Open markets in the transfer state.

I. Introduction

In this paper we make a simple point in elementary public choice theory, but one that has not, to our knowledge, been made. As the share of producers relative to nonproducers falls in a political economy, operating within broadly democratic institutions of governance, we may predict a reduction in the politicized restrictiveness of markets. The shortfall between total product actually generated and that which might be possible must, of course, increase with the increase in the share of nonproducers. But, within the producing sector itself, markets will be organized more "efficiently." This second effect will, at least to some small extent, offset the first.

In summary generalization, our prediction suggests that the emergence and extension of the redistributive or transfer state in the decades following World War II should have been accompanied by some relaxation of mercantilist-like market restrictions. Results seem broadly supportive here. If the redistributive or transfer state continues to grow, as measured by the share of nonproducers in the electorate, we should expect further opening of markets. In the international setting, the markets within and among welfare states would be more open than markets within and among more productive, but equally politicized, "capitalist" states (those with less extensive transfer activity).

The analysis here extends that which we developed in an earlier paper[1]. In that paper, we demonstrated that the political requirement for the organization of a coalition of cartels places severe limits on both the economic interests in, and the degree of, particularized market restriction, even on the part of members of specialized producer groups. The idealized situation for members of a single producing group, made up of the suppliers of all the inputs involved in the production of a single good, would be described by cartelization of the whole industry, with monopoly price and output adjustment, with all other industries in the economy operating under fully competitive conditions. The second part of this condition is important when it is recognized that the producers in the cartelized industry are, at the same time, consumers of the outputs generated in other sectors. As our earlier paper discussed in some detail, however, this ideal situation for a single producing group cannot be realized in a broadly democratic political regime. Any single producing group must recognize that attempts to secure a differentially advantageous position will be opposed by members of all other groups in the economy who, in terms of their own utility, will prefer that any industry, other than their own, remain workably competitive. Throughout this discussion, we assume that effective cartelization, whether by a single industry or by many industries, requires political enforcement and support.

In order to secure effective political support for producer-motivated restrictions on particular markets, a coalition among several producing groups must be organized. And the necessity that other industries will, also, secure support for cartelizing price and output policies reduces the gains that any single industry membership can expect to secure from market restrictions. If the effective coalition of cartels should become sufficiently inclusive and extend over a large share of the economy's production, there may arise support for constitutional limits on the organization of cartels, even from members of the separate producing groups. The analysis in our earlier paper was concentrated on the parameters that might generate this apparently counter-intuitive result.

In our earlier analysis, however, we did not allow for the influence of politically financed transfers on the size of a politically viable coalition of cartels. If we introduce the effect of transfer programs, the politics of coalition formation is altered in important ways. In particular, as opportunities to live off transfers increase, the minimal sized coalition required for political effectiveness increases, as measured by the number of member industries. The connection between the size of the redistributive or transfer state and the degree of competitiveness within the economy arises from the fact that, the more inclusive the coalition of cartelized industries, the less attractive are restrictions on competition, even from the perspective of members of the coalition.

II. A Simplified Model

It is useful to develop the analysis in a highly abstracted and stylized model of an economy under the following initial assumptions: All members of the effective electorate are employed in one of N industries in a closed economy, with each industry totally specialized in the sense that all input is supplied in the production of a single good or service; there are equal numbers of persons employed in each of the industries, each person produces an equal imputed share in the value product of the industry, and, at the same time, each person purchases an equal share of the product of all other industries; each one of the N industries faces an identical demand curve for its product and each industry is organized competitively with many separate producing firms.

Although each industry would ideally like to be the only recipient of political protection against competition, each industry also recognizes that such exclusive protection is unrealistic. In order for one industry to obtain a political grant of monopoly privilege, it has to join a politically controlling coalition of other industries seeking the same privilege. With the protection of one industry tied to similar protections for other industries, the desirable amount of protection is reduced, even from the perspective of the protected industries. Members of each industry have to accept the fact that the benefits they receive from higher prices for their product are offset to some extent by the higher prices they pay for the products of other protected industries.

In order to develop the connection between the desired level of protection (from the perspective of a coalition of cartels) and the number of industries receiving protection, we present a simple profit maximizing model of a coalition of cartels. Let n < N be the number of protected industries, with the remaining N - n industries remaining fully competitive. Assume that under full competition, and with no transfers, each industry employs L[.sup.*] workers (where NL[.sup.*] is the number of voters) and produces Q[.sup.*] units of output. That is, all persons work and all workers vote, each in accordance with economic interest. As already indicated, each industry is assumed to face an identical demand curve, and we ignore any change in consumer demands that might result from price changes caused by output restriction in the n protected industries. We also ignore any cost reductions that might result in the N - n competitive industries because of resource flows out of the protected industries.

Given this background, and assuming, for the moment, no transfers, the benefits received by the members of a single industry in the coalition of cartels is given by

[Mathematical Expression Omitted]

where P represents the inverse demand curve for each industry; Q is the common output level of all coalition industries and an increasing function of L, the number of workers employed by each protected industry, and the constant marginal cost of production, MC, is an increasing function of T, the amount of state transfer activity (temporarily assumed zero). The first bracketed term in (1) represents profits to an industry from cartel restrictions on its own output. The second term in (1) measures the total consumer surplus to an industry in the coalition from the products supplied by itself and other industries in the coalition.(1)

For a given size, n, of a coalition, the objective of the coalition is to choose the L, and therefore the Q, that maximizes (1). The maximizing choice of L necessarily satisfies the condition

[MR(Q(L)) - MC(T)]Q'(L)] + (n/N)[P(Q(L)) - MR(Q(L))]Q'(L) = 0 (2) or

[MR(Q(L)) - MC-(T)] + (n/N)[P(Q(L)) - MR (Q(L))] = 0, (2') where MR represents marginal revenue. Note that when n/N [arrow right] 0, which approximates the case where n = 1 and the cartel is interested only in producer profits, with no regard for the interests of its members as consumers, then (2') implies the standard monopoly solution, MR = MC. On the other hand, when n = N and the coalition is inclusive of all industries, then (2') implies the standard competitive solution, P = MC. When no industry is able to receive protection against competition that is not equally available to all other industries, then the interest of all is best served by universal competition.

It is clear that as n, the number of industries included in the coalition of cartels, increases, the output, and employment, of each protected industry also increases. But as n increases, so do the number of industries with employment less than L(*), the level of employment in a fully competitive industry. It is useful to consider how the reduction in the number employed in the coalition of cartels, given by n[L[.sup.*] - L], changes as the size of the coalition increases by recognizing that (2') defines L as a function of n. In other words, consider the sign of

n(L[.sup.*] - L)/ n = L[.sup.*] - L(n) - n ( L/ n). (3)

From (2') it can be shown that L / n > 0. For n = 1, with the cartel output being approximated by the monopoly solution, L[.sup.*] - L(n) is at its maximum and presumably exceeds n ( L/ n). So over some initial range of n, (3) is positive and increasing the size of the coalition increases the number of workers displaced by output restrictions by industries in the coalition. However, as n increases, the difference between L[.sup.*] and L(N) will diminish eventually to the point where (3) becomes negative and further expansions in the size of the coalition diminish the number of workers displaced by cartel restriction on output. When n = N and all industries are again competitive, there are no displaced workers.(2)

In Figure 1, the number of workers displaced by output restrictions in the coalition is shown as a function, D, of the number of industries in the coalition. As shown, when there are no industries in the coalition, all industries are competitive and no workers are displaced. The number of workers displaced increases as n increases up to a point, at which time further increases in n reduces the number of displaced workers until there are no displaced workers at n = N.

We now consider the question of the size of a politically controlling coalition. Political action is required to realize the protection against competition that is the purpose of forming the coalition. Until the coalition is of sufficient size to exercise decisive political influence, it remains, an unprotected collection of industries of little interest for the purpose of this paper. In a simple majoritarian setting, the minimum sized coalition for political effectiveness is one containing (P/2) + 1 members, where P is equal to NL[.sup.*], the number of members in the democratic electorate. If each industry in the coalition maintained the same number of workers under protections as under competition, then it would take only (N/2) + 1 of the N industries to form a politically effective coalition (recall that all industries employ the same number of workers under competition). But since the purpose of exerting political influence is to restrict output, and employment, a politically effective coalition has to contain more than (N/2) + 1 industries in our model.

In order to determine the minimum effective coalition size, reconsider Figure 1 where L[.sup.*] = P/N on the vertical axis is the number of employees (voters) in each industry when fully competitive. If (N/2) + 1 of these industries coalesced politically, they would initially have sufficient influence to obtain protection against competition. But taking advantage of that protection involves the necessary release of workers (voters) and, hence, reduces the coalition's political influence below that level needed to maintain the protection. Taking the worker displacement effect into consideration, the number of industries in the minimum effective coalition is seen to satisfy the equation(3)

nL(n) = P/2. (4)

We now plot the derivative of nL(n) with respect to n, or

[delta][nL(n)]/[delta]n = n([delta]L/[delta]n) + L(n), (5) which is shown as M in Figure I and referred to as the marginal employment curve. The intercept, L(0), reflects the fact that the smallest possible coalition would consist of an industry which employs L(0) workers. As the number of industries in the coalition increases, the number of coalition workers increases in accordance with (5). Only when the area under the curve n ([delta]L/[delta]n) + L(n) equals P/2 is (4) satisfied and the coalition is of sufficient size to be politically effective. As shown in Figure 1, this minimum effective coalition is reached at n*, which can be reached only after the marginal employment curve exceeds L *.

It is useful to consider the relationship between the displacement curve and the coalition's marginal employment curve in Figure 1. If the marginal employment curve is subtracted from L *, the result is L * - L(n) - n([delta]L/[delta]n), which, as can be seen from (3), is equal to the slope of the displacement curve. In other words, when marginal coalition employment from expanding the size of the coalition is less than L *, the expansion increases the displacement of workers, and when marginal coalition employment from expanding the size of the coalition exceeds L *, the expansion reduces the displacement of workers. The straightforward implication is that the minimum effective coalition, n *, occurs beyond the maximum point on the displacement curve, with the number of displaced workers decreasing with increases in n. Political equilibrium occurs where the overall degree of inefficiency from protection (as measured by the number of workers displaced because of protection) is decreasing with respect to the number of protected industries. (4)

We now turn to the question of the sensitivity of the minimum effective coalition size to the level of state transfer activity. It is assumed that transfers are paid out of the general productivity of the economy, with the burden shared equally over all industries. This transfer burden can be reflected by rewriting the object function (1) as

[Mathematical Expression Omitted]

Since the transfer burden represents a fixed cost, the necessary condition (2') is undisturbed, as is all of our previous analysis.

It is now straightforward to examine the effect of an increase in state transfer activity, T, on the minimum effective coalition size. In addition to defining L as a function of n, (2') also defines L as a function of T. Differentiating through (2') with respect to T and solving for [delta]L/[delta]T yields

[Mathematical Expression Omitted]

Not surprisingly, an increase in the availability of transfers, by increasing the marginal cost of labor, results in less labor being employed in the coalition of cartels. The result is that if we shift to a regime of higher transfer payments which increase the opportunity cost of employment, the number of workers displaced from the industries in the coalition of cartels increases for every n.(5) This implies that, beginning with the equality in (4), now rewritten

n*L(n*, [T.sub.0]) = P/2, (4') an increase in T to [T.sub.1] from [T.sub.0] results in

n*L(n*, [T.sub.1]) < P/2, (4'') which requires an increase in n to restore the equality.

As already established, as n increases, there is a decrease in the degree of protection provided by each industry in the coalition. Since political equilibrium lies in the range where worker displacement within the coalition decreases as the size of the coalition expands, the overall economy becomes more efficient, if we disregard the direct effects of the increase in T, as T increases. Since any increase in the number of transfer recipients reduces the size of the productive labor force, these direct effects must, of course, act to make the overall economy less efficient. The central point is, however, that one predictable consequence of the increase in T is the increase in n, which results in a more competitive coalition of cartels. A larger number of industries, and hence a larger share of the economy's total product, will be subjected to market restriction in the transfer regime. But the degree of restriction within each industry will tend to be lower, and this second effect will more than offset the first. There will be less displacement of workers from the restricted set of markets, although the displacement from the productive sector, generally, into the transfer sector may insure that, inclusively considered, the economy produces less value under the transfer regime.

Generalized support for constitutional prohibition on cartelization must increase as between the two regimes that are compared here. The net benefits from membership in the effective coalition of cartels falls directly with the increase in transfers and the number of nonproducers in the economy. These benefits may become negative when competitive rent-seeking pressures are counted, even though separate industries may still seek cartel protection and still secure differential advantages relative to nonprotected industries.

The central prediction of the model may readily be suggested when we introduce extreme values. The minimum effective political coalition required to secure support for market restriction must increase directly as the number of nonproducers increase. At some point, even the all-inclusive group of producing interests will become politically ineffective. Long before such a point is reached, producing interests will be led, by their own self-interest, to support general rules that prohibit cartelization in any market.

III. Qualifications to the Argument

As with all models of complex phenomena, our model incorporates simplifications which, to some degree, qualify our argument. We conclude the paper by considering what we see as the most important of these qualifications.

The supportive analytical argument for the hypothesis depends critically on the assumption that persons exert their ultimate influence on political results in such fashion as to reflect their economic interests, both as producers and consumers. Public choice objections, of sorts, may be raised here based on the differential orders of magnitude between producers' and consumers' interests. Persons will, in terms of this argument, always act predominantly in furtherance of their interests as producers, with little or no regard to their interests as consumers. As traditionally presented, however, this threshold difference between producer and consumer interests has been applied in reference to attitudes toward single markets, taken one at a time, in which setting, of course, concentrated and specialized producing interests dominate dispersed consuming interests. Both in our earlier paper and this paper, however, we emphasize that choices among constitutional rules that allow or prohibit cartelization require that persons consider their general consuming interests, over all markets, which, taken in total, are equally important with their concentrated producer interests. The rational ignorance-information-attention asymmetry simply does not hold when considerations of regime change arise. Further, and as stressed here, those persons who remain pure consumers must act in their generalized consumer interests since they have no other role in the economy.

To public choice economists, our neglect of the analytical implications of rent-seeking activity, both by those groups who seek politically supported restrictions on markets and by the politicians who are in positions to offer such support, may seem to limit the applicability of our generalized conclusions. A more comprehensive analysis would, of course, include these implications. It has seemed useful here, however, to proceed in stages and to limit this initial exercise to the analysis of majoritarian political processes.

It is also recognized that not all transfers increase the private cost of labor, resulting in workers disassociating themselves from productive activity. To the extent that transfers can be received by remaining on the job, our argument fails to hold. Some transfers do reduce the incentive to remain employed, however, and our argument relies on this obvious fact.

There is also the possibility that nonworking recipients of transfers will organize for the purpose of striking a bargain with the coalition of protected industries. In retum for supporting higher transfer payments, recipients of transfers could offer to provide their political support for coalition protection, thereby eliminating the need for an increase in the number of industries in the coalition. But it is not clear why the coalition would agree to larger transfer payments in order to maintain the existing coalition size (and level of protection), unless an increase in transfer payments is likely to occur without the coalition's support. in that case, however, the transfer recipients would have little motivation to support protection for the coalition.

A final objection to our argument may prove more damaging. We stated earlier that we should predict that, within and among regimes of transfer states, markets would be more open than among equally politicized regimes in "capitalist" states. The italicized words "equally politicized" may be called into question. It may be suggested that the same ideological forces that generate movement toward political intrusion into markets aimed at benefits to producing interests will also emerge to support increases in the number of transfer recipients. In other words, ideology rather than economic interest may offer the more important explanatory motivation for that which we observe in political results.

We do not suggest that ideology is unimportant; there may be common elements that arise in support of the transfer and the restrictive state. Our central analysis may be interpreted as the spinning out of the implications of a model in which economic interest predominates, with the final resolution to be sought in the empirical record. The supporter of the argument for the dominance of ideological motive finds it difficult to explain the movement toward deregulation in the 1970s and 1980s in the midst of continuing increase in the size of the transfer state. By contrast, our argument, by stressing economic interest, suggests that the increase in the number of pure consumers may, in itself, have offered the critically needed support for political movements that open markets.

As we stressed at the outset, our point is a very simple one. Those persons who are the recipient beneficiaries in the modem welfare-transfer state are pure consumers, and these persons, like others, have their own economic interests which we can expect them to express politically. To the extent that the interests of these recipient groups come to be more widely recognized, we must surely expect that pressures will mount for depoliticization and decartelization of those markets that have traditionally been closed in response to producers' interests.

(1.) Members of each protected industry also receive benefits from the competitive sector, but, by assumption, these benefits are independent of actions taken by the protected sector and therefore can be ignored. Buchanan and Lee[1] allow resource flows out of the protected sector to increase the consumer surplus available from the competitive sector. Ignoring this increased consumer surplus here has no effect on the primary implications of the analysis. (2.) Many, if not most, of the workers displaced by cartel restrictions will, of course, find employment in the competitive sector. However, such a move to the competitive sector leaves the basic thrust of our argument to this point unaffected. Output restrictions still diminish as the coalition of cartels becomes more inclusive. Also, the political implications of cartel restrictions on output and employment, implications considered momentarily, are unaffected by the fact that some displaced workers find other employment. It can be argued that the wage rate, and therefore MC, will be lowered in both the competitive and protected sectors by the displaced workers. We have explicitly ignored the former effect, and we assume that wages remain constant in the protected sector, despite worker displacement, as the gains from protection are shared with workers in the form of higher than competitive wages. Therefore MC is unaffected by worker displacement in the protected sector. (3.) Henceforth we ignore the discontinuities that arise from the fact that the numbers of industries and workers (voters) are integers. (4.) Although the construction of Figure 1 has the maximum of D (which occurs at the intersection between L * and M) at N/2 that does not have to be the case. But regardless of where L * and M intersect, it has to be the case that n * > N/2 since the area under M is strictly less than the area under L * over the interval [0,N/2]. Only when point n * is reached are the two areas equal. (5.) When transfers reduce employment in coalition industries, they also reduce employment below L * in each competitive industry. Yet L * remains the relevant benchmark against which to measure displacement, since the farther employment in each coalition industry, L(n), falls below L *, regardless of the reason, the larger n has to be for the coalition to command the support of a majority of the electorate.

References

[1.] Buchanan, James M. and Dwight R. Lee. "Cartels, Coalitions, and Constitutional Politics." Constitutional Political Economy Spring/Summer 1991, 139-61. [2.] di Pierro, Alberto. "Istituzioni e Modelli Producttivi." Politeia 18, 1990, 4-6.