Strike Strategies and the Minimum Effective Union SCOTT M. FUESS, JR.* University o f Nebraska, Lincoln, N E 68588 Research has shown that in an industry-wide strike, a union must be able to reduce output "'by a substantial percentage below competitive levels" to impose hardship on producers. But a union may also be effective by pursuing selective strikes. I f some producers are struck while others are free to operate, then the targeted producers may bargain with the union, and holdouts can be targeted for strikes. This article analyzes the effects of selective and general strikes on both a competitive industry and a duopoly, l f there are side-payments among producers, then general strikes are easier to mount. If there is no mutual aid among employers, then selective strikes are less costly to implement. It is also shown that strikes are easier to mount in a duopoly than in a competitive industry. This may contribute to union formation and collective bargaining in noncompetitive industries. The analysis is modified to allow for firms of different sizes. The results show that unions must be able to remove more output from larger firms than smaller ones, suggesting that union formation may be focused more on larger firms. I.
Introduction and Review
In both labor economics and labor relations, much attention has been focused on the effects of strikes. Many studies have been developed in a framework where unions can impose costs on employers through strikes, so it is in the interest of producers to bargain rather than to have output removed from production. ~The existence of a union, however, does not imply that bargaining takes place. In fact, a strike may not remove all output from production and may not lead a group of employers to bargain. Some producers have remained in operation during strikes; others have stockpiled inventories to reduce supply disruptions; and some have shifted production to nonunion workers. ~ In a recent study, Carter, Hueth, Mamer, and Schmitz (1987; hereinafter, CHMS) found that if a union strikes all producers in an industry but fails to drive *The author thanks Mark Loewenstein, James Fain, and Campbell McConnell for thoughtful comments and suggestions. The author gratefully acknowledges a research grant from the College of Business Administration of the University of Nebraska. 1 am responsible for any remaining shortcomings. JOURNALOF LABORRESEARCH Volume X1, Number 1
Winter 1990
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output to zero, then a strike might not reduce producers' profits; the effect of a higher output price may outweigh the reduction in output. A strike might move the industry away from the competitive equilibrium and closer to the joint-profitmaximizing level of output, thus making it difficult to induce producers to bargain. Similarly, Thompson (1980) and Maloney et al. (1979) have argued that strikes might restrict output and result in cartel-type profits. CHMS defined a minimum effective union (MEU) as one that has the ability, by striking, to impose economic hardship on a producer or industry. To be effective, a union must be able to remove enough output to reduce producer profits below the pre-strike level. For an industry of identical, price-taking producers, CHMS demonstrated that if all producers in the industry are struck, then to be effective the union must be able to reduce output "by a substantial percentage below competitive levels" (19. 122) - - in fact, a substantial percentage below the joint-profit-maximizing level. Using data from the California lettuce industry, CHMS reported that producer rents actually rose as a result of a 1979 strike. 3 In determining the minimum output removal necessary to induce bargaining with a union, CHMS focused on one type of strike: a general strike against all producers in an industry. In their analysis, all producers are equally affected by the strike. But a union may be able to impose economic hardship on producers by pursuing an alternative policy: "selective strikes." If a union strikes only a group of selected producers, then the targeted firms will face a reduction in output supply, possibly losing sales and profits, while the remaining competitors will be free to operate, possibly increasing profits. Struck producers may thus have an incentive to break ranks with the other firms and to bargain with the union. Once the selected producers agree to bargain, the union can then target the holdout employers for strikes. Thus, the union may achieve industry-wide bargaining by confronting employers one at a time.' Selective strikes - - also referred to as "whipshaw" strikes - - have been undertaken by unions in construction (Mills, 1980), airlines (Kahn, 1980), tires (Hirsch, 1969; Karper, 1987), and trucking (Livernash, 1963). 5 In 1983, the United Mine Workers departed from their traditional policy of industry-wide strikes - - "No contract, no work" - - and adopted a selective strike strategy to try to forge settlements with coal mine operators. ~ Among the targeted producers was Consolidation Coal Company, one of the largest firms in the industry. In the agricultural machinery industry, the United Auto Workers have selected a target company in collective bargaining rounds. Seeber (1987) described how strikes have often spread beyond the targeted companies; in fact, in 1979, there were strikes at each of the three major agricultural machinery producers. Unions have pursued different strategies in their efforts to bargain with employers and some unions have switched from (to) general strikes to (from) selective strikes, suggesting a trade-off in the respective tactics. This article extends the analysis of a minimum effective union by focusing on the effectiveness of selective strikes in imposing economic hardship on a group of producers and by com-
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paring the effects of selective strikes to those of a general strike. A simple model of a competitive industry is used to identify the conditions necessary for effective selective strikes and to show how such strikes can have asymmetric effects on producers. The conditions for an MEU under selective strikes are then compared to those for a general strike. Conditions are identified under which selective strikes are easier for a union to implement; that is, they require a smaller initial reduction in output than a general strike does. The MEU concept has only been studied in the context of an industry of price-taking producers. Unions also implement strikes in noncompetitive settings, where firms' actions are interdependent. Therefore, this study examines conditions for minimally effective strikes in a noncompetitive industry, specifically, a duopoly. 7 Section III shows conditions under which effective selective strikes are easier to implement than a general strike. To see how market structure changes the effectiveness o f different types of strikes, the duopoly results are compared with those for the competitive industry. It is shown that the MEU conditions are easier to meet in a duopoly than in a competitive industry. The UMW's selection of a large producer for a strike suggests that employer size may be a determinant of a selective strike's effectiveness. Section IV further 'extends the MEU concept by modifying the respective market models to allow for producers with different costs and, thus, different levels of output. It is also shown how an MEU is influenced by differences in producer size. II.
Strikes a n d the M i n i m u m E f f e c t i v e Union in a C o m p e t i t i v e Industry
Industry Equilibrium. Consider an industry of price-taking producers of a homogeneous good who have access to the same cost function. Suppose that producers in the industry can be grouped into two sectors and that firms and workers are aware of each producer's sector. Let F d e n o t e fixed cost, and let Qi represent the output of sector i. Following CHMS, suppose that there is a quadratic total cost function: C, -- aQ, + bQ~ + F, where C, denotes sector i's total cost and a, b, and F > 0. Let P denote the price of industry output, which is taken by each sector to be exogenous. Output is chosen in each sector in order to maximize profit, 7r,: 7r, = PQ, - aQ, - bQ 2, - F ; i =
1,2.
(1)
Assuming a linear inverse demand function for industry output, the price of output satisfies: P = a - /~(Q, + Q2); or, B > O.
(2)
Each sector's profit-maximization problem can be solved to yield the respective optimal output quantities, Qio. Letting Q* denote the output quantities associated with joint-profit maximization, it is straightforward to find:
Q,c = (or - a)/2(/~ + b) > Q* = (a - a)/2(2/~ + b); i = 1, 2.
(3)
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Let 7rlcrepresent sector profits at the optimal output quantities, and let rr* represent the sector profits associated with joint-profit maximization. Inserting the output quantities from (3) into (1) yields r,c = b(ot - a)2/4(/~ + b) 2 - F < 7r* = (or - a)2/4(2~ + b) - F ; i = 1, 2,
(4)
where it is assumed that 7r,.c_ 0. A G e n e r a l S t r i k e a n d t h e M i n i m u m E f f e c t i v e Union. Suppose that workers in the industry form a union and want to bargain with the producers. As CHMS discussed, to be effective the union must be able to remove enough output to impose hardship on the employers) Because 7r,o < ~'*, the union must be able to reduce each producer's output to Q,~,', satisfying 7tic (QS,~) = (~ - a - f3Q::)Qf$ - (:3 + b)(Q~,~)2 - F = rc~c;i :/: j.
(5)
Because producers are identical, Q, = Q2. Equation (5) can be solved using the quadratic formula to obtain the respective breakeven outputs: Q~,," = b(ot - a ) / 2 ( ~ + b)(2/~ + b); i = 1, 2,
(6)
which is the result o f CHMS. 9 For a general strike to be effective, it is necessary for the union to be able to reach the breakeven outputs in each sector. ,0 In the case o f the competitive industry, an MEU requires 2~(oL - a)/([3 + b)(2/3 + b) units o f output to be removed. The proportion of industry output removed under a general strike, ~', is thus ~" = 2/3/(2~ + b).
(7)
The breakeven output in each sector falls as/~ increases; the more inelastic the demand for output, the greater is the proportion o f industry output that must be removed initially. The breakeven outputs may rise or fall with b, as marginal cost becomes steeper, but ~s falls; the more inelastic the supply of output, the smaller is the proportion of industry output to be removed initially. Selective S t r i k e s a n d t h e M i n i m u m E f f e c t i v e Union. Instead o f a general strike of all producers, suppose that the union targets one sector of employers for a strike while the other sector remains in operation. Specifically, suppose that the union selects Sector 2 for a strike while the price-taking producers in Sector 1 remain free to adjust production optimally. From the point of view of Sector 2, the strike threatens a reduction in output and profit. From the point of view o f Sector 1, the strike may lead to a higher price for output and thus to increased production and profit. Consequently, there may be room for cooperation and mutual aid among the producers. If Sector 1 profits from the strike, then there may be a side-payment to Sector 2 that will keep it from bargaining with the union.
Mutual aid plans among competing producers - - to offset strike losses - i.e., profit pooling arrangements, are permissible (although they are restricted in the airline industry). 11Among the industries in which mutual aid plans have been implemented are airlines (Kahn, 1980, pp. 354-58) and tires (Karper, 1987, p. 96).
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Hirsch (1969) has described strike insurance plans in the rubber, rail, newspaper, and agricultural industries. Thompson (1980, p. 642) argued that mutual aid may also take the form of employers willing to "take turns" as strike targets. One group of employers may willingly endure a strike and not bargain with the union in exchange for a promise by other employers to endure a strike in the future. Selective Strikes in the Presence o f Producer Cooperation. Suppose that mutual aid among the competing sectors is possible. To be effective in Sector 2, the union must be able not only to reduce output to impose hardship on that sector, but also to keep industry profit from increasing. It is necessary to keep industry profit from rising in order to prevent a side-payment from Sector 1 to Sector 2, which keeps the targeted sector from bargaining with the union. Let Q~c denote the Sector 2 output under the selective strike. Allowing Q1 to adjust optimally, industry profit, ~sc, can be expressed in terms of Q1~c. It is straightforward to find that the value of Sector 2 ouput that maximizes industry profit, Q~sc,, is Q~gc. = b(ct-a)/(/32 + 4/3b + 2b2).
(8)
At the competitive equilibrium, a reduction in Sector 2 output increases industry profit: at Q2o > Q£~*, O~sc/OQ~~ < O. To be effective, the union must be able to reduce Sector 2 output far enough so that ~so(Q~) = re. Setting ~so(Qig,) equal to 7toand using the quadratic formula to solve for Q~" yields Q ~ = (2b 2 - /32)(ot - a)/2(/3 + b)(/32 + 4~b + 2b2).
(9)
If (2b ~ - /3~) > 0 or if b > (0.7071)/3, then there is a positive breakeven output associated with a selective strike of Sector 2. If the slope of marginal cost is sufficiently greater than the slope of industry demand, then an effective selective strike can be carried out. The intuition behind this result is clear. A reduction in Sector 2 output that is below the competitive level leads to an increase in the price of industry output; Sector 1 responds by increasing output and profit. To reduce Sector 2 output and keep industry profit from rising, the marginal cost must be sufficiently steep to keep the increase in Sector l's profit from outweighing the reduction in Sector 2's profit. For an effective selective strike, output supply must be sufficiently more inelastic than output demand. To induce Sector 2 to bargain, the union must reach Q£c, requiring the removal of/3(/3 + 2b)(a - a)/(/3 + b)(/32 + 4/3b + 2b 2) units. To achieve industry-wide bargaining, the union must not only be able to carry out a strike of Sector 2, but also a strike of Sector 1. Thus, for effective strikes in the industry, the union must be able to remove 2/3(/3 + 2b)(o~ - a)/(/3 + b)(/32 + 4/3b + 2b 2) units of output from production. Expressed as a proportion of industry output, ~'~: 0~~ = 2/3(/3 + 2b)/(/3 2 + 4/3b + 2b2).
(10)
Comparing the MEU conditions for selective strikes with those for a general strike, it can be readily verified that ~'~ > ~': effective selective strikes require
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the removal of a greater proportion of industry output (and thus more output) than a general strike does. Because Sector I expands output and profit as Sector 2 is struck, Sector 2 output must be reduced below Q~. Consequently, a selective strike policy requires the union to be able to remove a greater proportion of industry output than a general strike policy does. If the cost to the union of implementing strikes is positively related to output removed and if there is mutual aid among producers, then an effective general strike will be less costly to implement than effective selective strikes. Selective Strikes in the Absence o f Producer Cooperation. Although cooperation among producers in resisting a union is possible, it is by no means automatic. Airlines are statutorily restricted in their ability to form mutual aid pacts. Mills (1980, pp. 71-72, 75-76) described how internal dissension among competing rivals often prevents successful producer cooperation in resisting selective strikes. Further, both Bloom and Northrup (1981, p. 179) and Begin and Beal (1985, p. 222) observed that although cooperation is permissible, relatively few mutual aid pacts have been developed and those that have been implemented have not persisted. Employers have often broken ranks to bargain separately with unions. If mutual aid takes the form of employers taking turns in being struck, then those currently struck must believe that their rivals will follow through and willingly endure future strikes. In such a setting, it may be difficult to establish credible commitments. Even if commitments can be established, it is the unions that target employers for strikes. As a result, the same firms can be targeted over and over again.
Suppose that cooperation among competing sectors is not possible and Sector 2 is selected for a strike. To be effective, the union need only remove enough output to impose hardship on Sector 2. Let QTgc denote Sector 2 output under the selective strike. Allowing Q, to adjust optimally, Sector 2 profit, 7r~s"c, can be expressed in terms of Ql~"'. The value of Sector 2 output that maximizes Sector 2 profit, Ql~"~*, is Qg"'* = (~ - a)/(3/3 + 2b).
(11)
At the competitive equilibrium, a reduction in Sector 2 output increases that sector's profit: at Q2~ > Qg"'*, 07rl',"c/OQ~"c < O. The union must be able to reduce Sector 2 output far enough so that a~"c(Q~"c) = 7r2c. Setting ~ " ' ( ~ " ' ) equal to 7ru and using the quadratic formula yields ~ ' " = (13 + 2b)(a - a)/2(/3 + b)(3/3 + 2b).
(12)
At QT~"',Sector 1 profits are higher. Notice that QT~"~ > Q~; that is, a selective strike of Sector 2 requires a smaller output reduction than a general strike. For a minimally effective union industrywide, selective strikes require a smaller output reduction than a general strike. The proportion of industry output removed, ~"~, is ~"~ = 2/3/(3/3 + 2b) < ~s.
(13)
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Because there are no side-payments among the producers, the union need only remove enough output in a sector to reach the pre-strike profit level in that sector, without considering the impact of the strike on the profitability of the other sector. Because o f this, selective strikes are less costly to impose than general strikes are. As in the case of a general strike, the proportion of industry output to be removed for an effective selective strike increases the steeper the demand is and decreases the steeper marginal cost is. The analysis indicates that the ability of price-taking producers to cooperate in resisting a union is crucial in determining the effectiveness of different types of strikes. If side-payments among producers are possible, then selective strikes require a greater proportion of industry output to be removed than a general strike does. One might thus expect a union to pursue industry-wide strikes and bargaining in industries where effective cooperation among producers is possible. On the other hand, if there is no cooperation among producers, then selective strikes require a smaller proportion o f industry output to be removed than a general strike. In such a setting, selective strikes and individual bargaining can be expected to be observed.
III.
Strikes and the M i n i m u m Effective Union in a D u o p o l y
Industry Equilibrium. Because unions seek bargaining agreements in noncompetitive as well as competitive industries, it is interesting to see how market structure affects the MEU conditions. Suppose the two sectors of the industry represent duopolistic producers and their behavior generates the familiar Cournot-Nash equilibrium. Each sector's profit-maximization problem can be solved to yield the respective optimal output quantities, Q,d,o. It is straightforward to find: Q,d.o = (~ - a)/(3/3 + 2b) > Q*;i = 1, 2.
(14)
Letting a'ia.o represent sector profits at the optimal output quantities, then rr,d.o = (/3 + b)(o~ - a)2/(3/3 + 2b) 2 - F < 7r*; i = 1, 2.
(15)
A General Strike and the Minimum Effective Union. For a successful general strike in a Cournot-Nash duopoly, a union must be able to reduce output to the breakeven levels, Q~,~.o, satisfying 7rld.o(Q~.o) = 7r,duo.Because firms are identical and Q1 = Q~, it is straightforward to find: Q~,~,o = (/3 + b)(ot - a)/(2/3 + b)(3/3 + 2b).
(16)
The proportion of industry output to be removed from the duopolists, 0~g,o,is thus 0e~,. = /3/(2/3 + b).
(17)
Comparing the MEU condition for a general strike in Cournot-Nash duopoly with that for a competitive industry, it can be seen that 0~2,o< ~s; the proportion of industry output that a union must be able to remove is less in the duopoly than in a competitive industry. Because duopolists produce closer to the joint-profit maximizing output than price-taking producers, the reduction in output necessary to impose hardship on the duopolists is smaller than in a competitive industry.
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Selective Strikes a n d the M i n i m u m Effective Union. Suppose that mutual aid among the duopolists is possible and the union selects Producer 2 for a strike. Let Q~o denote Producer 2 output under the selective strike. Allowing Q1 to adjust optimally, industry profit, x~d~,can be written in terms of Q~2~o.The value of Producer 2 output that maximizes industry profit is less than Q~,~o, and O ~ o / a Q ' ~ o < 0 at the Cournot-Nash equilibrium.
The union must be able to remove enough output to keep industry profits from rising. The level of output satisfying r'~'o(Qi'2~uo) = 7r~o is Q~2~o = (4b z + 4/3b - /32)(a - a)/(3/3 + 2b)(/32 + 8/3b + 4b2).
(18)
If (4b 2 + 4/3b - /32) > 0 or if b > (0.2071)/3, then there is a positive breakeven output associated with a selective strike of Producer 2. In a duopoly, a reduction in Sector 2 output leads to a smaller increase in Sector 1 output than would occur in a competitive industry. Because of this, marginal cost need not be as steep for an effective selective strike. To achieve bargaining with Firm 2, the union must be able to remove 2/3(fl 42b)(ot - a)/(3/3 + 2b)(/32 + 8/3b + 4b 2) units of output from Firm 2's production. Thus, for minimally effective selective strikes in the duopoly, the union must be able to remove a proportion of industry output, ~ o , equal to ~ o = 2/3(/3 + 2b)/(/32 + 8/3b + 4b~).
(19)
It can be readily verified that 07~o > O~o. As in the case of a competitive industry, if in a duopoly it is possible for producers to cooperate in resisting a union, then selective strikes require the removal of a greater proportion of industry output (and also more output) than a general strike does. Suppose that mutual aid among the duopolists is not possible. In that case, the union needs only to be able to reduce output to impose hardship on Firm 2. Allowing Q~ to adjust optimally, Producer 2 profit, ~ , can be expressed in terms of Q2: ~o
= [(ct - a)(/3 + 2b)Q2 - (/32 + 4/3b + 2b~)Q~]/2(/3 + b) - F. (20)
At Producer 2's original output, Q2a~o,it can be verified that 0 7 ¢ ~ / a Q 2 > 0: any reduction in Producer 2's output, allowing Producer 1 to adjust its output optimally, reduces Producer 2's p r o f i t . Because there are no side-payments among the duopolists, the union only needs to remove enough output to impose hardship on Producer 2. Because Producer 1 adjusts its output optimally and explicitly takes into account the effect of its own production on the price of output, the induced increase in the price of output is not enough to keep Producer 2's profit from falling. If there are no side-payments, any output that the union can remove from a targeted producer will be effective. Hence, as in the noncooperative, competitive industry, effective selective strikes require a smaller proportion of industry output to be removed than a general strike does. And as in the case of a competitive
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industry, the MEU conditions for strikes in a duopoly depend crucially on the ability of producers to cooperate in resisting the union.
The Minimum Effective Union: Duopoly Versus Competition. The analysis indicates that effective strikes require the removal of less output from a Cournot-Nash duopoly than a competitive industry, suggesting that it is easier to mount strikes in a noncompetitive setting. This may be seen as an amendment to past analyses of union formation. Although others have argued that noncompetitive industries may be conducive to collective bargaining because the costs and consequences of wage concessions to unionized workers may be less than in a competitive industry, this study predicts that it is easier for a union to be effective - - that is, impose economic hardship - - in a duopoly than in a competitive industry. This may contribute to union formation and collective bargaining in noncompetitive industries. IV.
Strikes, the Minimum Effective Union, and Producer Size
The relative effectiveness of strikes hinges on the ability of producers to cooperate in resisting the union. So far, the analysis has only been carried out under the assumption of identical producers. As the UMW's selective strike policy illustrates, however, unions have taken into consideration employer size in targeting employers for strikes. To see how producer size may affect the MEU conditions, assume that producers' costs vary. To keep the analysis tractable, assume that the total cost in each sector is given by Ci = b,Q2, + F, where b~ = b and bl = 2b. Letting output demand remain as before, equilibrium for the competitive industry yields Q2~ = 2c~/(3/3 + 4b) = 2Qlc,
(21)
and Sector 2 profits are twice as large as Sector t profits. Suppose there is mutual aid in the industry. If the union strikes the large producers, then the union must be able to reach Q~c = 2ot(16b 2 _ 3/32)/(3/3 + 4b)(3/32 + 24/3b + 16b2).
(22)
If b > 0.4330)/3, then there is a positive breakeven output that the union must be able to reach in order to bargain with the large producers. If the union strikes the small producers, then the union must be able to reach Q~" = c¢(8b2 - 3/35)/(3/3 + 4b)(3/32 + 12/3b + 8b2).
(23)
If b > (0.6124)/3, then there is a positive output that the union must reach in order to induce bargaining with the small producers. Notice that the union must be able to remove more output (although a smaller percentage of output) from large producers than from small producers. Instead of selective strikes, the union could launch a strike against the industry. If the union implements a general strike such that Q~ = 2Q1, then the union
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must be able to reach Q~ = 4ba/(3~ + 4b)(3~ + 2b) = 2Q~',
(24)
to be effective. As was true for a competitive industry of identical producers, it is readily verifiable that selective strikes require a greater output reduction than an effective general strike does. In the general strike, more output is removed from large employers than from small employers. The same conclusions emerge for the case of duopoly: (1) if producers cooperate, then it is easier to impose an effective general strike than selective strikes, and (2) more output must be removed from the large firm than the small firm. Suppose that there are no side-payments among large and small producers. If the union implements selective strikes, then it must reach Q~.c = 2ot(/3 + 4b)/(5/3 + 4b)(3/3 + 4b), and
(25)
Q~.c = et(/3 + 2b)/2(/3 + b)(3/3 + 4b),
(26)
respectively. In the absence of cooperation, it is easily seen that selective strikes require a smaller output reduction than a general strike does. Once again, notice that more output must be removed from the large producers than the small producers. Similar results apply to a duopoly where there is no cooperation among producers. These examples suggest that for a union to be effective, organizing may be oriented more toward larger firms in an industry. V.
Conclusion
By striking, a minimum effective union (MEU) has sufficient power to reduce output and producer profits in an industry. CHMS showed for a competitive industry that if all producers are struck, then an MEU must reduce output "by a substantial percentage below competitive levels." But a union may be able to impose economic hardship on an industry and its producers by pursuing an alternative policy of "selective strikes." If only some producers in an industry are struck and the others are free to operate, then the targeted producers may have an incentive to bargain with the union. Thus, the union may be able to bargain with employers in the industry one at a time. This paper extends the analysis of the minimum effective union by analyzing the effects of selective and general strikes on both a competitive industry and a duopoly. Using simple models of industry equilibrium, conditions for minimally effective selective strikes were derived and compared to those for minimally effective general strikes. The ability of competing producers to cooperate in resisting the union is crucial in determining the effectiveness of strikes. If in a selective strike the sector that remains in operation is able to make side-payments to the struck sector, then an effective general strike requires the removal of a smaller proportion of industry output than a series of selective strikes does. If, on the other hand, side-payments are not available, then the opposite is true: effective selective strikes will require the removal of a smaller proportion of industry out-
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put than a general strike does. These conclusions hold for both competitive and duopolistic industries. The analysis was modified to consider an industry composed of producers of different sizes, but the basic results were unaffected. The analysis indicates that it is easier for a union to be effective in a duopoly than in a competitive industry. This suggests that union formation and collective bargaining are more likely to occur in noncompetitive industries. In an example where firm sizes were allowed to differ, it was shown that an effective union must be able to remove more output from large firms than from small firms. This suggests that union formation may be more concentrated among larger firms in an industry. The MEU conditions generated in this paper may shed light on observed bargaining/strike behavior. If producers can establish mutual aid, then industry-wide strikes and bargaining can be expected. If producers do not or cannot cooperate, then selective strikes are predicted. In construction, where cooperation among producers has been difficult to obtain, "no weapon is more effective for the unions than the selective s t r i k e . . . " (Mills 1980, p. 75). Perhaps it is not surprising to discover, as reported by Chamberlain and Kuhn (1986, p. 263), that building contractors have tried to obtain legislation preventing individual contractors from breaking ranks with other contractors and negotiating with unions. Manufacturers in the rubber industry have been targeted for selective strikes. In 1967, producers responded to the selective strike strategy by forming a mutual aid pact, whereupon a general strike of all (but one) producers ensued (Karper, 1987, pp. 95-96; Hirsch, 1969, p. 403); similarly, an industry-wide strike of all producers occurred in 1976. In the coal industry, the United Mine Workers have traditionally followed a general strike policy against mine operators. Over the 1968-1981 period, there were five general strikes against the Bituminous Coal Operators' Association (BCOA). By the early 1980's, however, 100 of 130 producers had left the BCOA. In 1983, before the 1984 bargaining round, the UMW switched to a policy of selective strikes. Specifically, the UMW targeted some of the largest producers in the industry for strikes. There were no widespread strikes in the coal industry in 1984, and the union was able to negotiate contracts covering 95 percent of its members. According to English (1984, pp. 85-86), by threatening holdout producers with selective strikes, the union was able to obtain contracts with producers who had left the BCOA. The observations here support the hypotheses of this study, although they do not represent systematic empirical evidence. To extend the analysis, work is currently being carried out on the effects of different types of strikes on the profitability of firms, specifically, the excess returns on firms' equity shares. The analysis may provide an extension to the study of collective bargaining problems. Because this study has focused on conditions necessary for bargaining to occur, it seems natural to investigate how an effective union will bargain with a group of employers. In other words, future research might explicitly study the
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bargaining games associated with the different types of strike strategies. Such analysis m i g h t reveal critical c o n d i t i o n s for m u l t i - e m p l o y e r versus f i r m - b y - f i r m bargaining.
NOTES ~Among the studies examining the bargaining between unions and employers are Ashenfelter and Johnson (1969), Warren-Boulton (1977), and Farber (1978). For a review of the literature on unions, bargaining, and strikes, see Hirsch and Addison (1986, Chapter 4) and Farber (1986). ~Livernash 0963) and Hendricks (1987) have offered examples where producers have been able-to remain in operation during strikes. Perry et al. (1982) discussed in detail the benefits and costs of attempting to remain in operation during a strike. Christenson 0953) and Miernyk (1980) presented examples of producers stockpiling coal to maintain the flow of sales. Cappelli (1987) noted that some airlines have tried to substitute nonunion workers for strikers. Koziara (1980) noted that producers in agriculture have used strikebreakers to avoid collective bargaining. 3CHMS assumed that the price of output adjusts to maintain output market equilibrium. If producers are not price-takers and bargain with customers over both price and output, then firms may have to ration their output quantities as they are struck; firms may not increase price and run the risk of driving away customers. If firms use quantity rationing, then their total revenue must fall. If total costs do not fall far enough, then firms are worse off as a result of the strike. Following CHMS, it is assumed in this paper that the price of output adjusts to allocate output in the market. 'Among those discussing selective strikes in their analyses of collective bargaining are Livernash (1963), Weber (1967), Ulman (1974, pp. 103-107), and Bloom and Northrup (1981, Chapter 4). ~Selective actions have been used by unions in other contexts. Katz (1987, p. 21) noted that the United Auto Workers threatened General Motors with a selective shutdown of unionized GM plants in the northern U.S. if the union continued to be unsuccessful in organizing nonunion GM plants in the south. Koziara (1980, pp. 274-76, 289-90) noted that the United Farm Workers have targeted certain producers for boycotts, trying to recuce the demand for those producers' goods. 6See Bureau of National Affairs (1984, pp. 193-98), English (1984), and Business Week (1984, pp. 70, 72). 'A duopoly setting appears to be especially useful in examining selective strikes. One might consider a noncompetitive industry with more than two producers; but because producers can be easily "aggregated" by summing marginal costs, they can be "redefined" so that there is a duopoly. 8As with CHMS, this paper focuses on conditions necessary for bargaining to take place between a union and a group of employers. Analysis of the various possible bargaining arrangements and outcomes is beyond the scope of this study. There is a substantial literature analyzing different bargaining arrangements and outcomes. Among recent bargaining models focusing on groups of employers and unionized workers are Davidson (1988) and Kovenock et ai. 0988). More general bargaining models are presented, reviewed, and cited in Roth (1985). 9CHMS observed that it is possible for a strike to increase production costs. This could be due to imperfect substitutability of nonunion workers or machinery and other equipment for unionized workers. For completeness, they solved for the MEU under the assumption that a strike causes a vertical upward shift in marginal cost. Not surprisingly, they found that a smaller reduction in output is necessary for an MEU. Because the conceptually important distinction in this paper is between the effects of selective strikes and a general strike per se, it is assumed that production costs do not change as a result of a strike. Given the analysis of CHMS, altering this assumption will alter the results in this paper in obvious ways and will not affect the conclusions about the different types of strikes.
S C O T T M. FUESS, JR.
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'°Rather than bargain, producers in the industry may respond to an effective strike by locking out the strikers and shutting down production. A lockout as a defensive measure against a strike may be legal, but there is uncertainty concerning what constitutes a permissible lockout (Bloom and Northrup, 1981, pp. 665-67). In the context of the model, a lockout/shutdown implies Q, = 0 and 7r, = - F < 0; i = 1,2. Producers incur a loss equal to the difference between total revenue and total variable costs, which is positive. Locked-out workers may be eligible for unemployment benefits or they may disperse and obtain employment elsewhere. Because striking workers have already foregone their wage earnings and to the extent that there exist alternative employment opportunities or unemeployment benefits, a lockout may not impose additional hardship on unionized workers. As a consequence, it is not surprising to discover that lockouts have occurred infrequently (Bloom and Northrup, 1981, p. 667; Begin and Beal, 1985, pp. 227,238). "For a discussion of mutual aid plans and the restrictions on the airline industry, see Bloom and Northrup (1981, pp. 178-79) and Begin and Beal (1985, p. 222).
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