Public Choice 78: 389-399, 1994. © 1994 Kluwer Academic Publishers. Printed in the Netherlands.

Technical progress in bureaucracies*

U W E C A N T N E R

T H O M A S K U H N

Universitiit Augsburg, Universitiitsstr. 2, 1)-89004 Augsburg

Accepted 30 June 1992

Abstract. In this paper we raise the question whether in bureaucracies incentives are existing to implement technical progress into public goods production as it may be observed in the private sector. Therefore the well-known models of the theory of bureaucracy will be enhanced by techni- cal progress modelled as process innovations. Depending on bureaucrats' preferences two results can be obtained: (a) If bureaucrats maximize their budget or if output or the classical production factors enter their utility function, R&D will be used efficiently due to cost reductions increasing the bureaucrats' budget or utility; (b) if bureaucrats prefer R&D as an end itself, they will use this factor like other factors by more than the efficient amount. In both cases an allocative inefficient output of the public good is produced. As a consequence society cannot benefit from gains by tech- nical progress since net social welfare is appropriated totally by bureaucrats, even if it is increased by R&D-efforts.

1. Introduct ion

It is well k n o w n f rom the economic theory of bureaucracy that public goods

p roduc t ion in bureaucra t ic organiza t ions may be characterized by allocative

a n d / o r p roduc t ion inefficiencies. This ou tcome is, on the one hand , explained

by the behaviour of the bureaucra ts maximiz ing ou tpu t or their discret ionary

budgets depending on their respective uti l i ty func t ion . On the other hand ,

bureaucra ts seem to exert a m o n o p o l y power to the degree of perfect price dis-

c r imina t ion al lowing them to appropr ia te all of the net social benef i t accruing

f rom publ ic goods p roduc t ion .

It is fairly evident that increases in economic welfare of societies depend -

besides others - more and more on the efficient use of the oppor tuni t ies

provided by technological progress. In this context we ma y ask whether

bureaucra ts are eager to gain the merits provided by technical improvements .

* We want to thank anonymous referees for valuable comments and the editors for an efficient cooperation. Especially we are very grateful for the discussion with and support by Horst Hanusch. Financial support by the German Science Foundation to Thomas Kuhn is appreciated.

390

At a first glance it should be expected that bureaucrats have no incentives to do so because contrary to private enterprises they do not act on competitive markets.

However, from a theoretical point of view, we show that bureaucrats engage in technical progress for quite different reasons. Since inefficiencies accruing from the traditional factors,are objects of severe public criticism, one is in- clined to ask whether bureaucrats try to demonstrate a thorough search for efficiency by engaging in R&D. In fact, the initiated cost reductions will pro- vide them with additional resources to be used for their own purposes. More- over, engaging in R&D might be an end in itself, increasing the bureaucrats '

utility. Thus, our paper deals with two questions. The first one investigates whether

R&D is used efficiently, if it is accomplished at all. The second one is concerned with the problem whether social welfare gains induced by technical change are shared by society or solely appropriated by bureaucrats.

In Section 2 our analysis begins with the discussion of an altruistic social planner striving for a Pareto-efficient production which will serve as a yard- stick for the bureaucrats ' behaviour. Their decisions concerning production are derived from well-known models of the theory of bureaucracy, enhanced by technical progress solely modelled as cost-reducing process innovations. In this respect Sections 3 and 4 employ the models of budget and utility maximiza- tion. In Section 5 we introduce a model where R&D is to be seen as increasing the bureaucrats' utility. Section 6 closes with a summary of our analysis.

2. Welfare-optimizing technical progress

The social planner's production decision will serve as a yardstick of our analy- sis. His objective is to maximize social welfare, and therefore he is ambitious to implement technical progress optimally (to the following, see Dasgupta and Stiglitz, 1980: 271). As a measure for social welfare we use the money-metric net social welfare as usually applied in partial equilibrium analysis.

p(q), the demand function of a public good, is revealed by the politicians and can be considered as the demand of the median voter. 1 This function is, as usual, declining, 0p/0q < 0.

Net social benefit w(q) is given by the difference between gross social benefit, as usually defined by the area under the demand curve (see Dasgupta and Stiglitz, 1980: 269), and the public good's cost of production C(q): 2

w(q) = lqP(q)dq - C(q)

0

(1)

391

The social planner may be able to engage in R&D leading to process innovations 3 which reduce the minimum marginal costs. 4 Further on we as- sume a cost function with minimum marginal costs c(R) constant in q. These will be reduced by R&D implemented by the amount R where c(R) shall be con- vex: 0c/OR < 0 and 02c/0R 2 > 0. This implies that cost reductions decrease with increasing R&D. The factor price of R&D is normalized to 1. Thus, total costs in (1) amount to

C(q,R) = c(R)q + R, with c(0) > 0, R > 0 (2)

Consequently, minimum costs are determined by the minimization of (2) over R .

By using this special cost function, net social benefit in (I) additionally de- pends on R. The maximization over q and R using Oc/0q = c(R) leads to the following optimality conditions assuring the Pareto-optimum:

p(q) = c(R) (3)

0c - - q = - 1 ( 4 ) OR

(3) provides the well-known condition for the welfare-optimizing output of the public good where the costs of an additional unit of output are equal to its price. (4) determines the optimal level of R&D where the induced cost reduction of an additional unit R&D is equal to the price of this last unit. Both conditions are satisfied simultaneously which implies that the Pareto-efficient output will only be produced at the optimum level of R&D. 5

However, the existence and uniqueness of this solution can only be guaran- teed if, in addition to the declining demand function, the following condition is satisfied:

o2c \OR / (5) >

0R 2 0p

0q q

Without any doubt, a strictly convex cost function would satisfy this condition. However, (5) requires an even less strictly defined cost function. Here, on the one side, the cost reductions must decrease, O2c/0R 2 > 0, but on the other side may not exceed a certain level so that the effect of R&D on net social welfare declines. This level, however, depends on the price elasticity of demand for the public good. Generally, low price elasticities as they are by and large common

392

for public goods (cf. Fisher (1988: 294) allow higher elasticities for R&D in- duced cost reductions. Precise relations hereto may only be deduced by specific demand and cost functions (for an example, see Dasgupta and Stiglitz, 1980: 272).

Conditions (3) and (4) characterize the welfare optimizing production of public goods accomplished by an altruistic social planner. In reality, however, bureaucrats providing public goods rarely behave altruistically but are rather to be regarded as selfish and egoistic.

3. Budget maximizing bureaucrats

There are several possibilities of analysing behaviour diverging from the max- imization of net social welfare. A first and very simple assumption that bureau- crats maximize their budget has been suggested by Niskanen (1971). Here bureaucrats are eager to realize their own goals as, e.g., "salary, prerequisites of the office, public reputation, power, patronage, output of the bureau" (p. 38). Following Niskanen, in this respect they hold the highest monopoly power in a bilateral monopoly where bureaucrats are the suppliers and politicians are the demanders of a public good.

This constellation is basically founded on the existence of asymmetric infor- mation about supply and demand conditions, stating that bureaucrats should have knowledge of the politicians' demand function whereas the politicians were unfamiliar with the minimum production costs of the public good. Thus, bureaucrats were able to appropriate the whole net social benefit. In this respect bureaucrats negotiate on a total budget basis and not on a per-unit basis. So-called "package offers" are designed in such a way that politicians can only just accept them. 6

Thus, the budget B(q) required for supplying the quantity q is given by:

B(q) = ~ ~qp(q)dq (6) i t

0

By assuming the same demand as above the budget is a strictly monotonous function of q for p(q) > 0.

By maximizing their budget bureaucrats may be constrained either by the de- mand side or by the production costs. As to the latter, the constraint means that total revenues must at least equal total costs, implying that no deficit may occur:

B(q) _ C(q,R) (7)

Here were argue with a constant level of R&D.

393

Since bureaucrats, contrary to private entrepreneurs, are not allowed to appropriate budget surplus they may be inclined to increase output up to the level until production costs just equal the budget. In return, this increase in output leads to an increase in the budget which is, however, most welcome and appreciated by the bureaucrats. This behavior results in an output above the Pareto-efficient one, however, produced efficiently at minimum costs. Fur- ther on, this is referred to as a solution constrained by the budget.

The second solution distinct f rom this result is constrained by demand where the global maximum is characterized by minimum costs lower than the budget. Here, the target of a maximum budget can then only be realized by a cost- inefficient production. Thus, besides allocative inefficiency, cost inefficiency can be observed. However, empirical relevance for this case is rather small if it is stated that the demand for public goods is satiated - if at all - at very large

quantifies. This model of budget maximization is enhanced by technical progress just

in the manner employed in the social planner's model. Here it is not solely the amount spent on own research and development laboratories (as in private firms like IBM, etc.) which count for R&D expenditures. We rather consider in a first instance those labor and capital input for various departments aiming at, e.g., rationalization of the administrative and production processes. These costs do not appear as an extraordinary position on the bureaucracy's balance. A great deal of technological know-how perhaps is purchased externally, such as software, services of computer centres or any other services.

When considering to accomplish R&D bureaucrats have to solve the follow- ing optimization problem: By using the cost function (2) and constraint not to run a deficit (7), the budget (6) is to be maximized, q and R being the decision variables:

max B(q) q,R s.t. B(q) _ c(R)q + R

(8)

To this problem the Kuhn-Tucker conditions are derived. These are sufficient for an optimum, if the function to be maximized as well as the constraint are concave. This is satisfied for B(q) because of the declining demand function, ap /aq < 0. Investigation of the constraint B(q) - C(q,R) leads to condition (5) above with the features already discussed.

For interpreting the Kuhn-Tucker conditions again we have to distinguish between the two cases, the one constrained by the budget and the other by de- mand, respectively. In the first case the constraint B(q) - C(q,R) reads with equality (k > 0). Hence, the bureaucrats ' allocation, (q*,R*), to be chosen meets the following conditions:

394

p(q) - c(R) (9) X+I

0c - - q = - 1 (10) OR

(9) provides the optimum output given in a range where the marginal budget p(q) is always lower than the marginal costs 0C/0q. Thus, with X > 0 more output is produced than in the Pareto-efficient solution determined by price equalizing marginal costs.

(10) repeats our above solution from describing the condition for the opti- mum use of R&D. Here again, R&D is accomplished as long as the induced cost reductions just match the cost of the last unit R&D. So, bureaucrats use all pos- sibilities of reducing costs. This means that the optimum output is produced cost-efficiently and that the whole potential for reducing costs is exploited. Only by this rule the bureaucrats are able to maximize output and, conse- quently, also their budget. This behaviour, however, does not increase the so- ciety's net welfare as the bureaucrats appropriate all of it. 7

Considering the solution constrained by demand X = 0 does hold as B(q) > C(q,R). Therefore bureaucrats simply and solely have to maximize their budget. The first order condition reads as:

p(q) = O, (11)

This case is only relevant when the demand for the public good is satiated. In this case, bureaucrats produce until the satiation level is attained when the

marginal budget is equal to 0. Since there minimum costs are lower than the budget, the maximum budget can only be realized by producing cost- inefficiently. However, whether these inefficiencies occur as an inefficient production at the technological level optimally attainable, whether production is inefficient in labor L and capital K, using an inferior technology, or whether we have a combination of both, a clear-cut answer cannot be given here. This would only be possible if we knew the bureaucrats' special preferences for production factors and the use of their budget. Such a specification is missing in this model. In the next chapter, however, we shall return to this question.

4. B u r e a u c r a t s m a x i m i z i n g ut i l i ty

Our results from the Niskanan-model imply the quite paradoxical situation that there are, by and large, no financial margins for such unproductive targets as high salaries, convenient working conditions or leisure which bureaucrats

395

are eager to realize by maximizing the budget. This inconsistency can be resolved in models of maximizing utility as has been introduced by Migu6 and B61anger (1974). There it is explicitly taken into account that the utility of bureaucrats not only depends on output but also on the so-called discretionary budget, defined as the difference between budget and minimum cost. This dis- cretionary budget, in return, should represent the above mentioned utility determining factors. Again, this model will be enhanced by considering the effects of technical progress.

The discretionary budget is defined as:

DB(q,R) := B(q) - C(q,R) (12)

The utility function with output q and the discretionary budget DB as argu- ments are supposed to reveal the usual features. Especially we assume that u is concave globally as well as in both arguments, q and DB. 8

u(q,DB) HI,U 2 > 0, Ull,U22 < 0, UltU22 -- (Ut2) 2 > 0 (13)

Using the Kuhn-Tucker optimization maximization of (13) subject to the con- straint (7) leads to the following sufficient 9 conditions for (q*,R*):

p(q) < c(R) (14)

0C - - q = - 1 ( 1 5 ) OR

Now, how are these results to be interpreted? (14) implies that for the produced output the marginal costs are higher than the marginal budget. Thus, again, here we may observe allocative inefficiency.

Considering R&D (15), the well-known condition for the optimum use of R&D is delivered. Therefore production is cost efficient and the potentials for cost reductions are completely exhausted. Hence, with increasing R the DB- function is shifted to the right until the optimum level R* is achieved, (0DB/0R > 0 for R < R*). This enables bureaucrats to produce increased out- put as well as to appropriate a higher discretionary budget.

The utility maximizing combination of output and discretionary budget is given at that point where the rate of transformation equals the rate of substitu- tion between both items:

396

0U

ODB _ Oq (16)

0q 0U

0DB

Our argument above has not yet answered the question: For which purposes do the bureaucrats use their discretionary budget? In order to give an answer, the utility function needs to be specified even further. Thus, bureaucrats may prefer a larger number of "menial" labourers who enable them convenient working conditions and help reduce their own working-load. Also job-security and the opportunities for promotion seem to be higher in expanding bureau- cracies. This perception which originates from "Parkinson's Law" (see Par- kinson, 1957) and from Williamson (1964) was modelled by Orzechowsky (1977). Here the bureaucrats' utility depends on output and labor input and is maximized subject to a neo-classicat production function as well as to cost- covering.

The integration of technical progress into such a model provides an R&D- induced increase of the production possibilities. However, the analytical insights basically do not differ from those obtained in the modified version of the Migu6 and B61anger-model. The results are even more specific as labour is used to a degree where the marginal product is lower than the wage rate. Responsible for this outcome is a bias in the shadow price of labor input which lies below the wage rate since labor has a positive marginal utility to bureau- crats. R&D, however, will again be accomplished here to an optimum degree. Of course, the same reasoning applies to the capital input if bureaucrats prefer capital instead of labor. THe more intensely used capital input is then revealed, e.g., in pompous administration buildings or by excess capacities in, e.g., the energy sector or in hospitals.

As a summary of these approaches, production is always allocative as well as cost inefficient. With respect to this non Pareto-efficient output, however, technical progress is accomplished optimally. As above, here too, the asso- ciated welfare gains are not transferred to the society. 10

5. Bureaucrats with preferences for R & D

So far, bureaucrats have not had any incentive to accomplish R&D ineffi- ciently. The provided potentials for cost reductions were always explored. Technical progress was only a means to the end of higher utility, higher budget, higher output or even an increased input of labour or capital. This, of course, implies that R&D expenditures were to be avoided to an extent where cost

397

increases exceeded cost reductions. Although it might sound somewhat para- doxical: Here technical progress furthers over-production and waste.

Alternatively bureaucrats may use a more convenient way of disguising in- efficiencies by engaging in R&D expenditures rather than rising the traditional inputs, capital or labor, which can even be accomplished within certain limits. Here we consider large-scale computer equipment or additional jobs for em- ployees engaged in R&D - or at least who are said to do so. Of course, as al- ready mentioned, it is also possible to "purchase technical progress" in order to rationalize administration. The public may regard such an engagement not only as a search for more efficiency but it is more likely to be accepted that bureaucrats require higher budgets due to uncertain search processes and thus high sunk costs. Therefore, bureaucrats preferring R&D (who are said to be very progressive) may be unaffected by a cut of the budget. They may even gain additional prestige in public opinion. Such a constellation only implies that bureaucrats have preferences for R&D, which now - besides output - enter their utility function, which is still assumed to have the usual properties:

u(q,R), Ul,U 2 > 0, Ull,UI2 < 0, Ull,U22--(U12 )2 > 0 (17)

Here, again, (7) serves as constraint. The sufficient conditions of the Kuhn- Tucker-maximization lead for (q*,R*) to:

p(q) < c(R) (18)

OC - - - q < 1 ( 1 9 )

OR

(18) shows again that here an allocative inefficient output of the public good is produced. Moreover, as provided by (19), R&D is accomplished to a degree where the last-unit R&D costs more than the induced cost reduction gained from it. Since bureaucrats render R&D as a matter of prestige, its shadow price is less than 1. All this, of course, leads to a production above minimum costs which, however, are covered completely by the budget. The cost-inefficiency observed here is solely based on the non-optimum use of R&D.

Enhancing the objective function by the traditional input factors we expect that these factors are also used inefficiently. This result, however, does not ex- ceed our analysis in Section 4.

6. S u m m a r y

As a summary, the following results can be obtained: We should not wonder any longer that bureaucrats have incentives to engage

398

in R&D or "pu rchase technical p rogress" . Even wi thout any special prefer- ences for R&D, due to cost reductions, technical progress provides an increase in the budget or utility depending on the bureaucrats objective funct ion as- sumed. In the enhanced models o f Niskanen, and Migu6 and B61anger we showed that fo r this result the efficient use o f R&D is a necessary condi t ion. On the contrary , with sub-opt imal R&D expenditures not all potentials fo r cost reduct ions are used so that , in return, there are less resources available for the

bureaucra ts ' selfish goals or less ou tpu t can be produced . In this case the bureaucrats would have to accept a loss in budget o r utility. The society, however, cannot benefit f rom the realized gains f r o m technical progress, since all net social welfare is appropr ia ted by the bureaucrats - even if there is an R&D-induced increase.

If , on the other hand, bureaucrats prefer R&D as an end in itself they will use this fac tor - as they do with other factors - to more than the efficient amount . Bureaucrats therefore do not engage in too little R&D, as suspected. They rather use too much o f it, however, with the same negative consequences for society as before since here, again, an allocative inefficient ou tpu t is p roduced at above-min imum costs.

These bureaucrat ic strategies make it increasingly difficult for the public to

detect inefficiencies. R&D engagement pretends a search for efficiency which should account for the society 's welfare but which actually only feeds the bureaucra ts ' utility. Since private enterprises engaged in R&D experience sunk- costs as inevitable inefficiencies, the private sector may not serve as a yardst ick for efficiency as is usually done by evaluating inefficiencies in the use o f the tradit ional inputs labor and capital.

Of course, since our results are derived within the f ramework o f well-known models o f bureaucracies, criticism concerning their underlying assumptions do apply here likewise. 11 In part icular the ma jo r points refer to the bargaining

power o f bureaucrats , the missing incentives and constraints bureaucra ts face as in the f r amework o f a principal agent approach , and the abstract ion f r o m different insti tutional settings.

Notes

1. Alternatively we could employ an aggregate of all individual demand functions which the poli- ticians are aware of. This would not change our argument.

2. Thus w(q) is the sum of consumer and producer surplus for quantity q. Since there should not arise any complications, we use the same symbol for the upper integration border and the in- tegration variable. With regard to the median voter c(q) has to be interpreted as the fraction of the total costs accruing to the median voter.

3. Of course, it would be interesting to discuss also product innovations. In this case the analysis would require a totally different kind of net social benefit function depending either on certain characteristics of goods as in the Lancaster tradition or a measure for goods vareity as in

399

models of horizontal product differentiation. Such an investigation, however, is beyond the scope of this paper.

We also have to exclude external effects to consumers connected with technical progress or the volume of output. We will refer to this point again in Section 3.

4. To classify the effects of technical progress by labour or capital saving is not necessary here because we only rely on its impact on the cost function.

5. It should be pointed out here that comparing this Pareto-optimum with the one without techni- cal progress output and net social benefit has increased.

6. This modelling is equivalent to the one of a monopolist with perfect price discrimination. 7. Despite Pareto-inefficiency, such an output can have external effects which may increase or

reduce the welfare of the society, e.g. investment in human capital or time saving effects of a greater staff.

8. The variables u i and uij refer to the first and second derivatives of the function u with respect to the i th and jth argument of u respectively.

9. The objective function and the constrained are concave by assumption and by (5), respectively. 10. Note 7 applies here accordingly. 1 I. For a critique of theses models see Breton (1974). Breton and Wintrobe (1975), Jackson (1982:

121), and the Migu6, B~langer and Niskanen interchange, appending Migu6 and B61anger (1974: 43-47).

References

Breton, A. (1974). The economic theory of representative government. Chicago: Aldine. Breton, A. and Wintrobe, R. (1975). The equilibrium size of a budget-maximizing bureau. Journal

of Political Economy 83: 195-207. Dasgupta, P. and Stiglitz, J. (1980). Industrial structure and the nature of innovative activity. Eco-

nomic Journal 90: 266-293. Fisher, R.C. (1988). State and local public finance. Glenview, tL , London: Scott, Foresman. Jackson, P. (1982). The political economy of bureaucracy. Oxford: Philip Allan. Migu6, J.-L. and B61anger, G. (1974). Towards a general theory of managerial discretion. Public

Choice 17: 29. Niskanen, W.A. (1971). Bureaucracy and representative government. Chicago: Aldine-Atherton. Orzechowsky, W. (1977). Economic models of bureaucracy: Surveys, extensions and evidence. In

T.E. Borcherding (Ed.), Budget and bureaucrats: The source of government growth. Durham: 229-259.

Parkinson, C.N. (1957). Parkinson's law and other studies in administration. New York: Ballan- tine Books.

Williamson, O.E. (1964). The economics of discretionary behavior: Managerial objectives in a theory of thefirm. Englewood Cliffs, N J: Prentice Hall.