Who Gain and Who Lose on International Outsourcing?

Transcription

1 CEBR Centre for Economic and Business Research Langelinie Allé 17 DK-2100 Copenhagen Ø Denmark Tlf: (+45) Fax: (+45) Homepage: Who Gain and Who Lose on International Outsourcing? Jan Rose Sørensen Discussion Paper No ISSN

2 June 2001 Who Gain and Who Lose on International Outsourcing? Jan Rose Sørensen Keywords: Outsourcing, labor market, welfare JEL classi cation: F12, J51 Abstract We analyze the implications of outsourcing in an economy where workers are organized in trade unions. We nd that the e ects on the wage rate, employment and welfare, of a decrease in the cost of outsourcing, depends on the initial level of the cost of outsourcing. However, one robust result is that at the level of the cost of outsourcing where a rm chooses to switch from no outsourcing to outsourcing of an activity, the rm becomes worse o and the trade union becomes better o. In a simple general equilibrium model, we nd that the welfare tends to increase when the cost of outsourcing decreases, except at the cost level where the representative rm switches from no outsourcing to outsourcing. University of Southern Denmark Odense, Denmark The main part of this paper was written while I was visiting University of California at Santa Cruz, and I gratefully acknowledge the support of the Department of Economics, UCSC. I have bene tted from comments by Mette Yde Skaksen, and seminar participants at UCSC, University of Aarhus, University of Southern Denmark, Odense, and by participants in Nordic International Trade Seminar, Copenhagen, May The work on this paper has been undertaken with nancial support from the Danish Social Science Research Council.

3 1 Introduction If you ask an economist whether outsourcing is good or bad, it is likely that she would answer that it is unambiguously welfare improving. The reason being that outsourcing implies that rms, and therefore the economy, get an activity done as cheap as possible. If you ask a layman the same question, it is likely that she would answer that outsourcing is bad as it gives rise to a loss of jobs. If all markets are perfectly competitive there is no doubt that the answer of the economist is the right one, but is it also the case under less favorable market conditions? In a lot of European countries, trade unions play an important role at the labor market, and under these circumstances can we still be sure that outsourcing improves welfare, or is it possible that the answer of the layman is the right one? In this paper, we show that, if trade unions have wage bargaining power, the e ects of outsourcing are ambiguous, and it is possible that outsourcing gives rise to an increase in the unemployment rate and a decrease in welfare. In recent years there has been a large number of analysis on whether international trade with low wage countries hurts (some) workers, especially unskilled workers. The root of this interest has been the increasing wage gap between skilled and unskilled workers in a number of countries, and not at least in the US. The conclusions in these analyses have been very diverged. For instance Leamer (1994) nds that increasing trade plays an important role in explaining the increasing wage gap, whereas, Krugman (2000) argues for the opposite. Feenstra and Hanson (1996,1999) nd that outsourcing has had some e ect on the wage gap. These analyses all focus on the relative wage between skilled and unskilled workers, and if labor markets are competitive, the relative wage is the right variable to consider. However, if labor markets are imperfectly competitive, it also becomes relevant to consider the wage level and the unemployment rate. This perspective may be relevant when considering European labor markets as economists tend to agree that European labor markets are characterized by rigidities and a lack of competition, at least partly due to the presence of trade unions. This view is supported by the fact that unemployment rates in most 1

4 European countries have been persistently high for several decades. With this in mind, the focus of the present paper is not on relative wages but on the wage level, unemployment and welfare in an economy which is characterized by an imperfectly competitive labor market. We start by considering a partial equilibrium model of a single domestic rm and a trade union. It is assumed that certain activities can either be done in the rm or they can be outsourced. An important ingredient in the model is that the wage rate is the outcome of negotiations between the trade union and the rm. Within the framework of this model, we analyze the implications of a decrease in the cost of outsourcing. It turns out that, depending on the initial level of the cost of outsourcing, a decrease in the cost may have quite di erent e ects on the economy. If the initial cost is su ciently high, a decrease in the cost has no implications on the economy. If the initial cost is at an intermediate level, and no outsourcing takes place, a decrease in the cost implies that the wage rate decreases, the trade union becomes worse of and the pro t increases. At the cost of outsourcing where the rm chooses to switch from no outsourcing to outsourcing, some surprising e ects arise. If the cost of outsourcing decreases below this level, there is a discontinuous upwards jump in the wage rate. The reason being that, at the intermediate level of the cost of outsourcing, the trade union has accepted a low wage in order to prevent the rm from outsourcing, but at this regime switching level of the cost of outsourcing, the trade union no longer accepts a wage which is su ciently low to prevent outsourcing. The trade union realizes that it cannot compete with the low cost of outsourcing, and there is a discontinuous upward jump in the wage rate. It is interesting to note that this jump implies that the rm becomes worse o and the trade union becomes better o. Hence, when the rm starts to outsource, we see a loss for the rm but a gain for the trade union. These results are found in a partial equilibrium model, but without assuming speci c functional forms of the production function and the pay o function of the trade union. In order to check the robustness of our results, and in order to analyze the implications of outsourcing on unemployment and net social welfare, we also consider a simple general equilibrium model of a small open economy. The cost of turning to a general equilibrium model is that we have to 2

5 assume speci c functional forms concerning the production function and the pay o function of the trade union. Within the framework of this simple general equilibrium model, we get similar results as in the partial equilibrium model. However, we also nd that if the cost of outsourcing decreases, there is in general a decrease in unemployment and an increase in net social welfare, except at the level of the cost of outsourcing where the representative rm switches from no outsourcing to outsourcing. At this level there is an upward jump in unemployment and a downward jump in welfare if the cost of outsourcing decreases. There are a number of papers which have analyzed the implications of decreasing trade costs when labor markets are imperfectly competitive (see e.g. Huizinga, 1993, Dri ll and Ploeg, 1995, and Naylor, 1998,1999), but all these papers look at trade in nal goods whereas outsourcing is trade in intermediate goods. Moreover, there are some ambiguities concerning the wage e ect of decreasing trade costs as some papers nd that it gives rise to decreasing wages (e.g. Huizinga, 1993 and Dri ll and Ploeg, 1995), while others nd that it gives rise to increasing wages (e.g. Naylor, 1998). With respect to welfare, the general conclusion is that, decreasing trade costs give rise to higher welfare. The paper most closely related to the present one is Naylor (1999). Similar to what we nd in our paper, Naylor (1999) nds that there is a discontinuous jump in the wage rate at the level of the trade cost where rms start to trade internationally. However, Naylor nds that there is a downward jump in the wage rate, whereas, we nd that the there is an upward jump. This di erence is partly due to the fact that Naylor considers trade in nal goods whereas we consider outsourcing. Moreover, Naylor nds that decreasing trade costs give rise to an unambiguous increase in welfare, whereas we nd that it depends on the initial level of the trade cost whether a decrease in trade costs increases or decreases welfare. The rest of the paper is organized as follows. In section 2, we consider the e ects of outsourcing in a partial equilibrium model where we do not assume speci c functional forms. In section 3, we analyze the implications of outsourcing in a simple general equilibrium model. Finally, we 3

6 conclude in section 4. 2 A partial equilibrium model 2.1 The model In this section, we set up a partial equilibrium model of a single rm and a single trade union. We assume that production in the rm consists of di erent activities, and in order to simplify the model, we assume that there are only two activities 1. An important assumption is that one of these activities must take place in the rm, but the other activity can be outsourced. The production function of the rm is assumed to be concave and given as 2 Q = F (N; H) ; F 1 (N; H) > 0; F 2 (N; H) > 0; F (0;H)=F (N; 0) = 0; (1) where N is the input of labor in the activity which must take place in the rm (from now on activity 1). H is the input of an intermediate good, and this input can either be produced in the rm, or it can be purchased abroad. The production in the rm of this intermediate good, we will term activity 2. The marginal productivities are assumed to be strictly positive, and both inputs are assumed to be essential in the sense that production is zero if either of the inputs is zero. The labor input in activity 2 is given as =H Z; (2) where Z is the amount of the intermediate good which is purchased abroad. We assume that this intermediate good and labor input in activity 2 are perfect substitutes. The unit cost of buying the intermediate good abroad is exogenously given as p. This cost covers production as well as 1 This way of splitting up the production process into di erent activities is similar to what is assumed in Skaksen and Sørensen (2001). 2 A subscript indicates that it is the derivative of the function. 4

7 transportation costs. We will assume that the production costs abroad are su ciently low that it would never be optimal for the domestic rm to export intermediate good 2. As the wage in the domestic rm always turns out to be above the competitive level (see below), one possibility for this to be the case is that foreign producers of this intermediate good face a competitive labor market. Total employment in the rm is now given as L = N +. It is assumed that it is the same kind of labor which is used in the two activities, and it is not possible to wage discriminate between the two activities. One reason for this could be that when both activities take place in the rm, it is not possible to control in which activity the rm uses a speci c worker. Therefore, if the wage was di erent in the two activities, the rm would, formally, only employ workers in the activity where the wage rate is lowest. The pro t of the rm is given as =Q wl pz; (3) where w is the wage rate. The price of the nal good is assumed (normalized) to be one. Maximizing the pro t gives rise to the following input demand functions. If w<p : N = N (w; w) ; N 1 (w; w) < 0; (4) = (w; w) ; 2 (w; w) < 0; (5) Z = 0: (6) If w>p: N = N (w; p) ; N 1 (w; p) < 0; (7) = 0; (8) 5

8 Z = Z (w; p) ; Z 2 (w; p) < 0; (9) where the rst variable in the input demand functions indicates the price of input in activity 1 (always labor), whereas, the second variable indicates the price of input in activity 2. The input demand functions are strictly decreasing in their own-price. Since labor and the foreign produced intermediate good are perfect substitutes in activity 2, the rm only uses the foreign produced good, if the price on this good is lower than the wage rate. We (arbitrarily) assume that if w = p, the rm chooses to employ domestic labor in activity 2. The pro t function may now be found to be = (w; v) ; v = min (w; p) : (10) Since the inputs in both activities will be strictly positive, the derivatives of the pro t function are strictly negative (i.e. 1 (w; v) < 0 and 2 (w; v) < 0). All potential workers in the rm are organized in a trade union which is assumed to have the following objective function: UT = UT (L; w) ; UT 2 (L; w) > 0; UT (0;w)=0;UT (L; 0) < 0: (11) The pay-o to the trade union is assumed to depend on employment as well as the wage rate, and it is assumed that the pay-o is strictly increasing in the wage rate (for a given employment). Moreover, the objective function has been normalized so that the pay-o is zero if employment is zero. As workers are assumed to get utility from leisure, the pay o to the trade union is non-positive if the wage rate is zero. We assume a right to manage model (see e.g. Nickell and Andrews, 1983) where the wage rate is determined in negotiations between the rm and the trade union. After the wage has been determined, the rm unilaterally determines employment. The outcome of the wage negotiations is assumed to be given by the Nash Bargaining Solution (see e.g. Binmore, Rubinstein and Wolinsky, 6

9 1986). The Nash Product is de ned as NP = UT s 1 s ; 0 <s<1; UT 0; 0; (12) where s may be interpreted as the bargaining power of the trade union. The bargaining parties are aware of how employment is determined after the wage rate is xed, and the outcome of the bargaining is given as bw = arg max NP: (13) We assume that bw is su ciently high that the labor supply is at least as high as labor demand 3. This is equivalent to assuming that workers prefer working to being unemployed, i.e. bw is higher than the marginal value of leisure. Since it seems most reasonably to assume that the pay-o to the trade union is increasing in the utility of the individual members, it follows that, evaluated at the equilibrium wage rate, the pay-o to the trade union is increasing in employment, i.e. 2.2 Implications of outsourcing UT1(L; bw) > 0: (14) Since the decision of outsourcing is determined endogenously by the rm, we will look at the implications of a change in the price of outsourcing (p) which is an exogenous variable. The qualitative implications of a change in the price of outsourcing may depend on the initial level of this price, and we de ne three possible regimes: Regime 1 (p p): The cost of outsourcing is su ciently high that potential outsourcing has no e ect on the wage bargaining. 3 This is the natural assumption to make since the purpose of trade unions in general is to bargain for higher wages than what would have been the outcome at a competitive market. 7

10 Regime 2 (p < p<p): The cost of outsourcing is at an intermediate level implying that there will be no outsourcing, but the potentials of outsourcing a ects the wage negotiations. Regime 3 (p <p): The cost of outsourcing is su ciently low that there is outsourcing and no employment in activity 2. Regime 1 is a regime in which the economy behaves as if there were no possibility for outsourcing. We will assume that under these circumstances, NP j regime1 is concave in w, and there is an interior solution to the maximization problem in (13). Moreover, in regime 3, the rm outsources activity 2, and given that this is the case, we will also assume that NP j regime3 is concave in w, and that there is an interior solution to (13). Since NP has an interior maximum in regime 1 and 3, it follows that 0 < bw <1 in these regimes. Therefore, if p!1, bw <p, and the economy is in regime 1. If p! 0, bw >p, and the economy is in regime 3. Hence, regime 1 and 3 always exist. Moreover, in this section, we assume that regime 2 also exists. In the appendix we analyze the case where only regime 1 and 3 exist, and it turns out that the results are very similar to what we nd in this section. In the following we use the notation that bw in regime i is equal to w ci. Ad. Regime 1: In this regime, the wage rate, w c1 ; and all other endogenous variables are independent of p. The lowest possible p which is consistent with w c1 being the outcome of the bargaining is p, and it is de ned as p = c w 1 : (15) In regime 1, the wage bargaining parties behave as if there were no possibilities for outsourcing, but this behavior is only possible as long as p cw 1. Moreover, since we assume that regime 2 8

11 exists, and there is no outsourcing in regime 2, it follows that the bargaining parties will choose cw 1 as long as p cw 1. This is so because w c1 is the wage giving rise to the unconstrained maximum of the Nash Product (NP) when there is no outsourcing, and the bargaining parties always seek to maximize NP. Ad. Regime 2: In this regime p<p, and the bargaining parties know that, if they want to prevent outsourcing, the wage rate must be lower than w c1 (= p). The reason why it may be optimal for the bargaining parties to prevent outsourcing, even though p<p, is that the trade union bene ts from a high employment level, and outsourcing implies that there will be no domestic employment in activity 2. As NP is concave in w, and with an interior maximum at w c1 as long as there is no outsourcing, it follows that the w maximizing NP; in this regime 2, is the w which is as close as possible to cw 1, but under the constraint that w< p. It follows that cw 2 = p: (16) If we turn to the implications of a change in the price of outsourcing, it follows immediately from (16) that w c2 is increasing in p. Therefore, even though there is no outsourcing, an increase in the cost of outsourcing a ects the economy through a higher wage rate. The implication for the pro t of an increase in p is given as d dp = 1 (p; p) + 2 (p; p) < 0: (17) Since the cost of inputs in both activities increases if p increases, it follows that the pro t decreases. With respect to the pay o to the trade union, it turns out that du T dp > 0: (18) 9

12 To prove this, we recall that, since c w 2 = p< c w 1, it follows that dnp dp > 0 4. Therefore, as NP is a geometric average of and UT,and is decreasing in p, it follows that UT is increasing in p. Finally, with respect to employment, we nd that dl < 0: (19) dp In this regime, the rm only uses one kind of input (domestic labor). When p increases, the price of this input increases (as w c2 = p), and the demand unambiguously decreases. To summarize, we nd that in this regime there is no outsourcing, but the potentials of outsourcing a ects the economy. In particular, a decrease in the cost of outsourcing implies that the trade union have to accept a lower wage rate in order to prevent the rm from using outsourcing. A lower wage rate implies higher employment and a higher pro t. Since the trade union has to accept a lower wage rate, it becomes worse o. Ad. Regime 3: First, we have to nd out, when the economy will be in regime 3 instead of regime 2. Since the bargaining parties seek to maximize NP, it follows that, for a given p, the wage rate is chosen to be either w c2 or w c3, depending on which wage rate gives rise to the highest NP. We assume that there exists a unique p satisfying the following condition NP j regime2;p=p= NP j regime3;p=p (20) If p p, w c2 (= p) is su ciently high that NP is highest in regime 2, whereas, if p<p, w c2 is su ciently low that NP is highest in regime 3. At p, the NP is the same in the two regimes. Turning to the implications of switching from regime 2 to regime 3, we compare the outcomes in the two regimes at the switching point (i.e. p = p) 5. We nd that 4 Again this is so because c w 1 is the wage rate which gives rise to the unconstrained maximum of NP. 5 If p = p, we have (arbitrarily) assumed that the economy is in regime 2. Therefore, strictly speaking, we 10

13 cw 3 j p=p > c w 2 j p=p= p; (21) L j regime3;p=p <Lj regime 2;p=p; (22) j regime3;p=p < j regime2;p=p; (23) UT j regime3;p=p >UT j regime2;p=p : (24) It follows immediately that w c3 j p=p p, otherwise there would be no outsourcing which is what de nes regime 3. w c3 = p is not possible either which can be seen as follows. If w c3 jp=p= p, the prices on all inputs would be the same in the two regimes, implying that the pro t would be the same in the two regimes (i.e. j regime3;p=p= j regime2;p=p), and the total amount of inputs would be the same (i.e. L j regime2;p=p= N j regime3;p=p +Z j regime3;p=p). Since total inputs would be identical in the two regimes, employment would be unambiguously lower in regime 3 (where activity 2 is outsourced), and from (14) it follows that the pay-o to the trade union would be lower in regime 3. However, since pro ts are the same in the two regimes, this would not be consistent with the Nash Products being identical (i.e. (20)) 6. Hence, it follows that wages cannot be identical, and there is a discontinuous upwards jump in the wage rate if the economy switches from regime 2 to regime 3 (i.e. at p). Continuing comparing the two regimes, if p = p, employment is lower in regime 3, and there are two reasons for that. Activity 2 is outsourced in regime 3, and the increase in the wage rate implies that there is also a decrease in employment in activity 1. The pro t is lower in regime 3 than in regime 2 because the wage rate is higher in regime 3 (i.e. the price of the input in activity 1 is higher), while the price of the input in activity 2 is the same in the two regimes. As the Nash Products are the same in the two regimes at p (i.e. (20) is satis ed), and the pro t is lower in regime 3 than in regime 2, it follows that the pay-o to the trade union is higher in regime 3 than compare the outcome of the economy when p = p (and the economy is in regime 2) to the outcome when p is an " below p (and the economy is in regime 3). 6 We recall that NP is a geometric average of and UT. 11

14 in regime 2. It is important to notice that, if the price of outsourcing decreases from p to a level which is an " below p, the economy switches from no outsourcing to outsourcing of activity 2. Even though it is the rm which decides whether to outsource, this move towards outsourcing coincides with the rm becoming worse o and the trade union becoming better o. It remains to analyze how the economy is a ected by a change in p when the economy is in regime 3 (i.e. p<p). However, within this regime it is not possible to get any unambiguous results without further restrictions on the production function and the pay-o function of the trade union. This we introduce in the following section. 3 A simple general equilibrium model 3.1 The model In section 2 we analyzed a general case without specifying functional forms, and we were able to get a number of unambiguous results with respect to the implications of outsourcing. However, in order to get more unambiguous results, and in order to analyze the welfare implications of outsourcing, we turn to a simple general equilibrium model. We assume a small open economy, and there is only one nal good which is a traded good. The price of this good is normalized to one (i.e. it is the nummeraire). Besides that there is an intermediate good which is traded as also assumed in section 2. The utility function of consumers is assumed to be linear and given as U i = y i + w (m l i ) ; (25) where y i is the income (equal to the consumption) of the consumer, l i is employment, m is the endowment of time, and w is the marginal value of leisure. In the economy there are two kinds of agents, capitalists who own the rms and do not work (i.e. l i =0), and workers who do not own capital. 12

15 There is a representative rm, and the production characteristics of this rm is as assumed in section 2, except that the production function is assumed to have the following decreasing returns to scale Cobb-Douglas form: Q = N H 1 ; 0 < <1; 0 < <1; (26) The workers are organized in a representative trade union which is assumed to be utilitarian, i.e. it seeks to maximize the sum of the utility of its members. This implies that the objective function of the trade union is gut = wl +(M L) w; (27) where M is the aggregate endowment of time of all trade union members. If trade union members (i.e. workers) have an equal probability of being employed, then UT=M g is the expected utility of a worker, and seeking to maximize (27) is equivalent to seeking to maximize the expected utility of a representative worker. In section 2, we assumed that the pay o to the trade union was zero if there were no employment (i.e. UT (0;w)=0). In order to get the same properties of the pay o function of the trade union in this section, we assume that the trade union seeks to maximize UT = g UT Mw = L (w w) (28) Maximizing (28) is equivalent to maximizing (27). Wage and employment are determined as assumed in section 2. With respect to welfare, we will assume a utilitarian welfare function to apply. By summarizing the utility of workers and capitalists, we nd that total welfare is given as W = Q + w (M L) pz: (29) We see that total welfare is determined as the total value of leisure (wm) plus the total value 13

16 of production of nal goods (Q) minus the costs of production for the society. These production costs consist of the value of lost leisure (wl) plus the cost of importing the intermediate good (pz). As the wage rate turns out to be higher than w, there are workers who are willing to work at the going wage rate, but who are not able to nd a job, i.e. they are unemployed. The unemployment rate is u = M L M : (30) By maximizing the pro t of the rm with respect to the input of labor (N and ), and the input of the intermediate good which may be purchased abroad (Z), we nd the following input demand functions If w<p: N = K 1 w 1 ; (31) = K 2 w 1 ; (32) Z = 0; (33) where K 1 = 1 (1 ) (1 ) (1 ) and K 2 = 1 1 (1 ). If w>p: N = K 1 w (1 ) 1 p (1 ) ; (34) = 0; (35) Z = K 2 w p 1 : (36) Next we turn to the three regimes as de ned in section 2. Ad. Regime 1 (p p): Given that we are in this regime, employment is determined by (31) and (32), and Z = 0. Then by using (3), (13), (26), and (28), the wage rate turns out to be 14

17 cw 1 = w µ1 + We see that the wage rate is a mark up on the marginal value of leisure. : (37) As long as the wage, given in (37), is lower than p, this is the wage which maximizes the Nash product. Therefore, the lowest p which is consistent with (37) being the outcome of the wage bargaining (i.e. p) is p = w µ1 + : (38) Ad. Regime 3 (p <p): When we are in this regime, employment is determined by (34), (35), and the input of Z is given by (36). By using these input demand functions, and (3), (13), (26), and (28), the wage rate turns out to be cw 3 = w µ1 + : (39) It is important to note that this wage is higher than the wage in regime 1. The reason being that, if there is no employment in activity 2, the elasticity of the labor demand with respect to the wage rate is smaller than if there is employment in activity 2. Hence, the relative cost for the trade union of seeking to increase the wage rate, in terms of lost employment, is lower than what is the case in regime 1. Therefore, in the wage negotiations, the trade union also succeeds in getting a higher wage rate. Ad. Regime 2 (p < p<p): The wage rate in this regime is determined as in (16), and p is implicitly de ned by (20). By using the functional forms of the model in (20), we nd that p must satisfy the following condition 15

18 s µ1 w p s = µ1 + s µ s³ p w : (40) It is easily shown that p exists 7.Ifp>p, the Nash product is higher in regime 2 than in regime 3, and the outcome of the bargaining is given by (16). If p<p, the Nash product is higher in regime 3 than in regime 2, and the outcome of the bargaining is given by (39). In the derivations above, we have assumed that all three regimes exist. This requires that p>p. For this condition to be satis ed, it must be the case that, if p = p, the Nash product in regime 2 is larger than the Nash product in regime 3. By using the same equations as the ones leading to (40), we nd that this is the case if s µ1 w p s > µ1 + s µ s µ p : (41) w By inserting p, as found in (38), it follows that this condition is satis ed if s>0 8. Hence, we may conclude that all three regimes exist in the sense that, depending on the realization of p, all three regimes are possible outcomes. 3.2 Implications of outsourcing As in section 2, we look at the implications of a decrease in the cost of outsourcing (i.e. p). In the following we start by looking at each of the three possible regimes, and after that we consider the implications of regime switching. Regime 1: As long as we are in this regime, the economy is not a ected by the price of outsourcing. Still, we consider this regime in order to get a kind of benchmark when analyzing the e ects of outsourcing. By using the wage derived in (37), we nd that 7 If we insert p = w, the right hand side is unambiguously larger than the left hand side, and if we insert p = w 1+ s(), the left hand side is unambiguously larger than the right hand side. Since the left hand side as well as the right hand side are continuous functions in p, it follows that there exists a p satisfying the condition. 8 If s =0, the labour market is competitive, and it can be shown that p = p = w. 16

19 1 w µ1 + M gut = (K 1 + K 2 ) w µ1 + u = 1 (K 1 + K 2 ) = (K K 1 K 2 ) w W = Kw +wm: õ1 + µ1 + µ1 + 1 ; (42) 1 + wm; (43) ; (44) 1! (45) where K = K 1 K (1 ) 2. Here, as well as in the following, we will assume that M is su ciently large that the unemployment rate is positive. We see that u and gut are increasing in w and s, whereas and W are decreasing. The reason for this being that, if the value of leisure, or the bargaining power of the trade union, increases, the wage rate increases. This gives rise to an increase in the unemployment rate and a decrease in pro ts and welfare. An increase in s makes the trade union better o as it is able to bargain for a wage which is closer to its most preferred wage, and an increase in w makes the trade union better o as the value of leisure increases. Regime 2: By using (16), it turns out that u = 1 (K 1 + K 2 ) M 1 p ; (46) 1 gut = (K 1 + K 2 )³p wp +wm; (47) = (K K 1 K 2 ) p W = K (1 ) p ; (48) + wm: (49) It is seen that unemployment is increasing, whereas, welfare and pro t are decreasing in p. Moreover, it can be shown that the pay o to the trade union is increasing in p 9. Hence, if the = p wp 1. This expressionis is positive if p<w 1, and by using that p is smaller than 17

20 of outsourcing decreases, unemployment decreases, capitalists become better o, and workers become worse o (in terms of expected utility). As argued in section 2, the main reason why we get these results is that a decrease in p implies that the trade union is forced to accept a lower wage in order to prevent outsourcing. Regime 3: The wage rate is given by (39), and by using this, we nd that u = 1 K 1 (1 ) 1 (1 ) M w p µ1 + (1 ) gut = K1w p µ1 + (1 ) = (K K1 K2) w p µ1 + 0 (1 ) W = Kw (1 (1 )) µ1+ (1 ) 1 (1 ) 1 ; (50) + wm; (51) ; (52) (53) µ1 + (1 ) 1 1 A + wm: We see that unemployment is increasing in p, whereas the pay o to the trade union, pro t and welfare are decreasing in p. Hence, when the economy is in regime 3, a decrease in the price of outsourcing gives rise to lower unemployment, and higher welfare for workers as well as capitalists. The reason for this is simply that a decrease in p implies that the economy gets a cheaper input which obviously increases the pro t. Moreover, it increases employment, and therefore it also bene ts workers. Switch from regime 1 to 2: As we are analyzing the implications of outsourcing, we consider what are the e ects of p decreasing. When p = p, it is easily seen that (42) and (46) give rise to exactly the same unemployment rate, and, similarly, we nd that g UT,, and W are identical when using the the wage given in regime 1, it is easily seen to be the case. 18

21 expressions for the two regimes. Hence, there is no discontinuous jump in any of our variables of interest when the economy moves from regime 1 and into regime 2. Switch from regime 2 to 3: If the price of outsourcing becomes su ciently low (p <p), the rm outsources activity 2, and the economy switches from regime 2 to regime 3. In order to check the implications of this switch, we compare the variables of interest in the two regimes, given that p = p. This comparison gives rise to the following results u j p=p; regime3 >uj p=p; regime2; (54) gut j p=p; regime3 >UT j p=p; regime2; (55) j p=p; regime3 < j p=p;regime2; (56) W j p=p; regime3 <W j p=p; regime2 : (57) We see that, similar to what we found in section 2, there is a discontinuous jump in all the variables of interest, if the economy moves from regime 2 into regime 3. The unemployment rate increases, but, in spite of that, the pay o to the trade union increases. However, the pro t as well as total welfare decreases. We recall that, when moving from regime 2 to regime 3, the economy switches from a case without outsourcing to a case with outsourcing. Again, it is interesting to note that this switch towards using outsourcing hurts the rm (capitalists) but bene ts the workers (i.e. the expected utility of workers increases), and the net e ect is a welfare loss. There are two reasons why the welfare decreases when the economy switches from regime 2 to regime 3, namely the increase in the wage rate and the fact that outsourcing starts taking place. To focus on the rst reason, let us assume that there is no outsourcing in regime 3, but the only di erence between the two regimes is that the wage rate in activity 2 is higher in regime 3 than in regime 2. Then the welfare would be lower in regime 3 because of the lower employment. This is so because, due to trade union in uence on the wage rate, the marginal product of labor is higher than w (in 19

22 both regimes) which is the marginal cost for the society of increasing labor input. On top of that, welfare decreases because outsourcing starts taking place when switching from regime 2 to regime 3. This is so because, since p > w, outsourcing implies that society pays a higher price for input in activity 2 in regime 3 (i.e. p) compared to what is the case in regime 2 (i.e. w). 4 Conclusion We have shown that in an economy where trade unions have wage bargaining power, the qualitative implications of a decrease in the cost of outsourcing are very sensitive to what is the initial cost of outsourcing. If the cost is in an intermediate range where the potentials of outsourcing puts downward pressure on the wage rate, but where the rms choose not to outsource, the rms become better o and the trade unions become worse o. However, a robust result of our analysis is that, if the cost of outsourcing becomes su ciently low, and the economy switches from a regime without outsourcing to a regime with outsourcing, the outsourcing rm becomes worse o and the trade union in the rm becomes better o. One reason for these e ects is that there is an unambiguous upwards jump in the wage rate. In a simple general equilibrium model, we were also able to analyze unemployment and net welfare implications of outsourcing. We found that, if the cost of outsourcing decreases, unemployment always decreases and welfare always increases, except at the cost of outsourcing where the rms switch from a regime without outsourcing to a regime with outsourcing. At this cost level, a further decrease in the cost of outsourcing gives rise to a discontinuous upwards jump in unemployment and a downwards jump in welfare. 5 References ² Binmore, K., Rubinstein, A. and Wolinsky, A., 1986, The Nash Bargaining Solution in Economic Modelling, Rand Journal of Economics 17, ² Dri ll, E.J. and van der Ploeg, F., 1995, Trade Liberalization with Imperfect Competition 20

23 in Goods and Labour Markets, Scandinavian Journal of Economics 97, ² Feenstra, R.C. and Hanson, G.H., 1996, Globalization, Outsourcing and Wage Inequality, American Economic Review 86, Papers and Proceedings, ² Feenstra, R.C.and Hanson, G.H., 1999, The Impact of Outsourcing and High Technology Capital on Wages: Estimates for the United States, , Quarterly Journal of Economics 114, ² Huizinga, H., 1993, International Market Integration and Union Wage Bargaining, Scandinavian Journal of Economics 95, ² Krugman, P., 2000, Technology, Trade and Factor Prices, Journal of International Economics 50, ² Leamer, E.E., 1994, Trade, Wages and Revolving Door Ideas, NBER Working Paper no ² Naylor, R., 1998, International Trade and Economic Integration when Labour Markets are Generally Unionised, European Economic Review 42, ² Naylor, R., 1999, Union Wage Strategies and International Trade, Economic Journal 109, ² Nickell, S. and M. Andrews, 1983, Unions, Real-Wages and Employment in Britain , Oxford Economic Papers. ² Skaksen, M.Y. and J.R. Sørensen, 2001, Should Trade Unions Appreciate Foreign Direct Investment?, Journal of International Economics, forthcoming. 21

24 6 Appendix In this appendix, we consider the case where regime 2 does not exist. We know that if p is su ciently high, the economy is in regime 1, and if p is su ciently low the economy is in regime 3. We assume that there exists a unique ep satisfying the following condition: NP j regime1;p=ep = NP j regime3;p=ep : (58) If p ep, the economy is in regime 1, and if p < ep, the economy is in regime 3. Now, it can be shown that c w 3 j p=ep > w 1 j c ; p=ep (59) L j regime3;p=ep <Lj regime 1;p=ep ; (60) j regime3;p=ep < j regime1;p=ep ; (61) UT j regime3;p=ep >UTj regime1;p=ep : (62) In order to have outsourcing in regime 3, and not in regime 1, it must be the case that c w 3 ep and c w 1 < ep. Hence, it must be the case that c w 3 c w 1.If c w 3 = c w 1 = p, the price on both inputs would be the same in the two regimes, and therefore the pro t would be the same. However, since employment is lower in regime 3, the trade union would be unambiguously worse o. An unchanged pro t, and a lower pay o to the trade union, would not be consistent with (58). It follows that the wage in regime 3 must be higher than the wage in regime 1. If p = ep, employment in regime 3 is unambiguously lower than employment in regime 1. The facts that the wage is higher in regime 3, and that there is outsourcing, both tend to give rise to lower employment in regime 3 than in regime 1. The pro t is lower in regime 3 because the price on one of the inputs is higher in regime 3 than in regime 1. As the pro t is lower in regime 3 than in regime 1, it follows from (58) that the pay o to the trade union must be higher. 22