The Simple Economics of Incentive Contracting

J. J. McCall

The American Economic Review, Vol. 60, No. 5. (Dec., 1970), pp. 837-846.

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incentive Contracting

'I'his paper presents an elementary economic analysis oi three different kinds of procurement contract: the fixed price contract, the fixed price incentive con-tract, and the cost plus fixed fee contract.'

In the fixed price contract, a firm agrees to deliver a particular product for a specified price. If the product's cost is less (more) than the fixed price, the firm incurs a profit (loss). The cost to the government is simply the fixed price. Once the fixed price is established, the govern- ment is unaffected by the product's cost- it shares in neither the firm's profits nor losses.

In the fixed price incentive contract, a firm initially establishes a provisional or "target" cost estimate. Target profits are estimated by multiplying the target cost estimate by a specified proportion. In addition, if actual costs are less (more) than the estimated cost, the government shares in the firm's "incentive" profits (losses). The extent of the sharing is indi- cated in the contract by a fixed proportion which, when multiplied by the profits or losses, represents the firm's share; the remaining portion is the government's share. This contract usually places limita- tions on both the total amduit of profits a firm can earn and on total government costs.

* Proiessor of economics, University of California, Los Angela. The author is indebted to K. L. Deavers and the referee for their valuable criticisms and sugges- tions.

The literature on the economics of incentive con-tracting is quite extensive. See I. N. Fisher, T. Mar-schak et al., F. T. Moore (1962, 1967), M. J. Peck and F. hf. Scherer, J. W.Pratt, and F. M. Scherer (1964a, 1964b). The analysis presented here is implicit in several of these studies, but has never been stated explicitly.

I11 the cost plus fixed fee contract (CPFF), the government pays a firm a fixed per- centage of an initial target cost. If actual costs exceed the target cost, the govern- ment usually pays the additional expenses. The fixed fee or "profits," however, remain

From an analytical point of view, the fixed price and the c ~ s ~ ~ l u s fixed fee con- tract are both special cases of the fixed price incentive contract. Accordingly, the same model can be used to analyze all three. To avoid needless repetition, only the fixed price incentive contract will be analyzed in detail.

It is frequently alleged and sometimes verified (for certain kinds of contracts) that an awkward tendency to underesti- mate costs dominates government con-., tracts in general, and military contracts in pa r t i~u la r .~I11their study of cost estimates for French public works, R. Giguet and G. Morlat have devised a purely statistical

For a more complete description of these contracts, see the studies by Fisher and Moore (1962,1967).

Neither the tendency to underestimate costs nor the indignant response to underestimates is peculiar to modern times. Roman decision makers faced similar problems in their construction activities: "The young magistrate (Herod, son of Atticus), observing that the town of Troas was indifferently supplied with water, obtained from the munificence of Hadrian three hun- dred myriads of drachmas (about a hundred thousand pounds) for the construction of a new aqueduct. But in the execution of the work the charge amounted to more than double the estimate, and the officers of the revenue began to murmur, till the generous Atticus silenced their complaints by requesting that he might be per- mitted to take upon himself the whole additional ex- pense." Edward Gibbon, The Decline and Pall of the Romatz Empire, Vol. 1, pp. 28-29, abridged by D. ,\I. Low, Washington Square Press, New York, 1962. Need- less to say, trariquilizers like Atticus are no longer available to sooth Congressional unrest.

explanation for this phenomenon. One of their basic analytic assumptions is that contractors are trying to obtain unbiased predictions of actual costs. An alternative economic explanation of the procurement process suggests that contractors may not try to be unbiased in estimating costs when this conflicts with their overriding object to maximize expected profits. The eco-nomic motivation of the contractor may be the major factor in determining his pro- pensity to over- or under-estimate costs.

When two organizations do business with each other, the profit maximizing behavior of one is symmetrical with the behavior of the other. This symmetry is not present in business-government rela- tions. One reason for its absence is the difference in the criteria each organization attempts to satisfy. The business firm's goal is to maximize profits; given the de- fense budget, the goal of the defense organization is to maximize national secu- rity, a much more ambiguous goal. Per- haps an even more basic factor is the difference in property rights between these two organization^.^ Within the firm, pri- vate property rights in the private sector make it relatively easy to transmit incen- tives consistent with its objective to maximize profits. Within a government organization, it is much more difficult to transmit incentives consistent with its primary objective.

The analysis indicates several problems associated with the use of incentive con- tracts. In brief, i t will be shown that when- ever the sharing proportion is less than unity, i.e., for any contract except the fixed-price variety, incentive contracting induces a perverse divergence between estimated costs and actual costs. This divergence is most perverse for the CPPF contract. Relatively efficient firms, i.e., firms whose actual costs of production are

See -1rmen Alchian

low, tend to submit estimated costs (bids) that are higher than actual costs; and relatively inefficient firms, i.e., firms whose actual costs are high, tend to submit esti- mated costs that are lower than actual costs. If the government chooses among firms on the basis of estimated costs, then it is possible it will select relatively in- efficient firms (high actual costs) instead of relatively efficient ones (low actual costs). The probability of selecting a high- cost instead of a low-cost firm is a decreas- ing function of the sharing proportion. The probability of making an inappropriate choice is highest for the CPFF contract where the sharing proportion is zero. To avoid such mistakes, the government's best policy is sometimes the paradoxical one of awarding contracts to firms sub- mitting the highest estimated costs (bids). Costs to the government of a given prod- uct are minimized only if this policy is followed. For this paradoxical policy to be optimal, firms must believe that the con- tract will be awarded to the lowest bidder. As soon as firms recognize that contracts are being awarded to high bidders, they will substantially alter their bidding be- havior. The impossibility of concealing such a policy from contractors, together with its paradoxical character, should con- vince the reader that this policy i s not being recommended. It is only mentioned to illustrate the difficulties inherent in the structure of incentive contracts.

In many cases the government awards contracts by some method other than competitive bidding. This alternative se- lection device has never been clearly specified, contract costs being targeted after the firm is selected. The foregoing re- marks will be relevant if the choice of a firm is conditioned by anticipated target costs.

Certainly, the government wishes to design contracts that attract efficient firms, and a t the same time adhere to con-

vcntionnl bidding practices. Incentive-type (mutracts clo not pcrrnit both of these goals to be achieved simu1t;ineously. The over- riding go21 of the government is to attract efficient firms. 'This can be accomplished either by altering the structure of incen- tive contracts or by imposing a set of bizarre bidding rules. The first alternative is clearly preferable.

J. An Econo~nic Ilfodel of Procurement

This section presents a simple economic model of procurement. The purpose of the model is to understand and predict the behavior of firms when they are confronted with alternative types of government con- tracts.

The firm is assumed to maximize ex-pected profits. This assumption neglects the influence of variance (risk) and higher order moments of the probability distri- bution of pr0fits.j 'The cost of producing a particular item is assumed to be a random variable with a known probability distri- bution. Similarly, the receipts obtainable from selling a product using similar re-sources in the private sector is also a ran- dom variable with a known probability distribution. The firm is assumed to have no knowledge of other firm's costs and, therefore, is ignorant of the bids com-petitors submit. To clarify the presenta- tion, the analysis first assumes that both the receipts from private sector production and the production costs are known. Then i t is assumed that only the production cost is a random variable. The adjustment required when both receipts and produc- tion costs are random variables is pre- sented in a footnote.

To begin with, it mill be assumed that the firm submits a single bid (target cost) on which all incentives are based. Since the firm is assumed to have the alternative

6 In Appendix 1attitudes towards risk are included in the analysis. .ilso see Fisher and G. R. Hall.

of producing in the private sector, it will never submit a target cost (bid) less than some minimum amount, this figure being determined by the profits expected in the private sector. Furthermore, being un-aware of the production costs of its com- petitors, the existence of competitors will deter the firm from submitting bids that are much above this m i n i m ~ m . ~ I n the model, target costs or bids are calculated to equate profits from selling to the govern- ment and to the private sector.'

In presenting the model, the following notation will be employed:

CI=A random variable denoting the actual cost of producing the prod- uct or service.

+= The probability density function associated with C1.

Cn=The cost of the product to the government.

R = A random variable denoting re-ceipts from producing in the private sector.

p = Target cost or bid the firm submits. nl= A random variable denoting profits

from selling in the private sector. nz=A random variable denoting profits

from selling to the government. a= The target profit rate, a proportion

that when multiplied by target

6 The relationship between the firm's bid and its un- certainty regarding the bids of competitors is examined in Appendix 2.

7 Typically, firms that produce products for the government establish a government division separate from the rest of the organization. Under these circuni- stances, it seems likely that the performance of the governnlent division will be judged relative to the per- formance of the other divisions. I t furthermore seems likely that the manager of the government division will try to match the rate of return on capital of the othel divisions. The importance of this influence will, of course, depend on how easily resources can be trans- ferred from the government sector to the private sector. I n the short run, firms with highly specialized resource; will be relatively less responsive to private market alter- natives. Nevertheless, this study assumes that, on the average, the influence of private market alternatives on individual contracts is both measurable and predictable.

840 THE AMERICAN ECONOMIC REVIEW

costs yields target "profits"; a>O. ap= Target profit^.^

p=The incentive profit rate, the frac- tion of the difference between p and C1 that accrues to the firm;

- o_<p_<1.C2= The maximum price the govern-

ment will pay for the product; the firm absorbs costs of production in excess of this maximum.

X?=The maximum profits allowed on a particular government contract ; profits in excess of the maximum are returned to the government.

The following relations are immediate consequences of these definitions:

The Fixed Price Incentive Contract

Given that the firm has the alternative of producing in the private sector, the competitive bids for government contracts will tend to equate profits from the govern- ment contract with alternative profits available in the private sector. Assume for the moment that both firm profits and government costs are unrestricted by the fixed price incentive contract, maximum profits S2and maximum costs Czare both set equal to infinity. The profits, 7r2 , deriv-able from the government incentive con- tract are given by

where p denotes the firm's bid or target cost, ap represents target profits, C1, a random variable, denotes the costs of pro- duction, and /3 is the proportion of the algebraic difference between p and C1 that accrues to the firm.

a The term target profits is commonly used in the literature on incentive contracts. It affects economic profits, but should not be confrised with them.

Alternatively, the profits, xi, obtainable in the private sector are

when R 2 C1 (4) = - C1,{t

when R < C1,

where R and C1 denote, respectively, re-ceipts and cost of production. If the firm's profits in the private sector are negative (R <Cl), in the long run the firm will always move to another industry where its profits are zero.

The bid or target cost the firm submits is calculated by equating 7rl and 7r2, and solving for p. This yields the relation

Production Costs Known

When C1 is known, firms whose private sector receipts exceed the production cost (R 2C1) are said to be efficient ; similarly, firms whose production costs exceed pri- vate sector receipts (C1 >R) are said to be inefficient. Under conditions of certainty and in the absence of government con-tracts, inefficient firms will move to other industries. In the presence of incentive contracts, however, i t may pay inefficient firms to remain in the same industry and offer all of their output to the g ~ v e r n m e n t . ~

The relation (5) between bid and actual production costs is shown in Figure l . 1 °

For efficient firms, the target cost is a de- creasing linear function of actual costs,

* This assumes that the zero profits guaranteed by the incentive contract are superior to any that could be made in a private industry. As usual, normal profits are included in costs.

10 In the fixed price contract, +9=1 and a = O and there is no divergence betveen the Ce and P curves of Figure 1. In the C P F F contract, p = 0 and hence for a given a the divergence between these two curves is maximal.

P (Target Cost) and C, (Government Cost)

where the rate of decrease nzl is

1 - 8 (6) nzl = -

a+P

For inefficient firms, the bid is an increas- ing function of actual costs, where the rate of increase wt2 is

Firms whose actual costs are less than R/(l+a) will submit bids greater than actual costs-an underrun will occur. These firms are efficient. Firms whose ac- tual costs are greater than R/(l+a) will submit bids less than their actual costs of production-an overrun will occur. This latter group includes efficient firms whose costs lie in the interval R / ( l +a),lZ and

all inefficient firms. Sotice that eliiciency and inefficiency may be equivalently de- fined in terms of underrun and overrun, respectively, only when the proportion cu is Set to zero.

The relation between government costs and actual costs is given by

'l'his is obtained by substituting ecluation (5) into the expression for government costs, Co=(l+cu) p+(l-p) ( C I - p ) . The C2 curve in Figure 1 represents this rela- tion. Government costs are constant and equal to R as long as contracts go to effi- cient firms. Government costs are equal to actual costs whenever the government does business with inef3cient firms.

As an example, suppose the government receives Lids from three firms labeled 1, 2, and 3. The production costs for these firms are respectively, C:, C:, and C;; the corresponding bids are, respectively, PI, pz, and p3, where p 2 = p 3 . Consequently, the government will reject firm 1 and be indiiierent between firms 2 and 3 ; whereas on the basis of costs (Cz curve), the govern- merit should reject firm 3 and be indiffer- ent between firms 1 and 2. Because of the perverse divergence between bid price and government cost, the government cannot distinguish between bids from an efiicient firm (p2) and from an inefficient firm (pa) ; ant1 even when the bids are not identical, it may select the inefficient firm (firm 3) instead of the efficient one (firm 1).

The presence of maximum cost and iilaximum profit restrictions necessitates a slight modification of the analysis. The first restriction affects only illefficient firms and is dciioted by

where tlic nl~xiinum cost to the govern- ment is

From equation (5) the bid submitted by the inefficient firm is

'This assumes that the maximum cost zs exceeds R; otherwise no bids will be sub- mitted. Solving equations (10) and (11) for p and C', gives

11-11ich ~ecprcsenf, respectively, the maxi- n?um bicl the inefficient firm subniitted ant1 thc actuxl production costs. .\ny firm

whose costs exceed c2will not submit a bid.

The second restriction, a specified maxi-mum profit, only affects efficient firms. The restriction requires that the firm's profits always be less than

(14) ap + p(p - C1) = 772

But efficient firms ~5 ill al\vays suljinit bids of amount

I? - (1 - P)Cl(15 ) P =

a + 8

Solving equations (14) and (15) for p a ~ i d C1 yields

The solution for p represents the maximuill bid submitted by an efficient firm. If the firm's production costs are less than R- iiz, it will not subinit a bid to the government but will instead produce in the private sector.

From equations (12) and (16), the maximum bid by an inefficient firm is less than the maximum bid by an efficient firm whenever the following inequality holds:

I t ~vould appear that this inequality is satisfied for a great many fixed price iu- centive contracts;" and the inequality implies the following paradoxical result. The governmeiit's optimal policy for the fixed price incentive contract is to accept the highest bid, provided it is high

11 In the tj-pica1 example preqeiited on page 6 of Sloore's study (1962), C1=$250,000, ? i 2 = $30,@OO,0 = .2. By equation (19), the maximum bid by an inefi?- cient firm is smaller than the maximum bid by an effi- cient firm if R>$130,000. But the actual production costs were equal to $185,000, so it docs not seem un- likely that receipts frotu protluction in the 1)rivate market would exceed $130,000.

eno~::h.'~ :Illy hid greater than (PC2)/ ioi+P) comca from an eficicl~t firm. The maximum cost restriction guarantees that no inefficient firm will submit so high a bid. The government, therefore, can be certain that for bids in this range its costs will be K. For any bid less than (PC2)/ (cr+P), the government cannot be certain whether it is dealing with an efficient firm incurring costs equal to K or with an in- efficient firm incurring costs greater than R.13

Producfio~z Costs Mot Known evitlz Certainty

Several modifications are necessary when production costs are not known with certainty.'.' The bid a firm submits is calculated to equate expected profits in the private sector with those in the gov- ernment sector. Expected profits in the private and government sectors are de-noted, respectively, by

and

" 'This polic), i j not heing recommended as noted earlier in this discussion.

l3 If the government chooses firms hy some method other than cor:ipetitive Lidding, presumably, tile firm so chosen retains the option of producing in the private sector. Consecjuei!tly, if the government chooses an of5cic.nt firm, the target cost should be greater than, or e~jual to, the bid that this firm would present in compe- titive t>idding. Indeed, in the face of hard government I~argaining the two should be equal. And this should ~~1.ohe true of inefficient firms. eve^ if the government utilizes 3.tlifferent selcction tlevice, actual costs will con- tinue to esceetl target costs for inefficient firms, whereas target costs will exceed actual costs only for efficient firms. I n addition, all of the precetling results are ap- plics.hle in this case, tlepencling on holy much antici- pattel t:rrget costs influence the government's choice of firm.

l4 The uncertainty of production costs in the private sector usually differs froin production uncertainty in the government sector. These differences could i e treated \tithin this model, but for siml)licity the two u~~certnill- tics are nssunietl to he identical.

Firms in the private sector are assumcd to switch industries whenever expected prof-its are negative.15 Equating (19) and (20), and solving for p yields

The expected costs to the government when i t selects n firm characterized by a probability distribution gi, are given hy

where

cti(R) = 0 when R < E[c~]

= 1 when X > E[c~]

and 4,(Cl) is the probability density func- tion of the random variable, Cl, for the i t h firm.

A probability distribution now charac- terizes each firm in the competition. The probability that the production costs are greater than market price will be large for

' 6 Of course, firms may (and do) experience losses in the private sector. In this model, however, expected profits are always nonnegative.

' 6 When both C1 and R are random variables, the firm's bid and expected government costs are, respec- tively,

and

where ER is the expected value of private market re-ceipts and I(K,Cl) is the joint prol~ahility densitj- func- tion of R and C1.

inefficient firms and small for efficient ones. The relation between the bid and these different probability distributions and the relation between goverrlment costs and these probability distributions have essen- tially the same form as the relations shown in Figurc 1. IYhereas before thc govern- ment was unable to discriminate between low- and high-cost firms, i t is now unable to discriminate between firms with efficient probability distributions and those with inefficient probability distributions.

'I'he incentive contracts the government currently uses appear to have a serious flaw. Because of the peculiar sharing rule that characterizes these cor-ttracts, it is difficult for the government to distinguish between high- and low-cost firms on thc basis of the submitted bids or target costs. The fact that efficient or low-cost firms must share some of their profits--difference between target costs and actual costs-with the government induces them to submit cost estimates higher than ex-pected costs. On the other hand, in-efficient or high-cost firms are permitted to share sonie of their losses with the govern- ment and, consequently, submit cost esti- mates that are less than expected costs. The problem of discriminating between efficient and inefficient firms becomes less serious as the sharing proportion rises, where this proportion is the fraction of profits (losses) the firms capture. Only when the sharing proportion is set equal to unity-a fixed price contract- are target costs or bids unambiguous indicators of the firm's expected costs.

Some of the previous analyses of cost estimation in government contracts has been primarily statistical. These statistical studies assume that contractors seek un- biased predictions of actual costs and they have been partially successful in explain- ing the tendency to underestimate costs.

In this study, an alternative eco~zomicex-planation of the procurement process suggests that contractors may bias their cost estimates to conform with their over- riding ohjective to maximize profits.

APPENDIX 1

'This Appendiu calculates a lower bound on the bid a vendor sub~nits for an incenti~e type contract. If the contracts are let under competitive bidding the bids will tend t o equal this lower bound. The vendor is as- sumed to have a constailt attitude tuward risk; that is, the risk premium required for a particular risk is independent of the firm's wealth. The firm may have constant risk aversion, constant risk indifference, or con- stant risk preference. Bids that firms submit are conditioned by the alternative oppor- tunities available to them. In particular, it is assumed that the bid is calculated so that the expected utility of the incentive contract is no less than the etpected utility of the best alternative opportuuity. A lower bound on the bid is obtained by equating these ex-pected utilities. The cost, C , of producing for the incentive co~ltract is a random variable with an arbitrary probability distribution. Similarly, the profits, II,obtainable on the bcst alternative opportunity are also a ran- don1 variable with an arbitrary probability distribution.

Cot~stantRisk A r e r s i o ~ ~

When the firm has constant risk aversion its utility function with respect to profits, IJ, may be denoted by

where p measures risk aversion, i.e., the risk aversion function is simply17

Profits, IIz,from the incentive are

l7 See llcCall ant1 Pratt.

845 McCALL: INCEN'YIVE CONTRACrI'ING

where a is the target proportion, p is the bid or target cost, @ is the sharing proportion, and C denotes the actual costs. If 111is op- portunity profits, then both IT1 and IIa are random variables with arbitrary cumulative distribution functions (c.d.f.), say, F1 and Fz, respectively.

A lower bound on the bid, p, submitted by the firm is obtained by equating the expected value of ul(II1) with the expected value of ul(fl2) and solving for p, where the first expectation is with respect to 111 and the second expectation is with respect to C. Symbolically,

Equating Eul(TI1) and Ezcl(n2) and solving for p yields

where Ql(t) denotes the moment generating function of IIl and \kz (t) denotes the moment generating function of Cz. For example, if FIl and C are distributed normally with mean and variance, nzl, a:, and mz, a:, respec-tively, then

I t follows thatl8

Ill 1 <0

where $p(/Yuz-& can be interpreted as the

the risk on the incentive contract is identical to that of its alternative opportunity and the risk premium is zero. The risk premium is positive when P>u1/u2 and negative when P<5 1 / 0 2 .

Also, assuming ml>O, the bid for a fixed- price contract (/3= 1) with a > O is given by

Similarly, the bid for a cost plus fixed fee contract (@= 0) with a > O is given by

t?ll - ;pa; (11) P = ,

a

which, of course, may be negative.

Constant Risk Indifference

For constant risk indifference,

(12) uz(IT) = a2 + b J I

and

(13) l:zdz(II) = a2 + b214:II

I t follows that a lower bound on the bid the firm will submit is

Constant Risk Preference

l:inally, if the firm's utility function ex-hibits constant risk preference,

(15) 24s(II) = 0 3 + hje?[p(~n), p > 0

(16) I < Z L ~ ( I I ~ ) + 6dl<[exp(pIIl)]=

(17) 1'.:243(&) = a a

i-b 3 ~ ( e x p [ p ( f f p+ @(P- C ) ) l ) ,

and

risk premium. Notice that when , ~ = U ~ / F ~ ,

lH It is acsurneJ t11:rt if expected alternative profits are negative, the lirlr~w i l l not protluce and will reduce 120r e~ar-i:plc, i f I l l an(1 C Lire tliqtrihuted its expectetl prof ts to zero. nornlally as before. then

846 1'HE AMERICAN ECONOMIC REVIEW

and

I t follows that a lower bound on the bid this risk preferent firm submitted is given by

Optimal Bidding U'lzen the Firm Possesses Probabilistic Informatio7z Regarding Com-petitors' Bids

I n Section I i t mas assumed that the firm had no knowledge of other firms' costs and was, therefore, ignorant of their bids. The case is now considered where firms have prob- abilistic information on competitors' bids. Let @,(4) denote the probability that the bids of the n competitive firms are all greater than (. If the bids are stochastically inde- pendent, then

where c t )%( l )is the probability that tlie i th con~petitor's bid exceeds 4.

:issunling the contract is awarded to the lirin submitting the lowest bid, the expected profits derived from a bid of P are given by

where 111 and I I z are defined as in Section I. The firm then chooses $2 to maximize ex-pected profits, E n ( $ ) , I p < co where 3 denotes the minimnnl bid the firm would ever submit.

REFERENCES

A. Alchian, "Electrical Equipment Collusion: Why and How," unpublished, Apr. 1961.

K. L. Deavers and J. J. McCall, Notes on In- centive Contracting, The R.4ND Corpora-tion, RM-5019-PR, Sept. 1966.

and -, An Analysis of Procure- ment and Product Improvenzent Decisions, The RAND Corporation, RM-3859-PR, Dec. 1963.

I. N. Fisher, "An Evaluation of Incentive Contracting Experience," Nav. Res. Log. Quart., Mar. 1969, 16, 63-83.

and G. R. Hall, "Risk and Corporate Rates of Return," Quart. J . Econ., Feb. 1969, 83, 79-92.

R. Giguet and G. Morlat, TIre Causes of Systenzatic Error in the Cost Estimates of Public Works, RAXD Translation T-76, translation by N. 111. Taylor, rev. Mar. 24, 1958.

G. R. Hall and R. E. Johnson, Aircraft Co- Production and Proczlrc17zelzt Strategy, The RAND Corporation, R-450-PR, Rlay 1967.

T. Marschak, T. K. Glennan, Jr., and R. Sum- mers, Strategy for R and D: Studies in the dIicroeco~zomics of Development, New York 1967.

J. J. McCall, "Competitive Production for Constant Risk Utility Functions," Rev. Econ. Stud., Apr. 1967, 34, 41 7-420.

F. T. Moore, d4ilitary Procuvenzeut aud Colt- tracting: AIZ Ecolzowzic Analjlsis, The RAND Corporation, RRI-2948-PR, June 1962.

, "Incentive Contracts," in S. Enlie, ed., Defense Econon~ics, Engle~vood Cliffs 1967, ch. 12.

M. J. Peck and F. M. Scherer, The Weapolzs Acquisition Process; Alz Ecolzonric Analysis, Boston 1962.

J. W. Pratt, "Risk Aversion in the Small and in the Large," Eco~zonict~ica, Jan.-Apr. 1964,32, 122-36.

F. M. Scherer, (1964a) "The 'l'heory of Con- tractual Incentives for Cost Reduction," Quart. J. Ecotz., May 1964, 278, 257-280.

(1964b) The TVeapons Acqzrisitiorz Process: EcorzonzZc I~zcetztives, Boston 1964.

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The Simple Economics of Incentive ContractingJ. J. McCallThe American Economic Review, Vol. 60, No. 5. (Dec., 1970), pp. 837-846.Stable URL:

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