) and Partnership, popular among infant firms in high tech sectors
LMF vis à vis conventional profit maximizing firm (PMF) in perfect competition: short run (SR) differences, long run (LR) coincidence. • SR: supply reacts negatively to price; odd labour demand. Higher fixed costs -> larger membership. These reactions based on the assumption that, in the SR, LMF can change membership size decided at the foundation.
New theory of Workers' Enterprises (WE) (Sertel, 1987; 1991; 1993; Fehr and Sertel, 1993). • WEs similar to LMFs, but for membership: A) size chosen at entry, not varied in SR. B) competitive memberships market -> the number of members can change in SR. In both cases "perversities" of the LMF shy away.
LR: LMFs, WEs and profit maxim firms (PMFs) are indistinguishable. LR comparison between PMF and WE confined to static framework -> entry not modeled.
AIM OF THE PAPER • Model entry with uncertainty and irreversibility and test LR convergence of WE and PMF. • Provide an interpretation of persistence of WEs (Hesse and Cihàk, 2007) despite ongoing mantra of their imminent demise.
AN OPTION - LIKE SCENARIO In an option - like scenario, firms observe market demand and choose size and price, that triggers entry regardless of market structure (Leahy, 1993, Grenadier 2002).
With certainty in a dynamic setting trigger prices of WEs and PMFs are equal (Moretto and Rossini, 2005) if labour fixed after entry. • Labour (firm) specific -> firms reluctant to vary it. Rigidity makes PMF close to WE.
The textbook case • WE produces Q with L and SR technology Q(L), with Q(0)=0, Q′(L)>0, Q′′(L)<0 and L∈[L,LG]. • WE sets membership maximizing surplus per worker [value added (y(p;L)) minus market wage (w)]: y(p;L) – w = [(p Q(L) - I)/L] - w (1) where I is the sunk, p market price. SR FOC: p Q′(LWESR) = y (p;LWESR) (2) if y(p;L) – w > 0 labor of WE is smaller than PMF.
Long Run features Fresh firms enter at the Marshallian point: pWE = AC(LMES) ≡ (w LMES + I) / [Q(LMES)], (3) with AC(LMES) = LR average total cost evaluated at the MES. PM and WE behave the same way, i.e. LWELR = LPMLR. No rents.
WE's entry under uncertainty Assumptions 1. entry cost I, sunk, can be delayed. 3. Instantaneous SR surplus per worker is (1) if w is constant over time. 4. Infinitely elastic demand function: price driven by trendless stochastic differential equation: dpt = σ pt dBt with σ>0 and p₀=p, (4) where dBt is the Wiener increment. 5. The project funded by WE members 6. L held fixed after entry
Only if the p is high enough, WE enters. First, for any L, the individual option to enter is computed. Subsequently, candidate members of WE chose L maximizing their (option) value at entry and the investment timing (T): fWE(p;L) = max E₀[(y(pT;L) - w) e-ρT|p₀=p] (5) • Each employee waits up to T and invests when pt reaches an upper value pWE.
The member's value function, before investing, is: fWE(p;L) = [y(pWE;L) – w] (p/pWE)β (6) for p<pWE. The WE invests when the price exceeds the break-even threshold: pWE = [β/(β-1)]AC(L) (7) the (deterministic) Marshall trigger AC(L) multiplied by β/(β-1)>1, due to irreversible entry.
Entry size of WE comes from equating the value marginal product [decreasing by concavity of the technology] to the "supplemented wage" > w: pWE Q′(LWESR) = w + fWE(LWESR)> w (8) where fWE(LWESR)≡ [1/(β-1)] [w + (I/LWESR)].
Long Run equilibria LR: option value to wait is zero (i.e. fwE= 0). However, by the infinite elasticity of demand, the optimal entry trigger (7) is not altered (Leahy, 1993, Dixit and Pindyck, 1994, Grenadier, 2002). All firms are alike and demand is infinitely elastic. Each member maximizes her option to enter. By doing that she chooses the optimal dimension of the industry as a whole: LWELR is the size of a industry WE.
Proposition a) LR competition makes WE larger than in the SR, i.e.: LWESR < LMES < LWELR b) trigger prices react in distinct ways in the LR vis à vis the SR, i.e.: ((∂pWESR)/(∂L))>0 ((∂pWELR)/(∂L))<0.
SUM UP The myopic WE enters with a size lower than LMES The farsighted (rationality: anticipating effects of LR entry) WE adopts a size > LMES. WE SR and LR triggers react in opposite ways to dimension.
With free entry firms exercise their option sooner since the potential entry of rivals reduces the value of waiting. In LR the WE chooses size equating the value marginal product to w as PMF.
A LR coincidence between WE and PMF emerges. The coincident entry of WE and PMF facing after entry labour rigidities explains persistence of WE in industries where human capital specificities make labour flexibility costly.
