- Email: [email protected]
Discriminatory public procurement policy and cost reduction incentives
Journal of Public Economics 67 (1998) 349–367
Discriminatory public procurement policy and cost reduction incentives Florence Naegelen*, Michel Mougeot Crese, University of Besanc¸on, 25030 Besanc¸on Cedex, France Received 1 June 1996; received in revised form 1 November 1996; accepted 16 April 1997
Abstract Discriminating in favor of domestic suppliers in the award of government procurement contracts is a widespread practice. In this paper, we extend the previous analysis of McAfee and McMillan (1989) [Government procurement and international trade. Journal of International Economics 26, 291–308] and Branco (1994) [Favoring domestic firms in procurement contracts. Journal of International Economics 37, 65–80] by considering in the same model the bidding competition stimulation effect and the favoritism effect. We prove that the optimal policy can be implemented by a modified Vickrey auction or by a complex modified first price auction. We also consider that firms can reduce their cost by a nonobservable effort. We show that taking moral hazard into account does not modify the awarding rule, but that the government must use the payment rule to require a greater level of effort from the favored firm. 1998 Elsevier Science S.A. Keywords: Auctions; Discrimination; Procurement; Moral hazard JEL classification: D44; D82; H57
1. Introduction Discriminating in favor of domestic suppliers in the award of government procurement contracts is a widespread practice in many countries. It can result from an explicit ‘buy local policy’. One example is the United States’ ‘Buy American Act’. The United States government offers a 6 percent preference for *Corresponding author. Tel.: 133 03 81666716; fax: 133 03 81666716. 0047-2727 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII S0047-2727( 97 )00068-6
350
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
domestic suppliers. This preference can be raised to 12 percent in the case of small businesses and firms in regions of high unemployment and 50 percent for military equipment. Explicit domestic preferences have also been applied in Canada, Australia, New Zealand and Turkey.1 Favoritism can also be implicit. For instance, the European governments do not have explicit preferential procurement policies, but according to the Atkins Management Consultants (1988) report, only 2 percent of government procurement contracts are awarded to foreign bidders.2 There is a general agreement that discriminatory policies should be eliminated. International organizations such as GATT and the European Union have set out rules to curb favoritism but, despite these agreements, favoritism continues. According to Vagstad (1995), one important reason is that asymmetric information makes favoritism difficult to detect. Another reason is that governments, even though collectively the source of the prescription, have been reluctant to implement it (Breton and Salmon, 1996). How can the existence of preferential public procurement policies be explained? Protection is often justified by the power of certain interest groups or by infant industry arguments. However, some papers on optimal auction theory show that such a practice could be justified by rational decisions of governments. First, if there are cost advantages for foreign firms, the governments should discriminate in favor of the domestic firms to stimulate competition and minimize expected procurement costs (McAfee and McMillan, 1989). Second, if governments prefer domestic to foreign profits, they have incentives to discriminate against foreign suppliers (Branco, 1994). These two arguments have been developed in the auction theory framework in partial equilibrium models.3 An essential aspect of procurement policy is that the governments are not likely to be perfectly informed about technological conditions in the suppliers’ industry. The nature of information asymmetry then plays a key role in the explanation of optimal procurement policy. Adverse selection explains the need to organize an auction and can justify some form of discrimination. Discrimination can also result from the government’s utility function. The McAfee-McMillan and Branco arguments refer to different objectives. The first one refers to efficiency and the second to distributional concerns. Let us consider the case where a domestic firm D and a foreign firm F can undertake a single indivisible project for a governmental agency. If costs of the two firms are drawn from the same probability distribution (i.e. if we consider the standard symmetric auction model), the only justification for a discriminatory policy is the existence of a greater 1
EU directive 90 / 531 involves a 3% price preference in natural monopoly sectors (water distribution, energy, transport and telecommunications). 2 The Japanese market for computers is another example: according to Robertson (1992), while US firms have 40% of the private market, their share of the government part of the market is only 0.4%. 3 The general equilibrium approach (see Baldwin and Richardson (1972), Joson (1986) and Miyagiwa (1991) is not taken into consideration here.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
351
weight on the domestic firm’s profit than on the foreign one when the government maximizes a weighted sum of consumer surplus and firms’ profit. Uneven weighting of profits creates favoritism, but favoritism increases procurement costs. If there is a positive social cost of public funds, the government has to trade off the increase of the domestic firm’s profit and the increase in the social cost resulting from the distortionary taxation. If we assume now that firms’ costs differ from country to country (costs of the two firms are drawn from different distributions), a preferential treatment can be used to induce firms to reveal their private information about their cost and prevent the most efficient one from bidding too high (Myerson, 1981 and McAfee and McMillan, 1989). In this paper, we consider the efficiency argument and the distributional argument in the same model. We characterize the optimal policy in the adverse selection case using a direct revelation mechanism.4 We show that the awarding rule amounts to adding to the domestic firm’s cost a term whose sign varies with comparative advantages, the social cost of public funds and the weight attached to the domestic profit. Thus, we obtain a benchmark model that allows us to analyze the trade-off between the protectionist discriminatory policy and the competition stimulation procurement policy. A second problem to consider after defining the optimal policy is the implementation of the optimal mechanism. McAfee and McMillan (1989) only consider the mechanism design approach that can be implemented by a Vickrey type auction. However, most of the procurement auctions are actually first price sealed bid auctions. It would be useful to characterize the first price auction that implements the optimal mechanism. Branco (1994) does it using an example, with the costs of the two firms independently uniformly distributed on [0,1]. In this paper, we prove that the general optimal discriminatory policy can be implemented by a Vickrey type auction in which the winner’s payment is independent from its bid or by a modified first price sealed bid auction, with non linear discriminatory rules. This result is obtained with general assumptions on the costs distributions. The usual drawback of protectionism is that domestic firms have no incentive to minimize cost. When discrimination is in favor of the domestic firm, this firm can win the auction with a higher cost than the foreign one and has no incentive to perform as best it can. To take this effect into account, we consider in this paper that firms can reduce their cost by a non observable effort. As the effort exerted by the firms entails a disutility, the firms must be motivated to make it. Then the government faces simultaneously a moral hazard problem and an adverse selection problem. So we have to consider an asymmetric bidding model that incorporates both moral hazard and adverse selection considerations. To do this, we build our analysis on the auctioning incentive contract model of Laffont and Tirole (1987). Departing from Laffont and Tirole (1987), we assume uneven weighting of profits 4
This paper does not consider favoritism resulting from non verifiable product quality. For an analysis, see Laffont and Tirole (1991), Laffont and Tirole (1993) and Vagstad (1995).
352
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
and asymmetric distributions of costs. Our first result is that the Laffont and Tirole dichotomy property still holds. The government has to use the discriminatory awarding rule to obtain allocative efficiency and the payment rule to obtain productive efficiency. So taking moral hazard into account does not modify the awarding rule defined in the benchmark model: the same term is added to the foreign firm’s cost. Moreover, we show that the government must always require a greater effort level from the favored firm. In Section 2, we present the optimal mechanism in the adverse selection case. Optimal procurement policy is characterized in Section 3. In Section 4, we consider the implementation of that policy by first or second price auctions. In Section 5, we present the optimal mechanism when both moral hazard and adverse selection are present. Section 6 concludes the paper.
2. The optimal mechanism in the adverse selection case Suppose the government wishes to undertake an indivisible project 5 that has value S for consumers. This project can be carried out by two suppliers: a domestic firm D and a foreign firm F.6 The government and the firms are risk neutral.7 Let the average cost of implementing the project be c i , i [ hD, Fj. Each firm privately knows its cost. The other firm and the government perceive this cost to be independently drawn from a cumulative distribution function Fi (.), i [ hD, Fj, on Di 5 [c] i , c¯ i ] Assume Fi (.) is continuously differentiable, with derivative fi (.). To characterize the optimal mechanism, we restrict attention to the regular case, which corresponds to the assumption that the hazard rate Fi (.) /fi (.) is non decreasing.8 We assume that the government seeks to maximize a weighted average of consumer surplus and domestic profit. It faces a mechanism design problem and has to design its procurement policy to maximize the expected domestic welfare subject to the constraints imposed by its lack of information about the suppliers’ costs. From the revelation principle (Myerson, 1981), we know that for any possible mechanism, there is an equivalent direct revealing mechanism in which the firms reveal their production cost and the project is awarded and payments are made according to the revealed costs. An optimal procurement mechanism can be summarized by four functions h pi (c), t i (c)j, i [ hD, Fj, where pi (c) and t i (c) are the probability of awarding the project and the expected payment to firm i and 5
The same analysis can be applied to the acquisition of an indivisible commodity. The results can be easily generalized to n firms. 7 The possibility of discrimination is linked to the possibility of arbitrage. So we assume that the government can prevent costless arbitrage among the bidders after awarding the contract. 8 ¨ This assumption is satisfied when F(.) is log-concave (see Bagnoli and Bergstom, 1989) and by most usual distributions. 6
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
353
c5(c D , c F ) is the vector of true costs. Thus the government’s problem is to choose the functions that maximize the expected social surplus subject to incentive compatibility, participation and possibility constraints. Let l .0 denote the shadow cost of public funds 9 and a, 0# a #1, the domestic firm profit weight. For simplicity, we suppose that the social value of the project is so high that it is worth producing for any c i .10 Let Ui (c i ) 5 Ec 2i (t i (c) 2 c i pi (c)) firm i’s expected utility. The government’s objective function is:
E
W 5 h( pD (c) 1 pF (c))S 2 (1 1 l)(t D (c) 1 t F (c)) 1 a (t D (c) 2 c D pD (c)j f(c) dc D
(1) with D 5 DD 3 DF and f(c)5fD (c D ).fF (c F ).W can be written:
E
W 5 h(S 2 (1 1 l)c D )pD (c) 1 (S 2 (1 1 l)c F )pF (c) D
2 (1 1 l 2 a )(t D (c) 2 c D .pD (c)) 2 (1 1 l)(t F (c) 2 c F .pF (c))j f(c) dc
(2)
As a #1, when l .0, the government dislikes leaving a rent to the supplier. Moreover, the government prefers this rent to go to the domestic firm as soon as a .0. The optimal mechanism minimizes the expected rent while at the same time considering the rent of each potential supplier differently. The existence of l and a leads to consider a distributional problem between consumers / taxpayers and suppliers and among suppliers. To characterize the optimal mechanism, three kinds of constraints must be considered (if we normalize the firms’ reservation utility to 0):
1. individual rationality constraints ;i Ui (c i ) $ 0 ;c i [ Di
(3)
2. incentive compatibility constraints ;i Ui (c i ) 5 Ui (c i , c i ) $ Ui (cˆ i , c i );c i , cˆ i [ Di
(4)
with Ui (cˆ i , c i ) 5 Ec 2i (t(cˆ i , c 2i ) 2 c i .p(cˆ i , c 2i )) 9 In the absence of lump sum transfer, the government must resort to distortionary taxation (see Meade, 1944, Vickrey, 1952 and for an estimation Ballard et al., 1985). 10 If S is not too large, the generalization of the results is straightforward.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
354
3. possibility constraints ;c [ D ;i pi (c) $ 0 and pD (c) 1 pF (c) 5 1
(5)
The Envelope Theorem applied to the maximization of (4) with respect to cˆ i yields dUi (c i ) ]] 5 2 E pi (c i , c 2i ) 5 2 Q i (c i ) c 2i dc i
(6)
which is a local incentive condition. From (6), Ui (c i ) is strictly decreasing in c i . So the individual rationality constraint is satisfied if Ui (c]i ) $ 0. It can be proved that condition (6) is sufficient if eD j pi (c i , c j )fj (c) dc j is non increasing in c i . Integrating (6) yields: c¯ i
E
Ui (c i ) 5 Ui (c¯ i ) 1 Q i (s i ) ds i
(7)
ci
Expected domestic welfare can then be written, after integrating by parts: W 5 2 (1 1 l 2 a )U (c] ) 2 (1 1 l)U (c] ) D
1
EHFS 2 (1 1 l)c D
F
D
D
F
F
G
FD (c D ) 2 (1 1 l 2 a )]] pD (c) fD (c D )
S
FF (c F ) 1 S 2 (1 1 l) c F 1 ]] fF (c F )
DG J
pF (c) f(c) dc
The optimal mechanism is the solution of the pointwise maximization of W with respect to pi (c) under pi (c) non increasing in c i and of the maximization of W with respect to Ui (c] i ), under Ui (c] i ) $ 0. We then obtain the following proposition, similar to those of Myerson (1981) and McAfee and McMillan (1989): Proposition 1. The optimal mechanism satisfies .U (c] ) 5 0 ;i i
i
.pD (c) 5 1 and pF (c) 5 0 if
S
D
S
FD (c D ) FF (c F ) (1 1 l 2 a ) c D 1 ]] 1 a c D , (1 1 l) c F 1 ]] fD (c D ) fF (c F )
D
(8)
Proposition 1 deserves some comment. Let us denote FD (c D ) and FF (c F ) respectively the left-hand and the right-hand sides of (8). Under our assumptions, these functions are strictly increasing and can be inverted. Then pD (c)51 and pF (c)50 if c D , F D21 (FF (c F )) ; DD (c F ). There is discrimination in favor of the
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
355
domestic firm if DD (c F ).c F . Symmetrically, pF (c)51 and pD (c)50 if c F # F F21 (FD (c D )) ; DF (c D ). The foreign firm is discriminated against if DF (c D ) , c D . Moreover, these conditions determine a break-even level c F* of c F or c *D of c D such that the foreign firm or the domestic firm never wins if its cost is greater than this value. Thus, DD (c *F ) 5c] D and DF (c *D ) 5c] F and Ui (c i ) 5 0 ;c i [ [c *i , c¯ i ].
3. Characterization of the discriminatory policy Proposition 1 includes the results of McAfee and McMillan (1989) and Branco (1994) as particular cases. The two causes of discrimination appear in the awarding rule. (8) can be written
S
FF (c F ) FD (c D ) FD (c D ) a c D 2 c F , ]] 2 ]] 1 ]] ]] 1 1 l fD (c D ) fF (c F ) fD (c D )
D
(9)
The first cause of discrimination results from the fact that the government places a positive weight on domestic profit. It can be considered as a favoritism effect: the government gives preferential treatment to the domestic firm by adding (a /(1 1 l))(FD (c D ) /fD (c D )) to the foreign firm’s cost. The second is a consequence of comparative advantages. When firms’ costs differ systematically, it appears as a competition stimulation effect. The government adds FF (c F ) /fF (c F ) 2 FD (c D ) / fD (c D ) to the foreign cost. If FF (c˜ ) /fF (c˜ ) $ FD (c˜ ) /fD (c˜ ) (hazard rate dominance) and if FF (c˜ )$FD (c˜ ) (first order stochastic dominance), the distribution FF (.) is more favorable than the distribution FD (.): it puts more weight on low costs. Then, the government adds a positive term to the foreign cost when the foreign firm is (on average) more eager to sell than the domestic firm. By increasing competition pressure on the low cost firm, the government forces it to bid lower.11 When the low-cost firm is the foreign firm, discrimination against the foreign firm is heavier. It is reduced when the domestic firm has a comparative advantage over the foreign firm. (9) can be rewritten with respect to the Ramsey term b 5(11 l 2 a ) /(11 l): FF (c F ) FD (c D ) c D , c F 1 ]] 2 b ]] fF (c F ) fD (c D )
(10)
Discrimination thus varies according to the sign of FF (c F ) /fF (c F ) 2 b FD (c D ) / fD (c D ). Table 1 summarizes the different cases. We can observe that the discrimination based on favoritism works in favor of domestic firms for all industries while the discrimination based on cost advantages varies from industry to industry. Then the government should offer preferential 11 As noted by McAfee and McMillan (1989), favoring the high-cost firm resolves the trade-off between the increase in procurement cost resulting from the increase of the probability that a high-cost firm wins and its reduction resulting from a higher competitive pressure on the low-cost firm.
356
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
Table 1 Characterization of the optimal discrimination
a 50, b 51
0, a #1, b ,1
FF (c F ) /fF (c F ) . FD (c D ) /fD (c D )
Discrimination in favor of the domestic firm (competition stimulation effect)
Discrimination in favor of the domestic firm (competition stimulation effect plus favoritism)
FF (c F ) /fF (c F ) 5 FD (c D ) /fD (c D )
No discrimination
Discrimination in favor of the domestic firm (pure favoritism)
FF (c F ) /fF (c F ) , FD (c D ) /fD (c D )
Discrimination in favor of the foreign firm (competition stimulation effect)
Discrimination in favor of the domestic (foreign) firm if FF (c F ) /fF (c F ).(,)b FD (c D ) /fD (c D ) No discrimination if FF (c F ) /fF (c F )5 b FD (c D ) /fD (c D )
treatment to comparative-disadvantage domestic industries and to some comparative-advantage industries. Owing to the social cost of public funds, the government should not always offer preferences to the domestic firm, even if the domestic firm’s profit enters the government’s objective.12 Note that the discriminatory rule implies that the low cost firm may not be the winner and that optimal public procurement without discrimination appears as a special case. Discriminatory treatment of a domestic or a foreign firm is a general rule as soon as the two firms are a priori different and / or the government takes care, even with a very low weight, of the domestic firm’s rent. Therefore, international regulations that enforce nondiscriminatory policies seem to be justified only in the absence of comparative advantages or when governments just take care of consumer surplus. As claimed by McAfee and McMillan, the zero preference is not the appropriate benchmark for evaluating the effect of public procurement regulations.
12 This result differs from McAfee and McMillan’s result because these authors do not take the social cost of public funds into account. A straightforward generalization of Theorem 3 of McAfee and McMillan (1989) shows that the government gives preferential treatment to the domestic firm (resp. foreign firm) if and only if FF (c˜ ) b /FD (c˜ ) is strictly decreasing (resp. increasing). Moreover, as usual in the optimal auction theory (see Bulow and Roberts, 1989 and Cairns, 1993), the optimal policy can also be interpreted according to the notion of third degree price discrimination. If ´i (c˜ ) is the elasticity of the probability that firm i has a cost of c˜ or less, discrimination works in favor of the domestic firm (resp. foreign firm) if b´F (c˜ ) . ´D (c˜ ) (resp. b´F (c˜ ) , ´D (c˜ )) and there is no discrimination if there is equality.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
357
4. Implementation As usual in the auction theory, the optimal direct mechanism can be implemented by two kinds of bidding rules: a second price auction or a first price auction, both modified with respect to the standard tendering mechanisms to take care of the optimal discrimination. This problem is not considered in McAfee and McMillan (1989), and Branco (1994) only gives an example. In this section, we define the two bidding procedures which implement the optimal mechanism defined in Section 3.
4.1. Modified second price auction This mechanism results directly from the previous developments. From (9), pD 51 if c D ,DD (c F ). Therefore the payment rules can be obtained from the definition of profit and using (7). Then: c¯ i
E p (s , c ) ds
t i (c) 5 c i .pi (c) 1
i
i
j
i
(11)
ci
which can be written t D (c) 5 Min(c¯ D , DD (c F )) if pD (c)51 and 0 otherwise. In the same way, as pF (c)51 if c F #DF (c D )), t F (c)5Min(c¯ F , DF (c D )) if pF (c)51 and 0 otherwise. Then we can characterize that auction by the following proposition. Proposition 2. The optimal mechanism can be implemented by a modified second price auction where: 1. Firms D and F transmit bids b D 5c D and b F 5c F ( because this auction results directly from the optimal mechanism, bidding its true cost is an optimal strategy) 2. bid b D is compared with DD (b F ) 3. if b D ,DD (b F ), the domestic firm wins the auction and receives a payment equal to Min(c¯ D , DD (b F )). If b D $DD (b F ), the foreign firm wins and receives a payment equal to Min(c¯ F , DF (b D )). 4. the firm which loses the auction neither pays nor receives anything. This auction is a Vickrey (1961) type auction belonging to the second price auction family insofar as the winner receives a payment which depends only on the other firm’s bid. We can observe that the discriminatory awarding rule D(.) which is defined over costs is not as simple as claimed by Branco (1994). Even in the case of a uniform distribution of costs on [c] i , c¯ i ], the preference rate
358
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
r5(c D 2c F ) /c F is defined as a fixed percentage only when c] D 5c] F 5 0. In the other cases, the preference rate varies non linearly with the level of the costs.
4.2. Modified first price auction The auction characterized by Proposition 2 is rather different from the standard tendering mechanisms in which the winner receives a payment equal to its bid. Due to legal requirements, public procurement auctions are often organized as first price sealed bid auctions. For such an auction to implement the optimal mechanism, the awarding rule (9) must be modified so as to depend on the bids transmitted. Let us first consider the domestic firm’s strategy. The discrimination based on the bids must necessarily correspond to the discrimination over the costs. Then, when the domestic firm’s cost is c D , its winning probability is equal to 12FF (DF (c D )). When the domestic firm uses its optimal strategy b D (.), a first order condition is dU(c˜ D , c D ) ]]] dc˜ D
U
c˜ D 5c D
5 0 ;c D
with U(c˜ D , c D ) 5 (b(c˜ D ) 2 c D )(1 2 FF (DF (c˜ D ))). Then, b D9 (c D )(1 2 FF (DF (c D ))) 2 (b D (c D ) 2 c D )fF (DF (c D ))D F9 (c D ) 5 0 ;c D This is a differential equation whose solution is, if we assume b D (c D* )5c *D and b D (c D )5c D for c D .c D* , with c *D 5hMin c D /(12FF (DF (c D )))50j *
cD
5
E (1 2 F (D (s))) ds F
F
cD
b D (c D ) 5 max c D , c D 1 ]]]]]] 1 2 FF (DF (c D ))
6
(12)
Similarly, by inverting the F and D indexes in (12), we obtain the foreign firm’s optimal strategy b F (c F ). As DD (c F ) and DF (c D ) are continuous and increasing over [c] F , c *F ] and [c] D , c D* ],13 b D (.) and b F (.) are increasing over these ranges. The awarding rule defined on the bids can be inferred from the awarding rule (8) defined on the costs by inverting the bidding strategies. Using the definition of DD (c F ), we have for c D [ [c] D , c D* ],14 pD (b D ) 5 1 if b D , b D (DD (c F )) ; D 1D (b F ) 13 14
In some cases, c i must be replaced by c *i * with c i* *5hmax c i /(12Fj (Dj (c i )))51, j ±ij ] 21 with DD (c F ) ; F 21 D (FF (b F (b F ))).
(13)
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
359
When c i* , c i for i[hD, Fj, firm j, j±i always wins the auction. Therefore, the first price auction that implements the optimal mechanism is defined by Proposition 3 Proposition 3. The optimal mechanism can be implemented by a modified first price auction such that 1. The two firms submit bids b D (c D ) and b F (c F ) defined by (12) 2. The domestic firm wins the auction if b D ,D 1D (b F ) and receives a payment equal to its bid b D 3. if b D .D 1D (b F ), the foreign firm wins and receives a payment equal to its bid b F 4. the firm which loses the auction neither pays nor receives anything. The modified first price auction in Branco (1994) is an illustration of this mechanism in the case of a uniform distribution function on [0,1]. The discriminatory rule based on bids is very complex even in the case of a fixed percentage preference rule over costs. It is generally non optimal for the government to employ a first price sealed bid auction and announce a linear price preference prior to bidding competition.15 This complexity can be an obstacle to the implementation of the optimal policy and we must note that the usual preference rules such as the Buy American Act are not optimal. As the two auctions defined in Propositions 2 and 3 implement the optimal mechanism, it can be verified that they give the same expected surplus and that the winning probabilities and the expected payments are equal in the two auctions.16 We then obtain a result which looks like the conclusion of the equivalence revenue theorem.
5. The optimal policy with adverse selection and moral hazard. According to the previous results, there is a discrimination in favor of the domestic firm if the foreign firm is on average the low cost firm and / or if there is a positive weight affecting the domestic firm’s profit. However, this does not induce the domestic firm to reduce its cost and it may remain less efficient in the long term. The previous model, which includes an exogenous constant marginal cost assumption, could not take this traditional drawback of protectionist policies into account. To formalize the discretionary actions that a firm may undertake to affect its cost, suppose that the cost functions are Ci 5c i 2e i , where c i is a non 15 So we cannot obtain an equivalence between our price preference policy and a tariff policy as in Kim (1994). 16 A complete proof of this result is available on request.
360
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
observable efficiency parameter and e i , e i $0, the firm’s non observable effort to reduce its cost. In such a situation, concerns about both adverse selection and moral hazard are present. When the two firms exert effort level e, they incur a disutility whose monetary value is w (e), with w (0)50, w 9(e).0, w 0(e).0 and w 90(e)$0. For expositional simplicity, we will consider a quadratic disutility function w (e)5e 2 / 2d, where d is a positive constant. We assume that ex-post cost is costlessly observable.17 The government is then able to reimburse the observed cost and compensate the winning firm by an additional monetary transfer t i (for it to accept to work). Each firm’s utility is Ui 5t i 2 w (e i ) when it undertakes the project and exerts effort e i . We consider that the government organizes an auction to select the firm. Thus, our framework is similar to Laffont and Tirole (1987). However, the model developed in this section departs from the Laffont and Tirole model because cost parameters c i are drawn from different distributions and because the foreign firm’s profit is not relevant for domestic welfare. Under incomplete information and holding our previous assumptions on the government’s objective function and the FF (.) and FD (.) functions, a revelation mechanism is a set of awarding functions pi (c), of monetary net transfers t i (c) and of cost targets Ci (c) with respect to the c vector, inducing truth telling from the firms and maximizing the expected domestic surplus.
5.1. The optimal mechanism From the revelation principle, the government must choose the functions pi (c), t i (c), Ci (c) that maximize the expected domestic social welfare (14) subject to participation constraints (15), incentive compatibility constraints (16) and possibility constraints (17). So it has to solve the following problem:
Max
p(.),t(.),C(.)
E E HSO p (c)DS 2 (1 1 l) O [t (c) 1 p (c)C (c)]
W5
i
DD DF
i
i
i
i
i
J
1 a [t D (c) 2 pD (c)w (e D )] fF (c F )fD (c D ) dc F dc D subject to Ui (c i ) 5 E (t i (c i , c j ) 2 pi (c i , c j )w (e i (c i , c j ))) $ 0 ;c i , ;i c j,j±i
(15)
17 As this must be true for both firms, we may suppose that the project is undertaken on the domestic market, in a Federal country or in an Economic Union where country D can audit cost on country F’s market.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
361
Ui (c i , c i ) 5 E (t i (c i , c j ) 2 pi (c i , c j )w (e i (c i , c j ))) $ Ui (cˆ i , c i ) c j,j±i
5 E (t i (cˆ i , c j ) 2 pi (cˆ i , c j )w (e i (cˆ i , c j ))) ;c i , ;cˆ i , ;i c j,j±i
O p (c) 2 1 5 0 and p (c) $ 0 ;c [ D, ;i i
(16)
(17)
i
i
As Ci (c) is the cost level required from the firm by the government and as the mechanism is revealing, the ex-post cost observability enables us to write e i 5c i 2 Ci and w (e i )5 w (c i 2Ci (c i , c j )). Following the derivations of Laffont and Tirole (1993), we can use the envelope condition (U 9i (c i ) 5 2 Ec j pi (c i , c j )w 9(c i 2 Ci (c i , c j ))) to integrate by parts. Then we can write the objective function as
E E HO p (c)[S 2 (1 1 l)[C (c ) 1 w(c 2 C (c ))]]
W5
i
DD DF
i
i
i
i
i
i
F
FD (c D ) 2 (1 1 l 2 a ) w 9(c D 2 CD (c D ))pD (c D , c F ) ]] fD (c D )
F
G
G
FF (c F ) 2 (1 1 l) [w 9(c F 2 CF (c F ))pF (c D , c F ) ]] 2 (1 1 l 2 a )UD (c¯ D ) fF (c F )
J
2 (1 1 l)UF (c¯ F ) fF (c F )fD (c D ) dc F dc D
(18)
As W is decreasing in Ui (c¯ i ), at the optimum, UF (c¯ F ) 5 UD (c¯ D ) 5 0. Maximizing pointwise with respect to CD (.) and CF (.) implies that the optimal effort levels required from the firms are solutions of [1 2 w 9(e D (c D ))] 5 bw 0(e D (c D ))FD (c D ) /fD (c D )
(19)
[1 2 w 9(e F (c F ))] 5 w 0(e F (c F ))FF (c F ) /fF (c F )
(20)
As Fi (.) /fi (.) is non decreasing, the two effort functions are non increasing. For the quadratic disutility of effort, we have for c D 5 c F 5 c˜ e D (c˜ ) 5 d 2 b FD (c˜ ) /fD (c˜ )
(21)
e F (c˜ ) 5 d 2 b FF (c˜ ) /fF (c˜ )
(22)
The first best effort level (under complete information, w ’(e)51 and e*5d) is exerted only by the firm with the lowest cost c] i . Note that the effort level for the two firms is the same as the effort that would be obtained in the monopoly case with the same government utility function. This is the separation property obtained independently by Laffont and Tirole (1987), Riordan and Sappington (1987) and
362
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
McAfee and McMillan (1989). However, in our asymmetric auction, the effort levels required from the domestic and foreign firms differ. The comparison of the optimal effort levels obtained in (21) and (22) allows us to state Proposition 4. Proposition 4. When the effort disutility is quadratic, the optimal effort level e *D (c D ) is greater than (equal to or lower than) the optimal effort level e *F (c F ) if and only if FF (c F ) /fF (c F ) is greater than (equal to or lower than) b FD (c D ) /fD (c D ) with b 5(11 l 2 a ) /(11 l). Table 2 summarizes the implications of Proposition 4 with respect to the values of l and a and to the respective hazard rates. Some consequences of Proposition 4 are rather counter-intuitive. First, the effort assigned to the domestic firm is all the higher as the government puts a high weight on the domestic profit in its objective function and as the foreign firm has cost advantages. Second, the effort assigned to the domestic firm is higher than the effort assigned to the foreign firm when FF (c F ) /fF (c F ) 2 b FD (c D ) /fD (c D ) . 0, i.e. in the conditions of a discrimination in favor of the domestic firm as defined in (9). As a matter of fact, following Proposition 4, a higher effort is assigned to the favored firm designed by (9). We still have to define the awarding rule. The expected surplus is maximized when pD (c)51 and pF (c)50 if
F F
G
FD (c D ) S 2 (1 1 l) c D 2 e D (c D ) 1 w (e D (c D )) 1 bw 9(e D (c D )) ]] . fD (c D ) FF (c F ) S 2 (1 1 l) c F 2 e F (c F ) 1 w (e F (c F )) 1 w 9(e F (c F )) ]] fF (c F )
G
(23)
Then, from (21) and (22) with a quadratic effort disutility
F
FF (c F ) FD (c D ) b 2 FD (c D ) c D , c F 1 ]] 2 b ]] 1 ] ]] 2d fD (c D ) fF (c F ) fD (c D )
G
2
F
1 FF (c F ) 2 ] ]] 2d fF (c F )
G
2
Table 2 Comparison of optimal effort levels
a 50, b 51
0, a #1, b ,1
FF (c F ) /fF (c F ) . FD (c D ) /fD (c D )
e *D (c D ).e F* (c F )
e D* (c D ).e F* (c F )
FF (c F ) /fF (c F ) 5 FD (c D ) /fD (c D )
e *D (c D )5e F* (c F )
e D* (c D ).e F* (c F )
FF (c F ) /fF (c F ) , FD (c D ) /fD (c D )
e D* (c D ).e F* (c F )
e D* (c D ) 5e F* (c F ) if FF (c F ) /fF (c F ) 5FD (c D ) /fD (c D )
.
.
,
,
(24)
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
363
and after rearranging, we obtain Proposition 5. Proposition 5. When the effort disutility function is quadratic, the awarding rule can be written: pD (c)51 and pF (c)50 if
F
FF (c F ) FD (c D ) c D , c F 1 ]] 2 b ]] fF (c F ) fD (c D )
GF
G
FF (c F ) FD (c D ) 2d 2 ]] 2 b ]] / 2d fF (c F ) fD (c D )
(25)
The awarding rule defined in (25) is a discriminatory rule. As was made for (9), (25) can be written: c D ,D eD (c F ). The foreign firm is discriminated against if D De (c F ).c F . More generally, the nature of the discrimination policy depends on the hazard rates, the announced costs, the effort disutility and the a and l parameters. To compare this result with the policy defined by Proposition 1 in the adverse selection case, let us consider the different cases involved with (25). The identity of the discriminated against firm depends on the sign of the product of the bracketed terms. The second bracketed term is positive as soon as the effort of one of the two firms is positive: as e *D is positive if b FD (c D ) /fD (c D ),d and e F* is positive if FF (c F ) /fF (c F ),d, b FD (c D ) /fD (c D )1FF (c F ) /fF (c F ),2d. The identity of the discriminated against firm depends then on the sign of FF (c F ) /fF (c F )2 b FD (c D ) /fD (c D ), which is exactly the condition defined by (10) in the adverse selection case. Taking moral hazard into account does not modify the discriminatory policy, which is defined in Table 1. The complementarity of the awarding rule and the cost target is then obvious. It is a consequence of the separation property. The awarding rule is used to obtain allocative efficiency and is the same as if there were no moral hazard. The preferential treatment does not change the effort level of the winning firm. The transfer is used to obtain productive efficiency. To give incentives for the firms to reduce their costs, the government has to use the payment rule which consists here of the reimbursement of a cost target C*(c)5C(e*(c)) (the firm that does not reach that target implicitly incurs an infinite penalty) and an additional payment t*.The comparison of Tables 1 and 2 shows that the government must always assign a higher effort to the firm which is favored, whether the domestic or the foreign firm. We now can compare the optimal policy without moral hazard and the optimal policy with moral hazard. From (10) and (24), it can be shown that preferential treatment is lower when the two firms can modify their efficiency by a non observable effort than when the costs are exogenous and this whatever the discrimination may be.
5.2. Definition of the transfers We can elicit the transfers corresponding to the optimal mechanism. As Ui (c¯ i )50, by using the envelope condition and the definition of profit, we obtain the following expected additional transfers ¯t i*
364
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
c¯ j
¯t i* 5
E t (c , c )f (c ) dc i
i
j
j
j
j
cj ] c¯ j
c¯ i
5
¯ cj
E w 9(e (s)) E p (s, c )f (c ) dc ds 1 E p (c , c )w(e (c ))f (c ) dc i
ci
i
j
j
j
j
c ]j
i
i
j
i
i
j
j
j
(26)
c ]j
with pD (c) 51 if c D ,min(c¯ D , D De (c F ) and pF (c)51 if c F #min(c¯ F , D Fe (c D ))
5.3. Implementation by a modified second price auction The optimal mechanism can be implemented by a dominant strategy auction (in which the announcement of the true cost parameter by a firm is a dominant strategy for any bid of the other firm) whose properties look like second price auction properties, but which is modified to take discrimination and incentives to exert effort into account. From (26), when the vector of announced costs is c5(c D , c F ), the additional transfer to firm t Vi (c i , c j ), is defined by min( c¯ i ,D ej (c j ))
t Vi (c i , c j ) 5 w (e i (c i )) 1
E
w 9(e i (s)) ds
if pi (c) 5 1
(27)
ci
50
otherwise
Proposition 6 summarizes these results. Proposition 6. The auction mechanism leading to the same effort function, rent level and firm selection as in the optimal mechanism is the following: 1. firms D and F transmit bids b D 5c D and b F 5c F 2. bid c D is compared with D De (c F ) 3. if c D ,D eD (c F ), the domestic firms wins the auction. Its total payment is equal to the cost target (C *D (c D )5c D 2e D* (c D )) reimbursement plus the corresponding effort disutility w (e *D (c D )) plus an additional rent equal to ¯ D , D eD (c F )) eCmin(c w 9(e D (s)) ds. If c D $D De (c F ), the foreign firm wins the auction D and its total payment is symmetrically equal to the cost target (C *F (c F )5c F 2 e *F (c F )) reimbursement plus the corresponding effort disutility w (e *F (c F )) plus e (c )) ¯ F, D F D an additional rent equal to eCmin(c w 9(e F (s)) ds. D 4. the firms that does not wins the auction neither receives nor pays anything. It is easy to check that the rent the winning firm obtains depends on the other firm’s cost. Moreover, discrimination in the auction amounts to a truncation of the
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
365
interval [c i , c¯ i ] to [c i , D ei (c j )] in the definition of the rent. Then there is a gain in the expected transfer from having an auction. Finally, we can note that, following Laffont and Tirole, the transfer function can be rewritten as a linear contract. It can be decomposed into a transfer a i (c)5t Vi (c) computed at the time of the auction and into a sharing of overruns s i (c i )5 w 9(e *i (c i )). As a consequence of the optimal discriminatory policy, the government must offer a different menu of linear contracts to the two firms. As e D* .e F* when b FD (c D ) /fD (c D ),FF (c F ) /fF (c F ), the domestic firm faces a contract with a greater slope than the slope of the incentive scheme offered to the foreign firm for the same level of the efficiency parameter.
6. Conclusion In this paper, we extended the McAfee and McMillan (1989) and Branco (1994) analyses of government procurement optimal auction. First, we explicitly took into account the local government preferences, the social cost of public funds and the costs differentials in the same model. We studied the properties of the optimal mechanism. This involves discrimination in favor of the domestic firm and in favor of the cost disadvantaged firm. A general rule consists of adding to the domestic cost a term equal to FF (c F ) /fF (c F )2 b FD (c D ) /fD (c D ) whose sign varies according to the prior distributions and the importance attached to domestic profit. Second, we considered the implementation of the optimal policy. We showed that both a modified first price auction and a modified second price auction can give the same expected domestic social surplus. However, the discriminatory awarding rule is in both cases very different from the linear rules used in procurement practices. Even in the case of an economywide preferential policy, the rules are very complex. This was shown by Branco in an example. We showed this to be true in a general framework. Moreover, when we considered cost differentials, the rule had to be differentiated from firm to firm and vary non linearly with the level of the cost. Third, we focused on the familiar drawback of discrimination by taking into account the possibility of reducing the cost. We showed that the awarding rule remains exactly the same when the firms can exert a non observable effort to reduce cost. Thus, discriminatory practices should not be eliminated from considerations of incentives to reduce production costs. Nevertheless, according to the separation property, the government must use the payment rule to induce the domestic firm to reduce its cost when there is a positive social cost of public funds. Our main result is that the government must always assign a higher effort (and then a lower expected cost) to the firm which is favored. It can for instance offer the favored firm an incentive contract with a greater slope than the slope of the scheme offered to the discriminated against firm for the same level of cost. Our results give some justification for protectionism in public procurement. They show that non discriminatory award of public contract is not the appropriate
366
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
way to induce domestic firms to be more efficient when the government is able to observe the expost cost. An open issue could be the analysis of the optimal policy when only the domestic firm’s cost is observable. An other open issue concerns implementation. The standard tendering mechanisms is the first price auction with a percentage preference rule. This auction is not optimal, but the complexity of the optimal modified first price auction can be an obstacle to its implementation. It could be important to design empirical work in such a way as to estimate the welfare losses associated with usual practices. However, it is well known that empirical studies of government practices produce biased estimates (McAfee and McMillan, 1989). Laboratory experiments could help to define the best practicable policy.
References Atkins Management Consultants, 1988. The Cost of Non-Europe: Research on the Cost of Non-Europe. Commission of the European Community, Office for Official Publications of the European Community, Luxembourg. ¨ Bagnoli, M., and Bergstom, T., 1989. Log-concave probability and its applications. CREST WP [89.23, University of Michagan. Baldwin, R.E., Richardson, J.D., 1972. Government purchasing policies, other NTB’s, and the international monetary crisis. In: English, H.H., Hay, K.A.J. (Eds.), Obstacles to Trade in the Pacific Area: Proceedings of the Fourth Pacific Trade Development Conference. Carleton School of International Affairs, Ottawa. Ballard, C.L., Showen, J.B., Whalley, J., 1985. General equilibrium computations of the marginal welfare costs of taxes in US. American Economic Review 75, 128–138. Branco, F., 1994. Favoring domestic firms in procurement contracts. Journal of International Economics 37, 65–80. Breton, A., Salmon, P., 1996. Are discriminatory procurement policies motivated by protectionism?. Kyklos 49, 17–68. Bulow, J., Roberts, J., 1989. The simple analysis of optimal auctions. Journal of Political Economy 97 (5), 1060–1090. Cairns, R.D., 1993. The optimal mechanism, a mechanism for optimal third degree price discrimination. Journal of Economic Behaviour and Organization 20 (2), 213–225. Joson, S.S., 1986. Substitutability of ‘buy local’ policy for tariff protection in small economies. Journal of Policy Modeling 8 (2), 223–239. Kim, I.G., 1994. Price-preference vs. tariff policies in government procurement auctions. Economics Letters 45, 217–222. Laffont, J.J., Tirole, J., 1987. Auctioning incentives contracts. Journal of Political Economy 95, 921–937. Laffont, J.J., Tirole, J., 1991. Auction design and favoritism. International Journal of Industrial Organization 9, 9–42. Laffont, J.J., Tirole, J., 1993. A Theory of Incentives in Procurement and Regulation. MIT Press, Cambridge, MA. McAfee, P., McMillan, J., 1989. Government procurement and international trade. Journal of International Economics 26, 291–308. Meade, J., 1944. Price and output policy of state enterprise. Economic Journal 54, 321–328.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
367
Miyagiwa, K., 1991. Oligopoly and discriminatory government procurement policy. American Economic Review 81, 1320–1328. Myerson, R.B., 1981. Optimal auction design. Mathematics of Operations Research 6, 619–632. Riordan, M., Sappington, D., 1987. Awarding monopoly franchises. American Economic Review 77, 375–387. Robertson, J., 1992. Japan agrees to hike U.S. computers buys. Electronic News 13, January, 1. Vagstad, S., 1995. Promoting fair competition in public procurement. Journal of Public Economics 58, 283–307. Vickrey, W., 1952. The revision of the rapid transit fare structure of the city of New York. Mimeo, Technical monograph No.3, Finance Project. Mayor’s Committee for management survey of the city of New York. Vickrey, W., 1961. Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance 16, 8–37.
Discriminatory public procurement policy and cost reduction incentives Florence Naegelen*, Michel Mougeot Crese, University of Besanc¸on, 25030 Besanc¸on Cedex, France Received 1 June 1996; received in revised form 1 November 1996; accepted 16 April 1997
Abstract Discriminating in favor of domestic suppliers in the award of government procurement contracts is a widespread practice. In this paper, we extend the previous analysis of McAfee and McMillan (1989) [Government procurement and international trade. Journal of International Economics 26, 291–308] and Branco (1994) [Favoring domestic firms in procurement contracts. Journal of International Economics 37, 65–80] by considering in the same model the bidding competition stimulation effect and the favoritism effect. We prove that the optimal policy can be implemented by a modified Vickrey auction or by a complex modified first price auction. We also consider that firms can reduce their cost by a nonobservable effort. We show that taking moral hazard into account does not modify the awarding rule, but that the government must use the payment rule to require a greater level of effort from the favored firm. 1998 Elsevier Science S.A. Keywords: Auctions; Discrimination; Procurement; Moral hazard JEL classification: D44; D82; H57
1. Introduction Discriminating in favor of domestic suppliers in the award of government procurement contracts is a widespread practice in many countries. It can result from an explicit ‘buy local policy’. One example is the United States’ ‘Buy American Act’. The United States government offers a 6 percent preference for *Corresponding author. Tel.: 133 03 81666716; fax: 133 03 81666716. 0047-2727 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII S0047-2727( 97 )00068-6
350
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
domestic suppliers. This preference can be raised to 12 percent in the case of small businesses and firms in regions of high unemployment and 50 percent for military equipment. Explicit domestic preferences have also been applied in Canada, Australia, New Zealand and Turkey.1 Favoritism can also be implicit. For instance, the European governments do not have explicit preferential procurement policies, but according to the Atkins Management Consultants (1988) report, only 2 percent of government procurement contracts are awarded to foreign bidders.2 There is a general agreement that discriminatory policies should be eliminated. International organizations such as GATT and the European Union have set out rules to curb favoritism but, despite these agreements, favoritism continues. According to Vagstad (1995), one important reason is that asymmetric information makes favoritism difficult to detect. Another reason is that governments, even though collectively the source of the prescription, have been reluctant to implement it (Breton and Salmon, 1996). How can the existence of preferential public procurement policies be explained? Protection is often justified by the power of certain interest groups or by infant industry arguments. However, some papers on optimal auction theory show that such a practice could be justified by rational decisions of governments. First, if there are cost advantages for foreign firms, the governments should discriminate in favor of the domestic firms to stimulate competition and minimize expected procurement costs (McAfee and McMillan, 1989). Second, if governments prefer domestic to foreign profits, they have incentives to discriminate against foreign suppliers (Branco, 1994). These two arguments have been developed in the auction theory framework in partial equilibrium models.3 An essential aspect of procurement policy is that the governments are not likely to be perfectly informed about technological conditions in the suppliers’ industry. The nature of information asymmetry then plays a key role in the explanation of optimal procurement policy. Adverse selection explains the need to organize an auction and can justify some form of discrimination. Discrimination can also result from the government’s utility function. The McAfee-McMillan and Branco arguments refer to different objectives. The first one refers to efficiency and the second to distributional concerns. Let us consider the case where a domestic firm D and a foreign firm F can undertake a single indivisible project for a governmental agency. If costs of the two firms are drawn from the same probability distribution (i.e. if we consider the standard symmetric auction model), the only justification for a discriminatory policy is the existence of a greater 1
EU directive 90 / 531 involves a 3% price preference in natural monopoly sectors (water distribution, energy, transport and telecommunications). 2 The Japanese market for computers is another example: according to Robertson (1992), while US firms have 40% of the private market, their share of the government part of the market is only 0.4%. 3 The general equilibrium approach (see Baldwin and Richardson (1972), Joson (1986) and Miyagiwa (1991) is not taken into consideration here.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
351
weight on the domestic firm’s profit than on the foreign one when the government maximizes a weighted sum of consumer surplus and firms’ profit. Uneven weighting of profits creates favoritism, but favoritism increases procurement costs. If there is a positive social cost of public funds, the government has to trade off the increase of the domestic firm’s profit and the increase in the social cost resulting from the distortionary taxation. If we assume now that firms’ costs differ from country to country (costs of the two firms are drawn from different distributions), a preferential treatment can be used to induce firms to reveal their private information about their cost and prevent the most efficient one from bidding too high (Myerson, 1981 and McAfee and McMillan, 1989). In this paper, we consider the efficiency argument and the distributional argument in the same model. We characterize the optimal policy in the adverse selection case using a direct revelation mechanism.4 We show that the awarding rule amounts to adding to the domestic firm’s cost a term whose sign varies with comparative advantages, the social cost of public funds and the weight attached to the domestic profit. Thus, we obtain a benchmark model that allows us to analyze the trade-off between the protectionist discriminatory policy and the competition stimulation procurement policy. A second problem to consider after defining the optimal policy is the implementation of the optimal mechanism. McAfee and McMillan (1989) only consider the mechanism design approach that can be implemented by a Vickrey type auction. However, most of the procurement auctions are actually first price sealed bid auctions. It would be useful to characterize the first price auction that implements the optimal mechanism. Branco (1994) does it using an example, with the costs of the two firms independently uniformly distributed on [0,1]. In this paper, we prove that the general optimal discriminatory policy can be implemented by a Vickrey type auction in which the winner’s payment is independent from its bid or by a modified first price sealed bid auction, with non linear discriminatory rules. This result is obtained with general assumptions on the costs distributions. The usual drawback of protectionism is that domestic firms have no incentive to minimize cost. When discrimination is in favor of the domestic firm, this firm can win the auction with a higher cost than the foreign one and has no incentive to perform as best it can. To take this effect into account, we consider in this paper that firms can reduce their cost by a non observable effort. As the effort exerted by the firms entails a disutility, the firms must be motivated to make it. Then the government faces simultaneously a moral hazard problem and an adverse selection problem. So we have to consider an asymmetric bidding model that incorporates both moral hazard and adverse selection considerations. To do this, we build our analysis on the auctioning incentive contract model of Laffont and Tirole (1987). Departing from Laffont and Tirole (1987), we assume uneven weighting of profits 4
This paper does not consider favoritism resulting from non verifiable product quality. For an analysis, see Laffont and Tirole (1991), Laffont and Tirole (1993) and Vagstad (1995).
352
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
and asymmetric distributions of costs. Our first result is that the Laffont and Tirole dichotomy property still holds. The government has to use the discriminatory awarding rule to obtain allocative efficiency and the payment rule to obtain productive efficiency. So taking moral hazard into account does not modify the awarding rule defined in the benchmark model: the same term is added to the foreign firm’s cost. Moreover, we show that the government must always require a greater effort level from the favored firm. In Section 2, we present the optimal mechanism in the adverse selection case. Optimal procurement policy is characterized in Section 3. In Section 4, we consider the implementation of that policy by first or second price auctions. In Section 5, we present the optimal mechanism when both moral hazard and adverse selection are present. Section 6 concludes the paper.
2. The optimal mechanism in the adverse selection case Suppose the government wishes to undertake an indivisible project 5 that has value S for consumers. This project can be carried out by two suppliers: a domestic firm D and a foreign firm F.6 The government and the firms are risk neutral.7 Let the average cost of implementing the project be c i , i [ hD, Fj. Each firm privately knows its cost. The other firm and the government perceive this cost to be independently drawn from a cumulative distribution function Fi (.), i [ hD, Fj, on Di 5 [c] i , c¯ i ] Assume Fi (.) is continuously differentiable, with derivative fi (.). To characterize the optimal mechanism, we restrict attention to the regular case, which corresponds to the assumption that the hazard rate Fi (.) /fi (.) is non decreasing.8 We assume that the government seeks to maximize a weighted average of consumer surplus and domestic profit. It faces a mechanism design problem and has to design its procurement policy to maximize the expected domestic welfare subject to the constraints imposed by its lack of information about the suppliers’ costs. From the revelation principle (Myerson, 1981), we know that for any possible mechanism, there is an equivalent direct revealing mechanism in which the firms reveal their production cost and the project is awarded and payments are made according to the revealed costs. An optimal procurement mechanism can be summarized by four functions h pi (c), t i (c)j, i [ hD, Fj, where pi (c) and t i (c) are the probability of awarding the project and the expected payment to firm i and 5
The same analysis can be applied to the acquisition of an indivisible commodity. The results can be easily generalized to n firms. 7 The possibility of discrimination is linked to the possibility of arbitrage. So we assume that the government can prevent costless arbitrage among the bidders after awarding the contract. 8 ¨ This assumption is satisfied when F(.) is log-concave (see Bagnoli and Bergstom, 1989) and by most usual distributions. 6
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
353
c5(c D , c F ) is the vector of true costs. Thus the government’s problem is to choose the functions that maximize the expected social surplus subject to incentive compatibility, participation and possibility constraints. Let l .0 denote the shadow cost of public funds 9 and a, 0# a #1, the domestic firm profit weight. For simplicity, we suppose that the social value of the project is so high that it is worth producing for any c i .10 Let Ui (c i ) 5 Ec 2i (t i (c) 2 c i pi (c)) firm i’s expected utility. The government’s objective function is:
E
W 5 h( pD (c) 1 pF (c))S 2 (1 1 l)(t D (c) 1 t F (c)) 1 a (t D (c) 2 c D pD (c)j f(c) dc D
(1) with D 5 DD 3 DF and f(c)5fD (c D ).fF (c F ).W can be written:
E
W 5 h(S 2 (1 1 l)c D )pD (c) 1 (S 2 (1 1 l)c F )pF (c) D
2 (1 1 l 2 a )(t D (c) 2 c D .pD (c)) 2 (1 1 l)(t F (c) 2 c F .pF (c))j f(c) dc
(2)
As a #1, when l .0, the government dislikes leaving a rent to the supplier. Moreover, the government prefers this rent to go to the domestic firm as soon as a .0. The optimal mechanism minimizes the expected rent while at the same time considering the rent of each potential supplier differently. The existence of l and a leads to consider a distributional problem between consumers / taxpayers and suppliers and among suppliers. To characterize the optimal mechanism, three kinds of constraints must be considered (if we normalize the firms’ reservation utility to 0):
1. individual rationality constraints ;i Ui (c i ) $ 0 ;c i [ Di
(3)
2. incentive compatibility constraints ;i Ui (c i ) 5 Ui (c i , c i ) $ Ui (cˆ i , c i );c i , cˆ i [ Di
(4)
with Ui (cˆ i , c i ) 5 Ec 2i (t(cˆ i , c 2i ) 2 c i .p(cˆ i , c 2i )) 9 In the absence of lump sum transfer, the government must resort to distortionary taxation (see Meade, 1944, Vickrey, 1952 and for an estimation Ballard et al., 1985). 10 If S is not too large, the generalization of the results is straightforward.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
354
3. possibility constraints ;c [ D ;i pi (c) $ 0 and pD (c) 1 pF (c) 5 1
(5)
The Envelope Theorem applied to the maximization of (4) with respect to cˆ i yields dUi (c i ) ]] 5 2 E pi (c i , c 2i ) 5 2 Q i (c i ) c 2i dc i
(6)
which is a local incentive condition. From (6), Ui (c i ) is strictly decreasing in c i . So the individual rationality constraint is satisfied if Ui (c]i ) $ 0. It can be proved that condition (6) is sufficient if eD j pi (c i , c j )fj (c) dc j is non increasing in c i . Integrating (6) yields: c¯ i
E
Ui (c i ) 5 Ui (c¯ i ) 1 Q i (s i ) ds i
(7)
ci
Expected domestic welfare can then be written, after integrating by parts: W 5 2 (1 1 l 2 a )U (c] ) 2 (1 1 l)U (c] ) D
1
EHFS 2 (1 1 l)c D
F
D
D
F
F
G
FD (c D ) 2 (1 1 l 2 a )]] pD (c) fD (c D )
S
FF (c F ) 1 S 2 (1 1 l) c F 1 ]] fF (c F )
DG J
pF (c) f(c) dc
The optimal mechanism is the solution of the pointwise maximization of W with respect to pi (c) under pi (c) non increasing in c i and of the maximization of W with respect to Ui (c] i ), under Ui (c] i ) $ 0. We then obtain the following proposition, similar to those of Myerson (1981) and McAfee and McMillan (1989): Proposition 1. The optimal mechanism satisfies .U (c] ) 5 0 ;i i
i
.pD (c) 5 1 and pF (c) 5 0 if
S
D
S
FD (c D ) FF (c F ) (1 1 l 2 a ) c D 1 ]] 1 a c D , (1 1 l) c F 1 ]] fD (c D ) fF (c F )
D
(8)
Proposition 1 deserves some comment. Let us denote FD (c D ) and FF (c F ) respectively the left-hand and the right-hand sides of (8). Under our assumptions, these functions are strictly increasing and can be inverted. Then pD (c)51 and pF (c)50 if c D , F D21 (FF (c F )) ; DD (c F ). There is discrimination in favor of the
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
355
domestic firm if DD (c F ).c F . Symmetrically, pF (c)51 and pD (c)50 if c F # F F21 (FD (c D )) ; DF (c D ). The foreign firm is discriminated against if DF (c D ) , c D . Moreover, these conditions determine a break-even level c F* of c F or c *D of c D such that the foreign firm or the domestic firm never wins if its cost is greater than this value. Thus, DD (c *F ) 5c] D and DF (c *D ) 5c] F and Ui (c i ) 5 0 ;c i [ [c *i , c¯ i ].
3. Characterization of the discriminatory policy Proposition 1 includes the results of McAfee and McMillan (1989) and Branco (1994) as particular cases. The two causes of discrimination appear in the awarding rule. (8) can be written
S
FF (c F ) FD (c D ) FD (c D ) a c D 2 c F , ]] 2 ]] 1 ]] ]] 1 1 l fD (c D ) fF (c F ) fD (c D )
D
(9)
The first cause of discrimination results from the fact that the government places a positive weight on domestic profit. It can be considered as a favoritism effect: the government gives preferential treatment to the domestic firm by adding (a /(1 1 l))(FD (c D ) /fD (c D )) to the foreign firm’s cost. The second is a consequence of comparative advantages. When firms’ costs differ systematically, it appears as a competition stimulation effect. The government adds FF (c F ) /fF (c F ) 2 FD (c D ) / fD (c D ) to the foreign cost. If FF (c˜ ) /fF (c˜ ) $ FD (c˜ ) /fD (c˜ ) (hazard rate dominance) and if FF (c˜ )$FD (c˜ ) (first order stochastic dominance), the distribution FF (.) is more favorable than the distribution FD (.): it puts more weight on low costs. Then, the government adds a positive term to the foreign cost when the foreign firm is (on average) more eager to sell than the domestic firm. By increasing competition pressure on the low cost firm, the government forces it to bid lower.11 When the low-cost firm is the foreign firm, discrimination against the foreign firm is heavier. It is reduced when the domestic firm has a comparative advantage over the foreign firm. (9) can be rewritten with respect to the Ramsey term b 5(11 l 2 a ) /(11 l): FF (c F ) FD (c D ) c D , c F 1 ]] 2 b ]] fF (c F ) fD (c D )
(10)
Discrimination thus varies according to the sign of FF (c F ) /fF (c F ) 2 b FD (c D ) / fD (c D ). Table 1 summarizes the different cases. We can observe that the discrimination based on favoritism works in favor of domestic firms for all industries while the discrimination based on cost advantages varies from industry to industry. Then the government should offer preferential 11 As noted by McAfee and McMillan (1989), favoring the high-cost firm resolves the trade-off between the increase in procurement cost resulting from the increase of the probability that a high-cost firm wins and its reduction resulting from a higher competitive pressure on the low-cost firm.
356
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
Table 1 Characterization of the optimal discrimination
a 50, b 51
0, a #1, b ,1
FF (c F ) /fF (c F ) . FD (c D ) /fD (c D )
Discrimination in favor of the domestic firm (competition stimulation effect)
Discrimination in favor of the domestic firm (competition stimulation effect plus favoritism)
FF (c F ) /fF (c F ) 5 FD (c D ) /fD (c D )
No discrimination
Discrimination in favor of the domestic firm (pure favoritism)
FF (c F ) /fF (c F ) , FD (c D ) /fD (c D )
Discrimination in favor of the foreign firm (competition stimulation effect)
Discrimination in favor of the domestic (foreign) firm if FF (c F ) /fF (c F ).(,)b FD (c D ) /fD (c D ) No discrimination if FF (c F ) /fF (c F )5 b FD (c D ) /fD (c D )
treatment to comparative-disadvantage domestic industries and to some comparative-advantage industries. Owing to the social cost of public funds, the government should not always offer preferences to the domestic firm, even if the domestic firm’s profit enters the government’s objective.12 Note that the discriminatory rule implies that the low cost firm may not be the winner and that optimal public procurement without discrimination appears as a special case. Discriminatory treatment of a domestic or a foreign firm is a general rule as soon as the two firms are a priori different and / or the government takes care, even with a very low weight, of the domestic firm’s rent. Therefore, international regulations that enforce nondiscriminatory policies seem to be justified only in the absence of comparative advantages or when governments just take care of consumer surplus. As claimed by McAfee and McMillan, the zero preference is not the appropriate benchmark for evaluating the effect of public procurement regulations.
12 This result differs from McAfee and McMillan’s result because these authors do not take the social cost of public funds into account. A straightforward generalization of Theorem 3 of McAfee and McMillan (1989) shows that the government gives preferential treatment to the domestic firm (resp. foreign firm) if and only if FF (c˜ ) b /FD (c˜ ) is strictly decreasing (resp. increasing). Moreover, as usual in the optimal auction theory (see Bulow and Roberts, 1989 and Cairns, 1993), the optimal policy can also be interpreted according to the notion of third degree price discrimination. If ´i (c˜ ) is the elasticity of the probability that firm i has a cost of c˜ or less, discrimination works in favor of the domestic firm (resp. foreign firm) if b´F (c˜ ) . ´D (c˜ ) (resp. b´F (c˜ ) , ´D (c˜ )) and there is no discrimination if there is equality.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
357
4. Implementation As usual in the auction theory, the optimal direct mechanism can be implemented by two kinds of bidding rules: a second price auction or a first price auction, both modified with respect to the standard tendering mechanisms to take care of the optimal discrimination. This problem is not considered in McAfee and McMillan (1989), and Branco (1994) only gives an example. In this section, we define the two bidding procedures which implement the optimal mechanism defined in Section 3.
4.1. Modified second price auction This mechanism results directly from the previous developments. From (9), pD 51 if c D ,DD (c F ). Therefore the payment rules can be obtained from the definition of profit and using (7). Then: c¯ i
E p (s , c ) ds
t i (c) 5 c i .pi (c) 1
i
i
j
i
(11)
ci
which can be written t D (c) 5 Min(c¯ D , DD (c F )) if pD (c)51 and 0 otherwise. In the same way, as pF (c)51 if c F #DF (c D )), t F (c)5Min(c¯ F , DF (c D )) if pF (c)51 and 0 otherwise. Then we can characterize that auction by the following proposition. Proposition 2. The optimal mechanism can be implemented by a modified second price auction where: 1. Firms D and F transmit bids b D 5c D and b F 5c F ( because this auction results directly from the optimal mechanism, bidding its true cost is an optimal strategy) 2. bid b D is compared with DD (b F ) 3. if b D ,DD (b F ), the domestic firm wins the auction and receives a payment equal to Min(c¯ D , DD (b F )). If b D $DD (b F ), the foreign firm wins and receives a payment equal to Min(c¯ F , DF (b D )). 4. the firm which loses the auction neither pays nor receives anything. This auction is a Vickrey (1961) type auction belonging to the second price auction family insofar as the winner receives a payment which depends only on the other firm’s bid. We can observe that the discriminatory awarding rule D(.) which is defined over costs is not as simple as claimed by Branco (1994). Even in the case of a uniform distribution of costs on [c] i , c¯ i ], the preference rate
358
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
r5(c D 2c F ) /c F is defined as a fixed percentage only when c] D 5c] F 5 0. In the other cases, the preference rate varies non linearly with the level of the costs.
4.2. Modified first price auction The auction characterized by Proposition 2 is rather different from the standard tendering mechanisms in which the winner receives a payment equal to its bid. Due to legal requirements, public procurement auctions are often organized as first price sealed bid auctions. For such an auction to implement the optimal mechanism, the awarding rule (9) must be modified so as to depend on the bids transmitted. Let us first consider the domestic firm’s strategy. The discrimination based on the bids must necessarily correspond to the discrimination over the costs. Then, when the domestic firm’s cost is c D , its winning probability is equal to 12FF (DF (c D )). When the domestic firm uses its optimal strategy b D (.), a first order condition is dU(c˜ D , c D ) ]]] dc˜ D
U
c˜ D 5c D
5 0 ;c D
with U(c˜ D , c D ) 5 (b(c˜ D ) 2 c D )(1 2 FF (DF (c˜ D ))). Then, b D9 (c D )(1 2 FF (DF (c D ))) 2 (b D (c D ) 2 c D )fF (DF (c D ))D F9 (c D ) 5 0 ;c D This is a differential equation whose solution is, if we assume b D (c D* )5c *D and b D (c D )5c D for c D .c D* , with c *D 5hMin c D /(12FF (DF (c D )))50j *
cD
5
E (1 2 F (D (s))) ds F
F
cD
b D (c D ) 5 max c D , c D 1 ]]]]]] 1 2 FF (DF (c D ))
6
(12)
Similarly, by inverting the F and D indexes in (12), we obtain the foreign firm’s optimal strategy b F (c F ). As DD (c F ) and DF (c D ) are continuous and increasing over [c] F , c *F ] and [c] D , c D* ],13 b D (.) and b F (.) are increasing over these ranges. The awarding rule defined on the bids can be inferred from the awarding rule (8) defined on the costs by inverting the bidding strategies. Using the definition of DD (c F ), we have for c D [ [c] D , c D* ],14 pD (b D ) 5 1 if b D , b D (DD (c F )) ; D 1D (b F ) 13 14
In some cases, c i must be replaced by c *i * with c i* *5hmax c i /(12Fj (Dj (c i )))51, j ±ij ] 21 with DD (c F ) ; F 21 D (FF (b F (b F ))).
(13)
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
359
When c i* , c i for i[hD, Fj, firm j, j±i always wins the auction. Therefore, the first price auction that implements the optimal mechanism is defined by Proposition 3 Proposition 3. The optimal mechanism can be implemented by a modified first price auction such that 1. The two firms submit bids b D (c D ) and b F (c F ) defined by (12) 2. The domestic firm wins the auction if b D ,D 1D (b F ) and receives a payment equal to its bid b D 3. if b D .D 1D (b F ), the foreign firm wins and receives a payment equal to its bid b F 4. the firm which loses the auction neither pays nor receives anything. The modified first price auction in Branco (1994) is an illustration of this mechanism in the case of a uniform distribution function on [0,1]. The discriminatory rule based on bids is very complex even in the case of a fixed percentage preference rule over costs. It is generally non optimal for the government to employ a first price sealed bid auction and announce a linear price preference prior to bidding competition.15 This complexity can be an obstacle to the implementation of the optimal policy and we must note that the usual preference rules such as the Buy American Act are not optimal. As the two auctions defined in Propositions 2 and 3 implement the optimal mechanism, it can be verified that they give the same expected surplus and that the winning probabilities and the expected payments are equal in the two auctions.16 We then obtain a result which looks like the conclusion of the equivalence revenue theorem.
5. The optimal policy with adverse selection and moral hazard. According to the previous results, there is a discrimination in favor of the domestic firm if the foreign firm is on average the low cost firm and / or if there is a positive weight affecting the domestic firm’s profit. However, this does not induce the domestic firm to reduce its cost and it may remain less efficient in the long term. The previous model, which includes an exogenous constant marginal cost assumption, could not take this traditional drawback of protectionist policies into account. To formalize the discretionary actions that a firm may undertake to affect its cost, suppose that the cost functions are Ci 5c i 2e i , where c i is a non 15 So we cannot obtain an equivalence between our price preference policy and a tariff policy as in Kim (1994). 16 A complete proof of this result is available on request.
360
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
observable efficiency parameter and e i , e i $0, the firm’s non observable effort to reduce its cost. In such a situation, concerns about both adverse selection and moral hazard are present. When the two firms exert effort level e, they incur a disutility whose monetary value is w (e), with w (0)50, w 9(e).0, w 0(e).0 and w 90(e)$0. For expositional simplicity, we will consider a quadratic disutility function w (e)5e 2 / 2d, where d is a positive constant. We assume that ex-post cost is costlessly observable.17 The government is then able to reimburse the observed cost and compensate the winning firm by an additional monetary transfer t i (for it to accept to work). Each firm’s utility is Ui 5t i 2 w (e i ) when it undertakes the project and exerts effort e i . We consider that the government organizes an auction to select the firm. Thus, our framework is similar to Laffont and Tirole (1987). However, the model developed in this section departs from the Laffont and Tirole model because cost parameters c i are drawn from different distributions and because the foreign firm’s profit is not relevant for domestic welfare. Under incomplete information and holding our previous assumptions on the government’s objective function and the FF (.) and FD (.) functions, a revelation mechanism is a set of awarding functions pi (c), of monetary net transfers t i (c) and of cost targets Ci (c) with respect to the c vector, inducing truth telling from the firms and maximizing the expected domestic surplus.
5.1. The optimal mechanism From the revelation principle, the government must choose the functions pi (c), t i (c), Ci (c) that maximize the expected domestic social welfare (14) subject to participation constraints (15), incentive compatibility constraints (16) and possibility constraints (17). So it has to solve the following problem:
Max
p(.),t(.),C(.)
E E HSO p (c)DS 2 (1 1 l) O [t (c) 1 p (c)C (c)]
W5
i
DD DF
i
i
i
i
i
J
1 a [t D (c) 2 pD (c)w (e D )] fF (c F )fD (c D ) dc F dc D subject to Ui (c i ) 5 E (t i (c i , c j ) 2 pi (c i , c j )w (e i (c i , c j ))) $ 0 ;c i , ;i c j,j±i
(15)
17 As this must be true for both firms, we may suppose that the project is undertaken on the domestic market, in a Federal country or in an Economic Union where country D can audit cost on country F’s market.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
361
Ui (c i , c i ) 5 E (t i (c i , c j ) 2 pi (c i , c j )w (e i (c i , c j ))) $ Ui (cˆ i , c i ) c j,j±i
5 E (t i (cˆ i , c j ) 2 pi (cˆ i , c j )w (e i (cˆ i , c j ))) ;c i , ;cˆ i , ;i c j,j±i
O p (c) 2 1 5 0 and p (c) $ 0 ;c [ D, ;i i
(16)
(17)
i
i
As Ci (c) is the cost level required from the firm by the government and as the mechanism is revealing, the ex-post cost observability enables us to write e i 5c i 2 Ci and w (e i )5 w (c i 2Ci (c i , c j )). Following the derivations of Laffont and Tirole (1993), we can use the envelope condition (U 9i (c i ) 5 2 Ec j pi (c i , c j )w 9(c i 2 Ci (c i , c j ))) to integrate by parts. Then we can write the objective function as
E E HO p (c)[S 2 (1 1 l)[C (c ) 1 w(c 2 C (c ))]]
W5
i
DD DF
i
i
i
i
i
i
F
FD (c D ) 2 (1 1 l 2 a ) w 9(c D 2 CD (c D ))pD (c D , c F ) ]] fD (c D )
F
G
G
FF (c F ) 2 (1 1 l) [w 9(c F 2 CF (c F ))pF (c D , c F ) ]] 2 (1 1 l 2 a )UD (c¯ D ) fF (c F )
J
2 (1 1 l)UF (c¯ F ) fF (c F )fD (c D ) dc F dc D
(18)
As W is decreasing in Ui (c¯ i ), at the optimum, UF (c¯ F ) 5 UD (c¯ D ) 5 0. Maximizing pointwise with respect to CD (.) and CF (.) implies that the optimal effort levels required from the firms are solutions of [1 2 w 9(e D (c D ))] 5 bw 0(e D (c D ))FD (c D ) /fD (c D )
(19)
[1 2 w 9(e F (c F ))] 5 w 0(e F (c F ))FF (c F ) /fF (c F )
(20)
As Fi (.) /fi (.) is non decreasing, the two effort functions are non increasing. For the quadratic disutility of effort, we have for c D 5 c F 5 c˜ e D (c˜ ) 5 d 2 b FD (c˜ ) /fD (c˜ )
(21)
e F (c˜ ) 5 d 2 b FF (c˜ ) /fF (c˜ )
(22)
The first best effort level (under complete information, w ’(e)51 and e*5d) is exerted only by the firm with the lowest cost c] i . Note that the effort level for the two firms is the same as the effort that would be obtained in the monopoly case with the same government utility function. This is the separation property obtained independently by Laffont and Tirole (1987), Riordan and Sappington (1987) and
362
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
McAfee and McMillan (1989). However, in our asymmetric auction, the effort levels required from the domestic and foreign firms differ. The comparison of the optimal effort levels obtained in (21) and (22) allows us to state Proposition 4. Proposition 4. When the effort disutility is quadratic, the optimal effort level e *D (c D ) is greater than (equal to or lower than) the optimal effort level e *F (c F ) if and only if FF (c F ) /fF (c F ) is greater than (equal to or lower than) b FD (c D ) /fD (c D ) with b 5(11 l 2 a ) /(11 l). Table 2 summarizes the implications of Proposition 4 with respect to the values of l and a and to the respective hazard rates. Some consequences of Proposition 4 are rather counter-intuitive. First, the effort assigned to the domestic firm is all the higher as the government puts a high weight on the domestic profit in its objective function and as the foreign firm has cost advantages. Second, the effort assigned to the domestic firm is higher than the effort assigned to the foreign firm when FF (c F ) /fF (c F ) 2 b FD (c D ) /fD (c D ) . 0, i.e. in the conditions of a discrimination in favor of the domestic firm as defined in (9). As a matter of fact, following Proposition 4, a higher effort is assigned to the favored firm designed by (9). We still have to define the awarding rule. The expected surplus is maximized when pD (c)51 and pF (c)50 if
F F
G
FD (c D ) S 2 (1 1 l) c D 2 e D (c D ) 1 w (e D (c D )) 1 bw 9(e D (c D )) ]] . fD (c D ) FF (c F ) S 2 (1 1 l) c F 2 e F (c F ) 1 w (e F (c F )) 1 w 9(e F (c F )) ]] fF (c F )
G
(23)
Then, from (21) and (22) with a quadratic effort disutility
F
FF (c F ) FD (c D ) b 2 FD (c D ) c D , c F 1 ]] 2 b ]] 1 ] ]] 2d fD (c D ) fF (c F ) fD (c D )
G
2
F
1 FF (c F ) 2 ] ]] 2d fF (c F )
G
2
Table 2 Comparison of optimal effort levels
a 50, b 51
0, a #1, b ,1
FF (c F ) /fF (c F ) . FD (c D ) /fD (c D )
e *D (c D ).e F* (c F )
e D* (c D ).e F* (c F )
FF (c F ) /fF (c F ) 5 FD (c D ) /fD (c D )
e *D (c D )5e F* (c F )
e D* (c D ).e F* (c F )
FF (c F ) /fF (c F ) , FD (c D ) /fD (c D )
e D* (c D ).e F* (c F )
e D* (c D ) 5e F* (c F ) if FF (c F ) /fF (c F ) 5FD (c D ) /fD (c D )
.
.
,
,
(24)
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
363
and after rearranging, we obtain Proposition 5. Proposition 5. When the effort disutility function is quadratic, the awarding rule can be written: pD (c)51 and pF (c)50 if
F
FF (c F ) FD (c D ) c D , c F 1 ]] 2 b ]] fF (c F ) fD (c D )
GF
G
FF (c F ) FD (c D ) 2d 2 ]] 2 b ]] / 2d fF (c F ) fD (c D )
(25)
The awarding rule defined in (25) is a discriminatory rule. As was made for (9), (25) can be written: c D ,D eD (c F ). The foreign firm is discriminated against if D De (c F ).c F . More generally, the nature of the discrimination policy depends on the hazard rates, the announced costs, the effort disutility and the a and l parameters. To compare this result with the policy defined by Proposition 1 in the adverse selection case, let us consider the different cases involved with (25). The identity of the discriminated against firm depends on the sign of the product of the bracketed terms. The second bracketed term is positive as soon as the effort of one of the two firms is positive: as e *D is positive if b FD (c D ) /fD (c D ),d and e F* is positive if FF (c F ) /fF (c F ),d, b FD (c D ) /fD (c D )1FF (c F ) /fF (c F ),2d. The identity of the discriminated against firm depends then on the sign of FF (c F ) /fF (c F )2 b FD (c D ) /fD (c D ), which is exactly the condition defined by (10) in the adverse selection case. Taking moral hazard into account does not modify the discriminatory policy, which is defined in Table 1. The complementarity of the awarding rule and the cost target is then obvious. It is a consequence of the separation property. The awarding rule is used to obtain allocative efficiency and is the same as if there were no moral hazard. The preferential treatment does not change the effort level of the winning firm. The transfer is used to obtain productive efficiency. To give incentives for the firms to reduce their costs, the government has to use the payment rule which consists here of the reimbursement of a cost target C*(c)5C(e*(c)) (the firm that does not reach that target implicitly incurs an infinite penalty) and an additional payment t*.The comparison of Tables 1 and 2 shows that the government must always assign a higher effort to the firm which is favored, whether the domestic or the foreign firm. We now can compare the optimal policy without moral hazard and the optimal policy with moral hazard. From (10) and (24), it can be shown that preferential treatment is lower when the two firms can modify their efficiency by a non observable effort than when the costs are exogenous and this whatever the discrimination may be.
5.2. Definition of the transfers We can elicit the transfers corresponding to the optimal mechanism. As Ui (c¯ i )50, by using the envelope condition and the definition of profit, we obtain the following expected additional transfers ¯t i*
364
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
c¯ j
¯t i* 5
E t (c , c )f (c ) dc i
i
j
j
j
j
cj ] c¯ j
c¯ i
5
¯ cj
E w 9(e (s)) E p (s, c )f (c ) dc ds 1 E p (c , c )w(e (c ))f (c ) dc i
ci
i
j
j
j
j
c ]j
i
i
j
i
i
j
j
j
(26)
c ]j
with pD (c) 51 if c D ,min(c¯ D , D De (c F ) and pF (c)51 if c F #min(c¯ F , D Fe (c D ))
5.3. Implementation by a modified second price auction The optimal mechanism can be implemented by a dominant strategy auction (in which the announcement of the true cost parameter by a firm is a dominant strategy for any bid of the other firm) whose properties look like second price auction properties, but which is modified to take discrimination and incentives to exert effort into account. From (26), when the vector of announced costs is c5(c D , c F ), the additional transfer to firm t Vi (c i , c j ), is defined by min( c¯ i ,D ej (c j ))
t Vi (c i , c j ) 5 w (e i (c i )) 1
E
w 9(e i (s)) ds
if pi (c) 5 1
(27)
ci
50
otherwise
Proposition 6 summarizes these results. Proposition 6. The auction mechanism leading to the same effort function, rent level and firm selection as in the optimal mechanism is the following: 1. firms D and F transmit bids b D 5c D and b F 5c F 2. bid c D is compared with D De (c F ) 3. if c D ,D eD (c F ), the domestic firms wins the auction. Its total payment is equal to the cost target (C *D (c D )5c D 2e D* (c D )) reimbursement plus the corresponding effort disutility w (e *D (c D )) plus an additional rent equal to ¯ D , D eD (c F )) eCmin(c w 9(e D (s)) ds. If c D $D De (c F ), the foreign firm wins the auction D and its total payment is symmetrically equal to the cost target (C *F (c F )5c F 2 e *F (c F )) reimbursement plus the corresponding effort disutility w (e *F (c F )) plus e (c )) ¯ F, D F D an additional rent equal to eCmin(c w 9(e F (s)) ds. D 4. the firms that does not wins the auction neither receives nor pays anything. It is easy to check that the rent the winning firm obtains depends on the other firm’s cost. Moreover, discrimination in the auction amounts to a truncation of the
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
365
interval [c i , c¯ i ] to [c i , D ei (c j )] in the definition of the rent. Then there is a gain in the expected transfer from having an auction. Finally, we can note that, following Laffont and Tirole, the transfer function can be rewritten as a linear contract. It can be decomposed into a transfer a i (c)5t Vi (c) computed at the time of the auction and into a sharing of overruns s i (c i )5 w 9(e *i (c i )). As a consequence of the optimal discriminatory policy, the government must offer a different menu of linear contracts to the two firms. As e D* .e F* when b FD (c D ) /fD (c D ),FF (c F ) /fF (c F ), the domestic firm faces a contract with a greater slope than the slope of the incentive scheme offered to the foreign firm for the same level of the efficiency parameter.
6. Conclusion In this paper, we extended the McAfee and McMillan (1989) and Branco (1994) analyses of government procurement optimal auction. First, we explicitly took into account the local government preferences, the social cost of public funds and the costs differentials in the same model. We studied the properties of the optimal mechanism. This involves discrimination in favor of the domestic firm and in favor of the cost disadvantaged firm. A general rule consists of adding to the domestic cost a term equal to FF (c F ) /fF (c F )2 b FD (c D ) /fD (c D ) whose sign varies according to the prior distributions and the importance attached to domestic profit. Second, we considered the implementation of the optimal policy. We showed that both a modified first price auction and a modified second price auction can give the same expected domestic social surplus. However, the discriminatory awarding rule is in both cases very different from the linear rules used in procurement practices. Even in the case of an economywide preferential policy, the rules are very complex. This was shown by Branco in an example. We showed this to be true in a general framework. Moreover, when we considered cost differentials, the rule had to be differentiated from firm to firm and vary non linearly with the level of the cost. Third, we focused on the familiar drawback of discrimination by taking into account the possibility of reducing the cost. We showed that the awarding rule remains exactly the same when the firms can exert a non observable effort to reduce cost. Thus, discriminatory practices should not be eliminated from considerations of incentives to reduce production costs. Nevertheless, according to the separation property, the government must use the payment rule to induce the domestic firm to reduce its cost when there is a positive social cost of public funds. Our main result is that the government must always assign a higher effort (and then a lower expected cost) to the firm which is favored. It can for instance offer the favored firm an incentive contract with a greater slope than the slope of the scheme offered to the discriminated against firm for the same level of cost. Our results give some justification for protectionism in public procurement. They show that non discriminatory award of public contract is not the appropriate
366
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
way to induce domestic firms to be more efficient when the government is able to observe the expost cost. An open issue could be the analysis of the optimal policy when only the domestic firm’s cost is observable. An other open issue concerns implementation. The standard tendering mechanisms is the first price auction with a percentage preference rule. This auction is not optimal, but the complexity of the optimal modified first price auction can be an obstacle to its implementation. It could be important to design empirical work in such a way as to estimate the welfare losses associated with usual practices. However, it is well known that empirical studies of government practices produce biased estimates (McAfee and McMillan, 1989). Laboratory experiments could help to define the best practicable policy.
References Atkins Management Consultants, 1988. The Cost of Non-Europe: Research on the Cost of Non-Europe. Commission of the European Community, Office for Official Publications of the European Community, Luxembourg. ¨ Bagnoli, M., and Bergstom, T., 1989. Log-concave probability and its applications. CREST WP [89.23, University of Michagan. Baldwin, R.E., Richardson, J.D., 1972. Government purchasing policies, other NTB’s, and the international monetary crisis. In: English, H.H., Hay, K.A.J. (Eds.), Obstacles to Trade in the Pacific Area: Proceedings of the Fourth Pacific Trade Development Conference. Carleton School of International Affairs, Ottawa. Ballard, C.L., Showen, J.B., Whalley, J., 1985. General equilibrium computations of the marginal welfare costs of taxes in US. American Economic Review 75, 128–138. Branco, F., 1994. Favoring domestic firms in procurement contracts. Journal of International Economics 37, 65–80. Breton, A., Salmon, P., 1996. Are discriminatory procurement policies motivated by protectionism?. Kyklos 49, 17–68. Bulow, J., Roberts, J., 1989. The simple analysis of optimal auctions. Journal of Political Economy 97 (5), 1060–1090. Cairns, R.D., 1993. The optimal mechanism, a mechanism for optimal third degree price discrimination. Journal of Economic Behaviour and Organization 20 (2), 213–225. Joson, S.S., 1986. Substitutability of ‘buy local’ policy for tariff protection in small economies. Journal of Policy Modeling 8 (2), 223–239. Kim, I.G., 1994. Price-preference vs. tariff policies in government procurement auctions. Economics Letters 45, 217–222. Laffont, J.J., Tirole, J., 1987. Auctioning incentives contracts. Journal of Political Economy 95, 921–937. Laffont, J.J., Tirole, J., 1991. Auction design and favoritism. International Journal of Industrial Organization 9, 9–42. Laffont, J.J., Tirole, J., 1993. A Theory of Incentives in Procurement and Regulation. MIT Press, Cambridge, MA. McAfee, P., McMillan, J., 1989. Government procurement and international trade. Journal of International Economics 26, 291–308. Meade, J., 1944. Price and output policy of state enterprise. Economic Journal 54, 321–328.
F. Naegelen, M. Mougeot / Journal of Public Economics 67 (1998) 349 – 367
367
Miyagiwa, K., 1991. Oligopoly and discriminatory government procurement policy. American Economic Review 81, 1320–1328. Myerson, R.B., 1981. Optimal auction design. Mathematics of Operations Research 6, 619–632. Riordan, M., Sappington, D., 1987. Awarding monopoly franchises. American Economic Review 77, 375–387. Robertson, J., 1992. Japan agrees to hike U.S. computers buys. Electronic News 13, January, 1. Vagstad, S., 1995. Promoting fair competition in public procurement. Journal of Public Economics 58, 283–307. Vickrey, W., 1952. The revision of the rapid transit fare structure of the city of New York. Mimeo, Technical monograph No.3, Finance Project. Mayor’s Committee for management survey of the city of New York. Vickrey, W., 1961. Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance 16, 8–37.