Unnatural monopoly

JOURNAL OF

ELSEWIER Journal of Public Economics 57 (1995) 471-488

Unnatural monopoly

Saul E&in”, David de Mezab’*

‘London Business School, Sussex Place, Regents Park, London, NW1 4SA, UK

bDepartment of Economics, University of Exeter, Amory Building, Rennes Drive, Exeter, EX4 4RJ, UK

Received May 1993, revised version received June 1994

Abstract

This paper investigates the merits of statutory monopoly as a means of preventing wasteful market fragmentation. The key result is that a public firm committed to price at cost may be unable to repel entry even when it is socially desirable that it should do so. Limited entry may be worse than either statutory monopoly or free entry. The robustness of results when competition stimulates a state firm to lower its costs is also examined.

Keywords: Statutory monopoly; Deregulation; Entry

JEL classification: LA3

It is obvious for example, how great an economy of labour would be obtained if London were supplied by a single gas or water company instead of the existing plurality. . were there only one establishment it could make lower charges consistently while obtaining the rate of profit now realised 1 J.S. Mill (1926, pp. 43).

There cannot be a doubt that if the law did not interpose its prohibition, the transmission of letters would be gladly undertaken by capitalists, and conducted on the ordinary commercial principles, with all that economy, attention to the wants of their customers, and skilful adaption of means to the desired end, which is usually practised by those whose interests are involved with their success. But the law constitutes the Post Office a monopoly. Its conductors are, therefore, uninfluenced by the ordinary motives to enterprise and good management; and however, injudiciously the institution may be conducted, however inadequate it may be to the

* Corresponding author.

0047-2727/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0047-2727(94)01468-X

472 S. E&n, D. de Meza I Journal of Public Economics 57 (1995) 471-488

growing wants of the nation, the people must submit to the inconvenience: they cannot set up a Post Office for themselves - Rowland Hill (quoted by R.H. Coase, 1939, pp. 430).

1. Introduction

There are a few goods for which it is illegal for private producers to compete with the monopoly state supplier. The most notable current example is letter delivery, which in almost every country is the exclusive right of the state post office.’ This paper investigates the circumstances in which there might be good reasons to take the drastic step of outlawing competition. The main finding is that in the presence of economies of scale, an average cost pricing public firm may be unable to deter the entry of lower cost private firms, but unless the cost advantage of the entrants is sufficiently great, consumers lose, whether or not the state firm is driven from the market. Even when the profits of the entrant are included in the social calculus, statutory monopoly may be justified.

The usual argument for prohibiting entry, as in the J.S. Mill quote above, is that the dissipation of economies of scale can thereby be avoided. In contrast, critics of statutory monopoly, exemplified by Rowland Hill, father of the Victorian penny post, invariably point to the stagnation of enterprise occurring, as Marshall puts it, “. . . under the deadly shades of official monopoly”. Friedman (1962) amongst others claims that no policy dilemma is posed by these conflicting arguments. Either scale economies really are significant, in which case no entrant could succeed in competition with an efficient nationalised firm, and there is no need to legislate against entry; or, if despite economies of scale, the public firm proves vulnerable to entry due to its inefficiency, legislating against entry would be a harmful constraint on innovation and competition. On this view, statutory monopoly is never beneficial and is sometimes deleterious, at least from the point of view of consumers. Some analytical support for this ‘survivability’ test of the desirability at repeal is to be found in the theory of contestable markets according to which invisible hand results apply (with a few exceptions) even in the presence of economies of scale (Baumol et al., 1982).

In challenging these claims, this paper drops the ‘hit and run’ assumption required for a contestable market and instead allows all firms to adjust price and output after entry. It also recognises that a statutory monopoly is invariably a nationalised industry unconcerned with profit-maximisation per se. The relevant descriptive literature suggests that average cost pricing is the objective actually adopted by public sector enterprises in practice (see,

1 Current exceptions include the United Kingdom for delivery priced at over El.00 and Sweden.

S. Estrin, D. de Mesa I Journal of Public Economics 57 (1995) 471-488 473

for example, Albon, 1987; Corby, 1979; Tulkens, 1968). In evaluating statutory monopoly, the first task is thus to find conditions under which private firms can profitably enter in the presence of a break-even price with economies of scale. If these conditions are met, the welfare consequences of entry are then examined.

The paper is organised as follows. Section 2 sets out the basic model and uses it to examine the trade-offs between the dissipation of scale economies and the gains from provision by a more efficient private firm. As long as the public firm survives, the repeal of the statutory monopoly either has no effect or, if entry occurs, price rises. Should the public firm be eliminated, or if it cuts its costs in response to the increased competition, results are not so clear cut. Section 3 investigates these issues using explicit functional forms. Even in the presence of quite modest economies of scale, inefficiency of the public firm must be substantial to justify repeal. The effects of multiple entry of private firms is considered in section 4. With freedom of entry, public and private firms tend not to co-exist though it is ambiguous whether this strengthens or weakens the case for statutory monopoly. Conclusions are drawn in Section 5.

2. The basic issues

Much public debate on liberalising the market in which public firms operate has centered on what is pejoratively termed ‘cream skimming’ or ‘cherry picking’. This is a phenomenon of multi-product firms with the efficiency issue concerning an entrant invading only the high profit segment of the public firms’ market. The loss of economies of scale forces the public firm to raise prices, eventually leading to an overall loss of consumer surplus. As with the single-product case, the question is whether fragment- ing the market by permitting firms which may be more efficient to enter involves such a loss of scale economies as to be harmful on balance. The multi-product case adds realism and complexity but is conceptually a minor extension. In what follows, attention is therefore confined to the single- product case.

A literature on ‘mixed’ duopoly markets involving a private and a public enterprise has begun to appear (see Vickers and Yarrow, 1988; De Fraja and Delbono, 1990; and Bos, 1991, for surveys). Market structure has generally been taken as given and the issue has been the welfare properties of various duopoly solutions, e.g. Cournot-Nash equilibrium by Bos (1986), Stackel- berg equilibrium by Beato and Mas-Cole11 (1984) and comparisons of the two by Cremer et al. (1989) and De Fraja and Delbono (1989). This paper differs from these works in its focus on the feasibility of entry and on its desirability.

474 S. Estrin, D. de Meza I Journal of Public Economics 57 (1995) 471-488

In a first-best world it is evident that if it is worth producing a good subject to economies of scale in production, it should be supplied by a single firm. Unfortunately, laissez faire cannot guarantee such a felicitous out- come, as illustrated by the basic free-entry Cournot-Nash model in which there is typically multiple entry involving the wasteful duplication of fixed costs. Suppose, for example, that market demand is of unitary elasticity and marginal cost is constant. If fixed costs are such as to allow five firms to enter, it can be shown that equilibrium price is 25% above marginal cost. With only one firm in the market, its break-even price is a mere 4% above marginal cost. Even so, prohibiting entry to all but approved firms may be undesirable. The obvious problem is that suppressing competition harms consumers, as illustrated by Seade’s (1980) result that however great economies of scale are, in a stable Cournot-Nash equilibrium the fewer the number of firms the higher is their selling price. It seems plausible that this is why private firms are not normally given statutory protection against entry even when the existence of scale economies is not in doubt. When restrictions on entry are actually awarded to private firms,* regulation by an independent agency is the norm. However, as we have noted, governments do sometimes prohibit competition with public firms whilst imposing only limited external supervision of the resulting monopoly. It is presumably hoped that the dissipation of economies of scale and scope will thereby be avoided without running the risk of exploiting consumers or requiring a costly and inflexible bureaucracyP

To explore the questions further, suppose a public firm, N, provides a single good subject to declining average cost. Its proximate goal is to maximise output subject to breaking even, behaviour reasonably in accord with the theoretical welfare literature (see Rees, 1984), public choice theories such as Niskanen (1971) and with at least British institutional practice (see Estrin and de Meza, 1988). Moreover, it is well known that break-even pricing achieves constrained social efficiency if N holds a monopoly position.

For now, we assume that there is but a single profit-maximising firm, M, capable of producing the good if the statutory monopoly were to be repealed. It also has declining average costs and may be more efficient than N. A two-stage game is specified. The firms first make simultaneous entry decisions, which involve sinking a fixed cost. If both enter, then at the next

’ For example, in the United Kingdom to British Gas in the household market, to BT and Mercury in telecommunications and to taxi-cabs.

3 Crew and Kleindorfer (1985) explore some of the issues.

S. E&n, D. de Meza ! Journal of Public Economics 57 (1995) 471-488 475

stage outputs are simultaneously chosen and variable costs are incurredP The second stage is modelled as a regular Cournot game except that N still seeks to break even. Even in a mixed duopoly, this is the appropriate welfare objective for the public firm. This is because, given the standard assumptions leading to downward-sloping, profit-maximising, best-response functions and a unique equilibrium, as N expands, M contracts by less and so price falls.5 Should N be unable to cover its total cost in the second stage, budgetary pressures from the government require that it does its best to break even and so make the greatest contribution to repaying fixed costs by maximising profit.

Fig. 1 shows the best-response functions for the second-stage game. If both firms were equally efficient and were to maximise profit, the best- response functions would be AA and BB and Nash equilibrium would be at 8. However, with average cost pricing, the response function of the public firm is modified. N will expand output whenever profit is positive along AA so as to eliminate the surplus. The best-response function of the public firm is thus ACD, where M* is the highest private output consistent with N breaking even.6 With break-even pricing by the public firm, the Nash equilibrium of the second-stage game is at E*. Fig. 1 provides a basis for identifying the relevant properties of the subgame-perfect equilibrium, summarised in three propositions.

Proposition 1. A mixed duopoly is impossible if the public firm is at least as efficient as the private jirm.

Proof. Inspection of Fig. 1 shows that average-cost pricing augments N’s output relative to M’s. Since N is at least as efficient and its output is higher, its realised average cost must be lower than M’s. As price equals N’s average cost, M must be loss-making. Hence, M would not enter. 0

Proposition 1 does not resolve whether a mixed duopoly can exist when the public firm is less efficient than the private firm. Under these circumstances, N’s response function shifts inwards as shown, for example, by

4 Results are not dramatically altered if tixed costs are non-recurrent and have already been sunk by N prior to the game starting. Essentially, some equilibria in which only M operates are eliminated.

5 Even if the entrant’s profits are included in the social calculus, average cost pricing by the public firm is normally a constrained optimum (Cremer et al., 1989).

6Notice that because fixed costs are sunk, there is no discontinuity in the second-stage response functions at M*.


Output of M

Fig. 1. Second-stage equilibrium.

FGF. The second-stage Nash equilibrium is at E, a public output below N*, the output at which, because of fixed costs, the private firm breaks even. There is thus an equilibrium with both firms active. Cases of this sort will shortly be explored numerically. However, if entry does occur, the welfare consequences are immediate.

Proposition 2. Mixed duopoly k worse for consumers than statutory monopoly.

Proof. Eliminating the private firm from a mixed duopoly causes a right- ward shift in the demand faced by the public firm. As average cost is falling and equal to price, consumers are better off under statutorymonopoly.

By an obvious extension,

Proposition 3. The mixed duopoly price is higher the more efjicient is private firm.

0

the

S. Estrin, D. de Meza I Journal of Public Economics 57 (1995) 471-488 477

3. The benefits of competition

Propositions 1 and 2 indicate that statutory monopoly may have merit because, for some configurations of demand and cost parameters, it will be privately profitable for M to enter the market, even though the emergence of duopoly will reduce consumer welfare. Indeed, at first sight the case for protecting the public firm is compelling since, if repeal has any effect, it is harmful. What is omitted from the analysis, however, is the possibility that repeal eliminates the public firm. Moreover, the introduction of competition may also stimulate efficiency gains in N.’ As results are now conditional, we explore possibilities numerically. In particular, market demand is assumed to be linear, marginal cost constant, and the declining average cost to be entirely due to a fixed cost. The modelling is detailed in the appendix.

The vertical axis of Fig. 2 shows the efficiency differential, A, which is the common percentage by which the public firm’s fixed and marginal costs exceed those of the private firm. The demand parameters are chosen so that if a fully efficient firm sets price equal to average cost, the price elasticity would be unity. The percentage of fixed costs in total cost at such a

0 5 10 14.6 F

Fig. 2. Market-structure partition.

‘Indeed, comparing Eastern Europe and Western Europe, this may be the major conse- quence of suppressing competition.

478 S. Estrin, D. de Mera I Journal of Public Economics 57 (1995) 471-488

configuration, F, is shown along the horizontal axis. As F varies, marginal cost is adjusted to preserve the efficient break-even average cost at unity.

In Fig. 2, locus A is the upper bound on h such that the public firm can just cover its cost in a mixed-duopoly equilibrium. From Proposition 1, this threshold occurs where the public firm is inefficient relative to the private firm. When fixed costs are high, potential profits are low, so lowering the maximum inefficiency level consistent with the public firm covering its costs. Moreover, break-even pricing then makes less of a difference to the public firm’s output and so lowers its strategic advantage. Hence, locus A is downward sloping. Break-even configurations are shown as 2 in Figs. 3(a) and 3(b). What differs between the two cases is that in Fig. 3(a), Z lies to the left of N*, the maximum public output at which the private firm can break even, whereas in Fig. 3(b), Z is to the right of N*. In Fig. 3(a), as the efficiency of N increases and its response function shifts up, a stable equilibrium is reached at W, where M just covers its cost. Configurations of this kind are shown in Fig. 2 by locus B, the lower bound on the inefficiency of N consistent with M just surviving. Efficiency differentials intermediate between those implicit in the two response functions support mixed duopoly, and in Fig. 2 appear as the region enclosed by locus A and locus B. In Fig. 3(b) economies of scale are higher than in Fig. 3(a) and as the efficiency of N is raised, the stable equilibrium occurs to the right of W. So,

(4 04

Output of M Output of M

0utpN;t of N

Fig. 3. Survival thresholds.

N output of N


if the efficiency of N is below that implicit in the lower response function, only M enters and if the firm’s efficiency exceeds this level, it is the sole entrant. When F is sufficiently high there is no mixed duopoly zone. As shown in Fig. 2 this is the case when F > 10% and then locus A is the boundary between the two kinds of monopoly.

Notice that in both Fig. 3(a) and 3(b) there are also stable equilibria at T. If these are anticipated outcomes, only the private firm enters and price is higher than under mixed duopoly. In assuming these equilibria do not emerge, Fig. 2 does not report the strongest case for statutory monopoly. When the industry is a natural monopoly, which for our assumptions is the case when F 2 14.6%, the only second-stage equilibria are like T, so only one firm will be active. Locus C plots (A, F) pairs where the private firm just breaks even and there is no equilibrium in which N covers cost. Finally, with locus D, the maximum A at which a statutory monopoly can break even, the ingredients are assembled to enable the parameter space to be fully partitioned between the various possible market structures consistent with repeal of statutory monopoly.

The welfare consequences of repeal are summarised in Fig. 4, which is based on the same assumptions as Fig. 2 and reproduces the partitioning loci A and D. Recall that for benefits to flow, it is necessary that statutory monopoly is replaced by a private monopoly. In Fig. 4 locus E shows combinations of F and A such that price is the same whether the supplier is public or private. Standard assumptions imply that on elimination of the public firm the private firm expands by less than enough to replace the lost output, hence locus E must lie above locus A. So only combinations above

2.4

0 5 10 F

Fig. 4. Welfare partition.


E and below D represent beneficial repeal. Economies of scale must be very low and inefficiency very high for entry to be desirable.

We have seen that if duopoly emerges, consumers are worse off provided that N’s cost function is unchanged. However, entry may force N to eliminate slack and this is a source of gain to consumers. Suppose that the post-entry efficiency differential is just large enough for M to cover its costs (i.e. is given by B). The locus X in Fig. 4 records the level of pre-entry X inefficiency of N such that, if wiped out when a mixed duopoly emerges, price remains the same as under statutory monopoly. To interpret X suppose that when F = lo%, prior to entry the public firm was operating with 19% inefficiency (the height of locus B in Fig. 2). Then as shown in Fig. 4, if 9% of this inefficiency were eliminated as a result of competition, mixed duopoly and statutory monopoly yield the same consumer surplus.

Public policy is more likely to be justified on the grounds that reform will benefit consumers than that it will boost profit. Nevertheless, it is of interest to look at the impact of repeal on the sum of profit and consumer surplus. In Fig. 5, locus G shows the threshold along which aggregate welfare is the same under mixed duopoly as public monopoly. Locus F represents points such that consumer surplus plus profit is the same under private monopoly as statutory monopoly. The regions under which repeal is strictly harmful are shaded. Including profit naturally eliminates some of the area where repeal is disadvantageous, but even with low scale economies and not too

Fig. 5. Profit inclusive welfare partition.


much inefficiency, there is a considerable area of the parameter space over which it is desirable to suppress competition. In particular, if there is a mixed duopoly with F > 5%, statutory monopoly is always preferable.

We can now interpret the various curves in Figs. 2, 4 and 5 together. Consider, for example, the case of fixed costs 5% of the statutory monopoly’s total cost. M does not enter if the post-entry efficiency differential is below 14%. If, 14 < A < 18.9, there is a duopoly and consumers lose, though if the entrants’ profits are included, aggregate welfare is unchanged. For consumers to gain, the locus X shows that competition must have eliminated at least 2.4% of pre-entry inefficiency. When A > 18.9% the only equilibrium is that the private firm is the sole producer. This is bad news for consumers unless the pre-entry efficiency differential exceeded 47.5%. Even if the criterion is consumer surplus plus profit, there will be welfare losses unless the efficiency differential exceeds 10.9%. Thus, according to Fig. 2, even quite modest economies of scale imply that repeal of the statutory monopoly is only beneficial with substantial inefficiencies.

4. Multiple entry

The analysis so far may seem to be biased in favour of statutory monopoly by a restriction to a single potential entrant. Replacement of a public monopoly by a private monopoly evidently leaves consumers vulnerable, but if repeal results in multiple entry, consumers will be protected by competition This is particularly so since, in contrast to a regular private industry, in a mixed oligopoly more entry raises profits. The reason is essentially that to cover cost, the public firm must contract its output by more than the entrant produces.

Proposition 4. In the presence of a public firm, profit per private firm is increasing in the number entering.

Proof. In Fig. 5 the mixed duopoly equilibrium is at A. With two private firms, their aggregate output is higher, given that of N, than a single firm would produce. This is a standard property of Cournot-Nash equilibrium (see Seade, 1980) and the implied response function of a private sector comprising two firms is labelled as such in Fig. 6, yielding Nash equilibrium at D. To establish the properties of D note that total output is the same at A and B since both are on the 45” line. It follows that at B the public firm has lowered its output by what the private firm produced in the duopoly


Private-sector output

entrant

0 Output of N

Fig. 6. Multiple entry equilibrium.

equilibrium. So at B, the residual demand of each private firm is the same as is faced by the single private firm in equilibrium at A. Hence, B is on the two-firm, private-sector response function. But at B the residual demand facing N is lower than at A since output by the rest of the industry is higher, implying that the average cost of N is higher at B than at A. As industry output and price are unchanged, it follows that B is not on N’s best response function which, for break even, must lie to the left of B. The Nash equilibrium of the second-stage game is thus at D. Industry output is lower than at A and price is higher. As the output of each private firm exceeds that at A and average cost is declining, the profit of each of them is higher than under duopoly. Cl

Proposition 4 evidently implies that multiple equilibria are on the cards. Either no private firms enter or lots of them do. In fact, if a purely private industry were to support n firms, a mixed oligopoly must also have it active firms. So, if there is a mixed equilibrium there must also be an all private equilibrium, and public monopoly may also be an equilibrium.


Proposition 5. The number of firms in a free-entry, mixed oligopoly k equal to the number of private firms entering if no public firm exists.

Proof. Suppose that the mixed oligopoly had fewer than n firms. For this to be an equilibrium it follows from Proposition 4 that the entry of another private firm causes the public firm to be loss-making. The extra firm is then sure to be profitable for it faces less competition than it would with n - 1 fully efficient profit maximisers. A contradiction also arises if the mixed oligopoly has more than n active firms. In such an equilibrium, the public firm is the budget producer. However, even if it produced the same output as the other firms, all the private firms would be loss-making since there is a private equilibrium with n firms. 0

As consumers can only gain if an all private industry has an efficiency advantage more than enough to preclude the entry of the public firm, for welfare purposes it is enough to compare price under a free-entry private oligopoly with that under statutory monopoly. The number of firms entering depends on the level of fixed costs. For the various natural oligopoly intervals, Fig. 7 shows the combinations of A and F yielding equal price. So above the line is where repeal is advantageous. Finally, notice that Figs. 2 and 7 show that limited entry may be worse than statutory monopoly or free entry. Suppose A = 6% and F = 6%. Then, from Fig. 2, allowing a single

h

26.7

25.0

20.4

16.1

0 314.3 7.2 14.6 F

Fig. 7. Free-entry partition.


entrant results in a disadvantageous mixed duopoly, but with free entry a welfare-enhancing quadropoly equilibrium exists,

5. Conclusion

The message of this paper is that in a simple quantity-setting Nash game it may be desirable to award a public firm statutory protection against entry.8 In the absence of such a policy it is not true that a public firm can necessarily repel entry even when it is socially desirable that it should do so. Equally, there is a danger that statutory monopoly may preserve a public firm when it would be better that it is replaced by more efficient private enterprises. In short, there is merit in the views of both Hill and Mill. Matters cannot be decided a priori.

Acknowledgments

This paper is an extension of part of the theoretical and simulation work reported in Estrin and de Meza (1988). Polly Vizard provided excellent research assistance. We wish to thank two anonymous referees, John Black, Bob Gould, Ben Lockwood, Clive Southey, John Sutton, Hugh Wills, and participants in seminars at the Universities of Bristol, Exeter, Guelph, Quebec B Montreal, Western Ontario and the London Business School, for many helpful comments. Responses to earlier versions by Dobbs and Richards (1990) led to many corrections and modifications.

Appendix

The equations generating Figs. 2, 4, and 7 are derived from the following system:

C,=F+cM, (1)

C, = (1 + h)(F -t cN) , (2)

P=a--(M+N). (3)

‘Alternatively, it may be better to follow the Demsetz (1968) proposal of allowing private firms to compete for the monopoly, awarding the franchise to the firm promising the lowest consumer price. There are well-known problems with this scheme, but the issues are not relevant here. Our focus is not on how to handle a natural monopoly but on the merit of the government in creating a monopoly when competition is feasible.

S. Estrin, D. de Meza i Journal of Public Economics 57 (1995) 471-488 485

Eqs. (1) and (2) are the total cost functions of the private and the public firm, and Eq. (3) is the inverse market demand curve. The output of an efficient break-even pricer is the largest root of

a-PN=FIN+c. (4)

Costs are normalised so that the solution of Eq. (4) is N = P = 1 and hence cx = 1 + p is imposed. Moreover, the plotting is for the case that, with efficient break-even pricing, demand elasticity is unity, which requires (Y = 2 and p = 1. As F varies, the price set by an efficient break-even pricer is maintained at unity by adjusting c. Thus,

c=l-F. (5)

To put A and F in percentage terms divide each by 100 in all equations. A mixed-duopoly equilibrium requires that both firms be on their best-

response functions. For the private firms this is the standard condition that

M=0.5(2-c-N). (6)

The public firm selects the highest output at which price equals average cost, which, from Eqs. (3) and (4), implies that

N = [2 - (1 + h)c -M + v((1 + A)c - 2 + M)2 - 4(1+ h)F]/2. (7)

Solving Eqs. (6) and (7) and picking the largest root yields the stable, mixed-duopoly equilibrium in the second-stage game. The output of the private firm is then

M = (-(12~ - 8 - 8(1+ A)c)

+ v( 12c - 8 - 8( 1 + A)c)~ - 32(8( 1 + A)c - 8c + 4F( 1 + A) + c24A) / 16 .

(8)

Locus A. The public firm is at its survival threshold in a mixed-duopoly equilibrium so its response function is tangent to that of M. This requires that there is a single root to (8). Making use of Eq. (5) to substitute for c, the locus is

A=

(1-F)*+2(1-F)+2F-~((1-F)2+2(1-F)+2F)2-(1-F)*((1-F)z+4(1-F)) -1

2( 1 - F)*

(9

Locus B. For M to break even in the mixed-duopoly equilibrium it follows from Eqs. (l), (3) and (6) that

M=vF. (10)


Setting the RHS of Eq. (8) equal to q/F and solving for A yields locus B:

A = 2(1- F) - (1 - F)* - F0.5(3(1 - F) - 2) - 2F _ I

2(1 -F) + F - 2F0.5(1 - F) - (1 -F)* ’ (11)

Locus C. When F > 14.6 and A > 0 the public firm cannot cover its costs in the second-stage, mixed-duopoly equilibrium. This locus represents the value of A just high enough for the private firm to cover its cost. Solving Eq. (5) and the analagous profit-maximising response function for the public firm, N = (2 - AC - M)/2, yields the regular Cournot-Nash equilibrium

M = (2 + c[l - 2(h - 1)]}/3. (12)

Solving Eqs. (10) and (12),

A=l.SdF-F-1. (13)

Locus D. Under statutory monopoly, the output of the public firm is the largest root of

2-N=(l+A)(FIN+c), (14)

which is

N = 0.5(2 - (1 + h)c + .\/((l + A)c - 2)* - 4(1+ h)F) . (15)

If the public firm is too inefficient it cannot cover its cost even under statutory monopoly. The relevant survival threshold occurs when there is a single root to Eq. (15), i.e. the expression below the square root sign is zero, which implies

A=2-21h-F)2_1 (1-F)’ *

Locus E. If the private firm has a monopoly its output is

M = 1 - 0.5c . (17)

Consumers are as well off as under statutory monopoly if the outputs determined by Eqs. (15) and (17) are equal, which requires

(1 + F)* - 4

Locus X. Suppose that the public firm is just sufficiently inefficient for a mixed-duopoly to emerge, that is F and A satisfy Eq. (11). As the private firm breaks even, its average-cost curve is tangent to its residual demand curve, which requires

S. Estrin, D. de Mera I Journal of Public Economics 57 (1995) 471-488 487

P=vF+c. (1%

Now suppose that prior to entry the cost function of the public firm is C, = (1 + h + X)(F - cN) so that X is the proportion of inefficiency eliminated by competition. Solving Eq. (15) for this augmented cost function and finding the associated price, it is set equal to the price determined by Eq. (19) to obtain

x= l-F+2F’.‘--F*

1_~0.5+F+F1.5_F*-~-*’

Finally, Eq. (11) is used to substitute for A. So Eq. (20) gives the percentage by which entry must cause the public firm’s cost to decline if a threshold mixed-duopoly leaves consumers just as well off as under statutory monopoly. Note that this is a lower bound on the X-inefficiency required to justify repeal in that if A lies above locus B, the loss from mixed duopoly is greater so the offsetting efficiency gain must be larger if it is to offset the dissipatory effects of entry.

Locus F. The profit of a private monopoly is

rr = 0.25(1+ F)* - F . (21)

Making use of Eqs. (15) and (17) the difference between price under public and private monopoly is

A = OS( 1 - h) + 0.5v( hc - 2)* - 4hF . (22)

Adding the profit of the private firm to the loss of computer surplus, when a statutory monopoly is displaced by a private firm, aggregate surplus is unchanged if

T-0.54*-NA=O. (23)

Locus F is found by substituting Eqs. (15), (21), (22) in (23).

Locus G. This repeats the exercise of locus F for the mixed-duopoly case. Using Eq. (6), total output is 2 - c - M, where M is given by Eq. (8). Price is then found from the inverse demand curve as c + M, so profit is M* - F. Relative to statutory monopoly, the increase in price is 2 -N - M - c. With these redefinitions, locus G is the plot of Eq. (23).

Fig. 7. In a free-entry Cournot-Nash equilibrium with identical profit maximisers standard calculations give the number of active firms as the largest integer no greater than

n = (1+ F)F-0.5 - 1. (24)

488 S. Estrin, D. de Mesa I Journal of Public Economics 57 (1995) 471-488

Eq. (24) locates the various oligopoly intervals in the figure. Taking the total output of an industry of n private firms engaged in Cournot-Nash competition and setting it equal to output under statutory monopoly, as given by Eq. ‘( 15), yields the welfare partition of the figure:

h = 4(n - l)‘/(n + 1)’ + 4(1- F)‘(nl(n + 1))’ - 8(1- F)n(n - l)(n + 1) - 4 _ 1

4(1 - F)nl(n + 1) - 4(1 - F)(n - l)l(n + 1) - 4(1 - F) - 4F

(25)

References

Albon, R., 1987, Privatise the post, Policy Study No. 82 (Centre for Policy Studies, London). Baumol, W.J., R. Panzar and R.D. Willig, 1982, Contestable markets and the theory of

industrial structure (Harcourt, Brace, Jovanovich, New York). Beato, P. and A. Mas-Colell, 1984, Marginal cost pricing as a regulation mechanism in mixed

markets, in: M. Marchand, P. Pestieu and H. Tulkens, eds., The performance of public enterprises (North-Holland, Amsterdam).

Bos, D., 1986, Public enterprise economics (North-Holland, Amsterdam). Bos, D., 1991, Privatisation: A theoretical treatment (Clarendon Press, Oxford). Coase, R.H., 1939, Rowland Hill and the penny post, Economica 6, 423-435. Corby, M.E., 1979, The postal business 1969-79 (Kogan Page, London). Cremer, H., M. Marchand and J.-F. Thiesse, 1989, The public firm as an instrument for

regulation on oligopolistic markets, Oxford Economic Papers 41, 283-301. Crew, M.A. and P.R. Kleindorfer, 1985, Governance costs and rate of return regulation,

Journal of Institutional and Theoretical Economics, March. Demsetz, H., 1968, Why regulate utilities ?, Journal of Law and Economics 11, 55-65. De Fraja, G. and F. Delbono, 1989, Alternative strategies of a public enterprise in oligopoly,

Oxford Economic Papers 41, 302-311. De Fraja, G. and F. Delbono, 1990, Game theoretic models of mixed oligopoly, Journal of

Economic Surveys 4, 1-17. Dobbs, I. and P. Richards, 1990, A critique of the DHL report on the monopoly, The Post

Office. Estrin, S. and D. de Meza, 1988, Should the Post Office’s statutory monopoly be lifted?,

London School of Economics, mimeo, September. Friedman, M., 1962, Capitalism and freedom (University of Chicago Press, Chicago). Mill, J.S., 1926, Principles of political economy (Largrass, London). Niskanen, W.A., Jr., 1971, Bureaucracy and representative government (Aldine-Atherton,

Chicago). Rees, R., 1984, A positive theory of the public enterprise, in: M. Marchand, P. Pestieau and H.

Tulkens, eds. The performance of public enterprises (North-Holland, Amsterdam). Seade, J., 1980, On the effects of entry, Econometrica 48, no. 2, 479-489. Tulkens, H., 1968, Programming analysis of the post service (Librarie Universitaire, Louvain). Vickers, J. and G. Yarrow, 1988, Privatisation - an economic analysis (MIT Press, Cambridge,

MA).

Unnatural monopoly

Documents

Transcript of Unnatural monopoly