Durable Goods Produced by State Owned Enterprises

Transcription

1 Durable Goods Produced by State Owned Enterprises Gregory E. Goering Department of Economics University of Alaska PO Box Fairbanks, AK USA Ph. (907) Sudipta Sarangi Department of Economics 107 Patrick F Taylor Hall Louisiana State University Baton Rouge, LA USA sarangi@lsu.edu Ph. (5) Draft: June 1, 009

2 Durable Goods Produced by State Owned Enterprises Abstract: A two-period durable-goods monopoly model is analyzed where the durable good is provided by a state owned enterprise (SOE). First, we suppose that the SOE is under pressure to provide employment, and therefore has an employment goal, as well as the traditional profit and consumer surplus objectives. Assuming that the SOE has difficulty committing to current buyers with respect to its profit and employment motives, we find that as the employment burden increases, the SOE tends to move further away from the efficient durability and provides a lower durability level than a pure profit maximizer. Additionally, we show that a durable-goods SOE without commitment power, will wish to partially privatize to help mitigate its commitment problem with buyers and increase social welfare. Both of these findings provide economic rationale for the partial privatization of SOEs in transitioning economies that have not been identified in the literature prior to this. Key words: State owned enterprise, durable goods, privatization JEL classification: L3, D4 I. Introduction The behavior of a state owned enterprise (SOE) has generated considerable interest in the last several decades, particularly as it relates to privatization and employment burdens that are placed on them (see, for instance, Bodmer (00), Guo and Yao (005) on the issue of employment burden, and for different measures of this Li (008)). An excellent discussion of all the different objectives faced by SOEs, from a financial perspective, can be found in Megginson (005). However, an important aspect of this problem that has been ignored in the literature is the durable nature of many of the products manufactured by SOE s (e.g., automobiles). We find the durable character of the goods, likely has profound effects on a SOE s behavior, both in terms of their actions before they privatize, as well as their incentive to privatize (see Waldman (003) for a review of the durable-goods literature). In terms of a durable-goods SOE s behavior before privatization, we show that the SOE has an incentive to practice planned obsolescence, that is not only more severe than the simple 1

3 durable goods monopoly case, but that also tends to increase as the SOE s employment burden increases. In terms of the privatization of a SOE, it is normally thought that the sale of SOE shares, such as in China, helps transform the SOE to private profit maximizing incentives. It is further expected that the sales of state shares to the private sector will help improve the SOE s efficiency through changes in the corporate governance structure, etc. For example, Sun et al. (005), show that in a mixed oligopoly market (SOE with an employment burden and pure profit maximizing rivals), if the SOE is less efficient than its rival, it is, in general, inefficient to fully privatize or to have complete state ownership. However, these earlier works generate the partial privatization results by assuming that the SOE does not have a pure social welfare goal and is cost inefficient in a mixed oligopoly market. 1 We show that when the good is durable (as the output of many SOE s in transiting economies are), the optimal partial privatization result can be obtained in a pure welfare maximizing setting with no rivals. In durable-goods markets this occurs because of the SOE s inability to commit to current buyers. The outline of the paper is as follows. In section II we set up a simple two-period durable-goods monopoly SOE framework. Then in section III both rental (committed sales) and uncommitted sales solutions are explored, where the SOE selects product durability, given it faces an employment burden. We then suppose that a welfare maximizing SOE without commitment ability can privatize by allowing it to sell state shares to the private sector in section IV. We show in this section that even in pure monopoly market (no rival firms), the SOE will wish to partially privatize to lessen the durable-goods commitment problem. Concluding remarks are presented in the final section. 1 For more on this see Yarrow and Jasiński (1996), Lee and Hwang (003), Lee (006) and Capuano and De Feo (008).

4 II. Basic SOE Durable Goods Model with an Employment Burden We begin by exploring a scenario that was quite typical in transition economies for SOEs involved in manufacturing durable goods. In keeping with the spirit of an SOE we assume that it maximizes welfare but also has been assigned the task of maximizing employment. In other words, the SOE is asked to also directly place a weight on the employment of workers in its objective function. As in Bulow (198, 1986) we suppose a simple two-period durable-goods world. Let δ [0, 1] represent the fraction of a durable unit in period one that remains for use in period two. The stock of durable units available for use in each period is, Q 1 = q 1 and Q = δ q 1 + q, respectively. With a linear inverse service demand we know: (1) p1 = a bq1 p = a b δ q1+ q and ( ), are the inverse demands for the flow of services in period one and two respectively. Let the marginal production cost in each period be given by c 1 ( δ ) > 0 and c > 0 respectively, where c ( δ) > 0 and c ( δ) > 0. Thus, manufacturing costs are constant with respect ' " 1 1 to output, but increasing in product durability. As Swan (1970) and Schmalensee (1979) note, this cost assumption removes any of the confounding impacts of output levels on durability choice. Hence, as we show in section III, the socially optimal product durability simply minimizes the discounted costs of providing a unit for service (use) in period two. 3

5 The typical SOE is assumed to maximize profits as well as consumer surplus. Additionally, following Sun et al. (005) we assume that the SOE is under pressure to provide employment opportunities. As they note, the employment burden or pressure typically arises from the government s wish to ensure steady work and thus stability for the populace. This is often done by propping up state owned firms through low interest loans or other state mechanisms. One way to model this is by allowing the SOE to place a higher weight on revenue generation than a pure social welfare maximize. Let θ 0 represent this degree of employment pressure or additional weight that the state places on the SOE s revenue generation. As θ increase from zero, it indicates the SOE will place a higher weight only on the production of units (revenue). If we suppose β [0,1] represents the discount factor, the SOE s objective function, given (1), can be written as: () bq1 W = ((1 + θ)( a bq1) c1( δ) ) q1+ + b( δ q + q ) 1 ((1 + )( q1+ q)( a b( q1+ q)) cq + ) β θ δ δ. where the third and fifth term capture consumer surplus. Note that in () when θ = 0 the SOE s objective function collapses to the standard social planner s (public firm) objective function, since the employment burden disappears. In contrast, as θ increases from zero, a larger emphasis is placed on revenue and output. The two period maximization problem of the durable goods monopoly has some interesting features. The SOE wishes to maximize (), however, it can only do so in a dynamically consistent fashion if it rents/leases all of the durable output. Otherwise, the firm faces a classic commitment problem with buyers first noted by Coase (197). In the sales case, 4

6 we suppose the SOE cannot credibly commit to its profit or employment motive (see Butz (1990), Goering (1997), and Goering and Pippenger (00) for examples of commitment mechanisms, such as, best-price provisions and forward contracts). In other words, once the firm has moved to the second period, any output sold in the first period is water under the bridge and the SOE will face pressure to maximize current profits and employment. Thus, in contrast to the discounted portion of (), the SOE s objective in period two with sales is: (3) b( δ q + q ) 1 = (1 + θ) ( ( δ 1+ )) +. W q a b q q cq In (3) the SOE only considers current output in terms of its profit and employment (revenue) motive and not the durable units still held by period one buyers ( δ q1 ). Rational period one buyers of the durable good will, however, also expect the SOE to maximize (3) instead of the discounted portion of (). Hence, as we show in the next section, unless the SOE can credibly commit to these buyers, the maximal solution of (3) becomes a constraint on a selling SOE s behavior. Of course the SOE still accounts for consumer surplus in (3). One could conceive of cases where the SOE may revert to pure-profit maximizing behavior in the future, but this is not assumed in (3). III. SOE Rentals and Uncommitted Sales with an Employment Burden In this section, we focus on the SOE s behavior before they privatize. In particular, what product durability or quality will a SOE likely manufacture if it has an employment burden? 5

7 This is an important issue since SOEs often have some employment burden (as noted in the previous section). A. Rentals We first calculate the rental (committed sales, i.e. when the SOE can act like a renter ) solution to show that the efficient (cost-minimizing) durability is unaffected by the employment burden ( θ 0 ). 3 The superscript r in the first order conditions below denotes the fact that we are dealing with the rental problem. (4) r W = a (1 + βδ )(1 + θ) bq ( 1+ βδ q + βδ q 1)(1+ θ) c 1( δ ) = 0 q 1 W q r (5) β a θ b( δq1 q θ c = ( (1 + ) + )(1+ ) ) = 0 (6) r W δ = β(( a(1 + θ) b( δq + q )(1+ θ) c ( δ) ) q = 0. ' Simplifying (4) and (6) with (5), yields: W = a (1 + ) b (1+ ) q c ( ) + c = 0 q r (7) θ θ 1 1 δ βδ 1 (8) r W δ = ( βc c ( δ) ) q = 0 ' 1 1 We believe that relaxing this assumption would violate the spirit of the SOE s problem. 3 In transition economies committed sales has another interpretation. If the durable good is produced by one SOE for purchase by other government entities (as a part of central planning) this is tantamount to committed sales. 6

8 By substituting θ = 0 into (5), (7), and (8) we can calculate the socially optimal bench mark solution (since the employment burden is zero in the objective function ()). Focusing on the product durability, it is immediately apparent from (8), that the SOE s durability will be socially optimal. Equation (8) shows a SOE will provide the optimal (cost-minimizing) durability regardless of the employment burden θ. Essentially, the SOE has no incentive to stray from the durability that minimizes the discounted costs of providing a unit for service in the second period. Note that the SOE can provide a unit for service (use) in the second period in either of two ways: (i) either by increasing period one product durability (more durable units remain), or (ii) by simply manufacturing additional units in period two. Equation (8) simply reflects these tradeoffs at the margin, and shows SOE s product durability is independent of its employment burden, i.e., δ = 0. θ Note that if the SOE can commit to buyers in sales markets we get the same solution, implying (8) also holds for committed sales solutions, (e.g., situations where the SOE sells to other state agencies). 4 This result is summarized in the proposition below. Proposition one: An SOE that is renting or has committed sales will choose the socially optimal (cost-minimizing) level of durability, irrespective of its employment burdenθ 0. sales markets. Next we show that this proposition will not hold in uncommitted dynamically consistent 4 Even though renting or committed sales SOE will select the socially optimal durability level shown in (8), it will not produce the welfare maximizing output levels unless the employment burden θ is zero. Thus, even though its durability is independent from the employment burden, (5) and (7) indicate, as one would expect, that these outputs do depend on θ. 7

9 B. Uncommitted sales To calculate the dynamically consistent solution the SOE must maximize () subject to the maximal solution to (3). To see this we solve in reverse order, starting in the final period two, using the superscript s to denote uncommitted sales. The maximization of (3) with respect to period two output q gives: s a(1 + θ ) bθδ q1 c (9) q =. b(1+ θ ) Although the selling SOE wishes to maximize the discounted welfare stream of the durable (), consumers will rationally forecast the SOE s period two behavior in (9). Hence, (9) becomes a constraint on the seller s behavior if it cannot credibly convince these buyers it will include their durable units still in service ( δ q1 ) in its period two re-maximization. We suppose the SOE does not have this ability, i.e., we do not simply endow the SOE with this sort of credibility. Thus, focusing on the selling SOE s product durabilityδ, this constrained maximization gives: (10) s W bδq1 (1 + θ) ' = ( βc c1( δ) ) q1 = 0. δ 1+ θ From (10) we see that a selling SOE will no longer provide the efficient cost-minimizing durability found in (8). There is an additional negative term in (10), not present in (8), that is due to the SOE s commitment problem with current buyers. Since the SOE cannot credibly convince the buyers that it will take their capital loss on existing units into account when it expands output in period two for both pure profit and employment purposes, it constrains the SOE. Indeed, (10) 8

10 indicates the SOE will respond by providing a less durable good in this sales case compared to the efficient level in (8). Proposition two: An SOE engaged in uncommitted sales will not choose the socially optimal (cost-minimizing) level of durability. Such an SOE will tend to produce output with lower durability than the efficient level. Moreover, unlike the rental case, the degree of this planned obsolescence outlined in proposition two, is in large part determined by the employment burden parameter. In other words, δ 0 θ in the uncommitted sales case. 5 Implicitly differentiating the SOE s first-order conditions gives: (11) δ β(1 + θ)( a(1 + θ) bq ) bδ q = θ H (1+ θ) 1 1, where H > 0 is the negative definite Hessian matrix. The sign of (11) is, of course, determined by the sign of ( a(1 + θ ) bq ). This term reflects the impact of the employment burden on the 1 SOE s period one output q 1. In the normal case we would expect the SOE to produce more period one output which implies ( a(1 + θ ) bq ) > 0, and the sign of (11) is negative so 1 5 However as (3) indicates, even in the case of a zero employment burden ( θ = 0 ) a SOE still practices planned obsolescence given that it faces a credibility problem with respect to its profit motive. Interestingly, the degree of planned obsolescence is more severe than a pure durable-goods monopoly even in this case. It is easy to show that, a profit-maximizing durable-goods selling monopolist without commitment ability, will select a optimal durability according to: (βc bδq 1 c ' (δ ))q 1 1 = 0. With smaller output levels under the monopoly scenario, it is clear that this durability will be higher than a SOE without the employment burden ( θ = 0 ). The intuition is that, even without any employment burden the SOE still has higher period one output than the monopolist. Consequently, it has a more severe commitment problem on any durable units and wishes to decrease durability to help mitigate this. 9

11 durability declines as the employment burden increases. 6 In this case, the SOE produces more output to satisfy its employment objective, but this increases its commitment problem with period two buyers. To help mitigate this problem the SOE decreases the product s durability. Indeed, in this case it is even less than a pure profit maximizing firm level. Hence, a SOE without commitment ability and an employment objective may well practice the highest degree of planned obsolescence and sell relatively shoddy products. Proposition three: An SOE engaged in sales will tend to practice a higher degree of planned obsolescence the greater its employment burden, given the employment burden increases current output. Proposition three is of particular interest, since anecdotal evidence often suggests, that when a SOE is privatized the quality or durability of the firm s output increases markedly. For example, Ellis (000, pg. 3) notes that the cars produced by the Czech manufacture Škoda used to provide Western comedians with an easy target for jokes. Today Škodas are made on one of the most advanced production lines in the world; 80 percent of the cars are exported to 70 countries. Now an integral part of the Volkswagen group, Škoda Auto s quality ratings are considered excellent even by VW standards. Usually, this sort of durability/quality improvement is attributed, somewhat loosely, to better management and efficient operating principles. Propositions 3 indicates fundamentally one of the underlying mechanisms that may be at work: namely employment burdens on SOEs may cause decreases in the durability or quality of the good. 6 Note that if we assume the employment burden is bounded from above with maximum weight θ = 1 we see that this term simply collapses to the service price in period one which is positive. However, if we take the polar case of θ = 0 this expression collapses to the marginal revenue for the service demand in period one. This maybe positive or negative when θ = 0, depending upon the SOE s period one marginal production cost, amongst other c ( δ ) 1 things. Hence, if one supposes that the employment burden causes a decrease in period one output, proposition three will be reversed. 10

12 IV. Partial Privatization of a Welfare Maximizing Monopoly Durable Goods SOE. In this section, we introduce partial privatization of the durable goods monopoly as an alternative to the previous section. This is also an important issue since one of the most common suggested solutions to improve SOEs has been their privatization. However instead of prescribing privatization in an exogenous manner, in this paper we ask whether the SOE would chose to privatize on its own. We assume neither the SOE nor the private firm has any employment burden ( θ = 0 ). This is the kind of private firm that one expects to see in a transition economy. For reasons of tractability, we further assume that SOE s durability is exogenously fixed at the level δ [0, 1]. 7 However, we now allow the welfare maximizing SOE to privatize by selling shares in the firm to the private sector. Thus, the SOE becomes a so called joint stock company, with both private and state owned shares (controlling interest). This fraction is given by λ [0, 1], where λ = 0 is full privatization and λ = 1 is fully state owned (no privatization). We suppose the government decides, before any production takes place, on the degree of privatization or state control λ. Then output levels are determined over the two-period horizon in an analogous fashion to the previous section. Presumably, the private share holders will wish to maximize profit while the state owned fraction will wish to maximize discounted social welfare. Thus, the objective function of the government is simply () with a zero employment burden θ = 0 and fixed durability δ : 7 One interpretation could be that durability change requires substantial expenditures that are only feasible in the long run. 11

13 (1) bq1 W = ( a bq1 c1) q1+ + b( δ q + q ) 1 (( q1+ q)( a b( q1+ q)) cq + ) β δ δ. Private shareholders, on the other hand, are interested in pure discounted profit given by (13): = ) + ( + + ). (13) π ( a bq1 c1 q1 β ( δq1 q)( a b( δq1 q)) cq Obviously, if the state also controls the fraction of shares held and controlled by the private sector, it can, in effect, select the weight placed on (1) and (13) by the SOE. For example, if the state has complete control ( λ = 1), then the SOE would engage in pure welfare maximization, and with full privatization ( λ = 0 ) it would be a pure for-profit firm. In other words, at the first-stage of the game the objective of the government is the maximization of social welfare in (1) with respect to the share fraction λ, given that its agent (the SOE) will maximize (14) in stage-two: (14) G = λw + (1 λ)π = (a bq 1 c 1 )q 1 + β((δq 1 + q )(a b(δq 1 + q )) c q ) + λ( bq 1 + βb(δq + q 1 ) ). As in the previous section, to ensure dynamically consistent (sub-game perfect) solutions, we solve the game in reverse order starting in period two. 1

14 A. Rentals We first calculate the rental solution to show that the government will always wish to retain complete control of the SOE ( λ = 1) regardless of the durability of its output. Differentiating (14) with respect to second period output and solving gives: r a c (15) q = δ q1. b( λ) Maximizing (14) subject to (15), with respect to first period output gives optimal rental period one output: r a c1+ βδc (16) q1 = b( λ). Finally, we can maximize (1) subject to (15) and (16) to obtain the optimal state share (17): (17) λ = 1. As one would expect, in the rental case (or fully committed sales) where no dynamic consistency issue exists, the government would simply want the SOE to adopt fully its objective of welfare maximization so λ = regardless of the product s durability δ. This result is summarized in 1 the proposition below. Proposition four: A durable goods SOE will remain under complete government control (zero privatization) in rental (or fully committed sales) markets regardless of the product s built-in durability δ. B. Uncommitted sales To calculate the dynamically consistent sales solution for the government in sales markets we first need to construct its second period objective function. From (14), note that in the final second period a SOE with no commitment ability with regard to its profit motive maximizes (18). 13

15 (18) b( δ q1+ q) G = q( a b( δq1+ q)) cq + λ As in (3), the objective function in (18) supposes that the SOE will still wish to account for consumer surplus in its objective function even though it cannot commit to period one buyers with respect to its profit motive. 8 Maximizing (18) with respect to second period output gives optimal sales output in period two as: s a c δq1(1 λ) (19) q =. b( λ) ( λ) Now we can maximize (14) subject to (19) to obtain the period one sales output: s ( λ)( a c1+ βδc) (0) q1 =. b( βδ + ( λ ) ) Maximizing (1) subject to (19) and (0) will yield the optimal state share λ in sales markets. Note that even in this highly stylized model the first-order condition for this sales problem is a complicated fifth order equation in the variable of interest λ. 9 Hence, we take a different approach here and evaluate this first-order condition at λ =1 which yields: 8 As noted earlier in section II, one can think of more severe commitment problems where the SOE would simply revert to pure profit maximizing behavior in future periods, say due to 100% privatization, but this is not addressed here. 9 Details of this are available from the authors on request. 14

16 (1) W λ λ=1 = βδ((c + δc 1 )(c 1 βδc ) + (1+ δ + βδ )a a(c 1 (1+ δ + βδ ) ((1+ δ )βδ + β δ 3 1)c )) b(1+ βδ ) 0 The derivative in (1) clearly shows that complete state ownership, λ = 1, of the SOE is suboptimal in sales markets as long as the good is durable ( δ > 0 ). Note the derivative in (1), only collapse to zero (for all parameter values) if the good is non-durable ( δ = 0 ). This indicates it is the durability of the product with its associated commitment problem Due to the SOE s commitment problem with period one buyers, the government will in fact generally wish to partially privatize the SOE by setting λ <. Hence, partial privatization may occur for this 1 reason, as long as the good is durable, even in the absence of competitive or technological efficiency considerations. Proposition five: A welfare maximizing durable goods ( δ > 0 ) SOE will wish to partially privatize in sales markets ( λ < 1), due to commitment problems with current buyers. The driving force for this result, once again, is the SOE s commitment problem with first period buyers. Partial privatization ( λ < 1) allows the governmental agency (SOE) to credibly commit itself to period one buyers of the durable-good. First period buyers know the SOE has little incentive to take into account their capital loss in the future period on the existing stock owned by them. Partial privatization, which instills a stronger profit motive, forces the SOE to provide less output and, consequently, implies higher future prices. Thus, the state can use partial 15

17 privatization to credibly commit its agent (the SOE) to these buyers. 10 Note that partial privatization is an endogenous outcome in our model. In other words, the commitment problem of the durable goods monopoly provides a completely new rationale for partial privatization (see also Maw (00) for a discussion of other causes underlying partial privatization). To illustrate that this is indeed the case, we now provide a numerical example of an uncommitted sales and rental case where all the second-order conditions and other relevant restrictions (positive prices, interior solutions, etc.) hold. Suppose the parameters in the model are: a= 10, b= 1, β =.9, δ =.5, c1 = 1, and c =. We can then use equations (1) through (0) to calculate all the relevant rental and sales variables for given state shares λ in each case. The rentals case is shown in Table 1 while the uncommitted sales case is given in Table. All of the variables are defined as before, with the exception that we also calculate discounted consumer surplus separately: bq1 b( δ q1+ q) CS = + β. Note also, that the prices calculated in both tables are the demand for service prices found in (1). Table 1: Rental Case where No Privatization is Optimal a= 10, b= 1, β =.9, δ =.5, c = 1, and c = Parameter values 1 λ W = π + CS π CS q 1 q p p Note that our result is related to Fershtman and Judd (1987) and Sklivas (1987) finding, that firm owners, whose sole goal is the maximization of profits, may wish to give their agent (manager) a different goal (e.g., a linear combination of profit plus revenue). This commits the firm to a higher output level and ensures a larger market share in the subsequent Cournot output game with rival firms. In our case, the state wishes to commit its agent (the SOE) to a lower output stock in the subsequent game with buyers, by giving the SOE, in effect, a different objective than pure welfare maximization through the partial privatization. 16

18 We see from table 1, as we found analytically in (17) and summarized by proposition four, a renting durable goods SOE would remain under complete government control ( λ = 1). There is no incentive for the government to partially privatize here. With no commitment or dynamic consistency problem, we see from the table that the government would just wish the SOE to place all weight on welfare maximization with λ = 1. As (1) indicates we now show that this does not occur with uncommitted sales. Table : Uncommitted Sales Case where Partial Privatization is Optimal a = 10, b= 1, β =.9, δ =.5, c = 1, and c = Parameter values 1 λ W = π + CS π CS q 1 q p p From this table it is immediately apparent that full government ownership ( λ = 1) is no longer social welfare maximizing. In table, a finer cut of the state share λ yields that the maximum welfare actually occurs between λ =.85 and λ =.95. Indeed if we solve the selling SOE s firstorder condition ( W = 0 ) numerically we find that the optimal value of the state share is λ λ =.8878 in this sales case. 11 This illustrates that partial privatization (roughly 11% private ownership) is optimal with this parameterization, confirming proposition five. As noted earlier, 17

19 the intuition here is that, partial privatization allows the SOE to credibly commit itself to period one buyers. V. Conclusion In transitioning economies the production of durable goods often was done by a monopoly state owned enterprise (SOE). Yet, such enterprises and their commitment problem have not really been explored in detail. Our paper contributes to this small body of literature by exploring two interesting scenarios. First, we examine what happens to durability choice when the SOE faces an employment burden along with standard welfare maximization. We find, that when faced with a commitment problem, durable-goods SOE engaged in sales will produce output with socially sub-optimal levels of durability. Moreover, this planned obsolescence tends to increase as the employment burden on the SOE is raised. However, even if SOE does not have an employment burden, we find it decreases product durability below that of a pure monopoly seller. This provides a further rationale for the stylized fact that SOEs tend to manufacture inferior products vis-à-vis private firms (e.g., state made Škodas versus privately manufactured Škodas under VW control). Second, we explore what is often touted as a panacea to problems of transition economies, namely privatization. In fact, we ask whether a SOE would chose to privatize on its own by making privatization an endogenous choice variable. Interestingly, we find that a welfare maximizing durable goods monopolist with commitment problems will prefer to choose a positive level of privatization. Two key facts emerge from this. First, we believe that the latter result has not been pointed out in the earlier literature and deserves further exploration in 11 In fact the only real solutions possible to this fifth-order equation, are λ =.8878 and λ = 0, the later clearly 18

20 transition economies since it provides a purely economic motive for privatization. Next, both of these findings taken together provide additional rationale for the partial privatization of SOEs in transitioning economies. is not a maximum. 19

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