The composition of public expenditure in a dynamic macro model of monopolistic competition.

• Author: Balvers, Ronald J.

1. Introduction

   It is well known that market power causes firms to underproduce from a social welfare perspective. Widespread existence of monopolistic elements, as documented for example by Hall [14; 15] and Lebow [16], may provide an argument for government policy designed to increase production at the aggregate level. The literature on macro models of monopolistic competition, e.g., Rotemberg [26], Blanchard and Kiyotaki [10], and others finds that changes in the money stock in principle do not affect aggregate production; a further source of market imperfection in the form of a nominal rigidity is necessary to allow changes in the money stock to generate production effects.

   Another branch of literature considers public expenditure policy rather than monetary policy. Aiyagari, Christiano, and Eichenbaum [1] most recently, and others, such as Barro [6], examine a perfectly competitive economy where public expenditure stimulates output, possibly with a multiplier effect, via its effect on the marginal utility of wealth and labor supply. Starting from Pareto optimality such policy, however, will lower rather than increase welfare. Rotemberg and Woodford [27; 28] study the effect of public expenditure in an imperfectly competitive economy. An increase in current expenditure entices individual firms to deviate from a collusive equilibrium so that mark-ups fall and aggregate production and welfare are enhanced.

   In these papers public expenditure provides a pure stabilization good that has neither a direct utility benefit nor a productivity benefit. Recent work by Aschauer [2; 3], Morrison and Schwartz [20], and others, see the survey by Munnell [21], reveals however that public expenditure apart from providing a spending stimulus may be important in providing a productivity stimulus. In this vein, Barro [7] considers a publicly provided good that serves as an input in the private production processes of a perfectly competitive economy. He concludes that such a good should be provided in the same quantity as would be produced in a perfectly competitive industry. Glomm and Ravikumar [13] similarly consider a publicly provided good that enhances private sector productivity in a perfectly competitive economy. They, however, allow for different degrees of non-rivalry (congestion) in this good and demonstrate that the optimal proportional tax is independent of the degree of nonrivalry.

   My paper intends to examine the consumptive and productive benefits of a publicly provided good within a dynamic macro model of monopolistic competition. To this end, I introduce monopolistic competition in the neoclassical growth model of Long and Plosser [18]. This model is chosen for several reasons. First, it is generally known and presents a simple closed-form solution. Second, it incorporates a diversity of sectors that allows, for instance, a distinction between investment and consumption-oriented production. Differences in the degree of monopoly power between sectors with a different investment content may affect how optimal expenditure policy should be conducted. Third, the different sectors enable examination of different types of government expenditure programs, including those in which the government provides an input to the production process. It thus becomes possible to examine in addition to the effect of the level of government expenditure, also the effect of the composition of government expenditure on aggregate activity. The composition issue was first addressed in the context of a traditional macro model by Barth and Cordes [9] and Ramirez [22] and is here re-examined in the context of a dynamic general equilibrium model.(1)

   Section II generalizes the Long and Plosser model to allow for monopoly power, which requires not only the introduction of monopolistic competition in some subset of the sectors, but also requires a disaggregative approach different from Long and Plosser's, who may rely on a social planner due to the equivalence of the perfectly competitive outcome and the social planning outcome. The solution in section III demonstrates that overconsumption (relative to the Pareto optimal outcome) is inherent, even if investment-oriented sectors exhibit the lower degree of monopoly power. Section IV first points out that a micro-management approach to government policy in the sense of an industrial policy may lead to a social welfare optimum. Such a policy imposes tremendous information requirements on the government and would seem to be impracticable.

   Section IV thus continues by discussing a smaller class of policies - macro-based policies - and, in particular, those based on government expenditure. It is found that expenditure on infrastructure and other types of government investment can improve welfare and should be provided in higher quantity than would be produced under privatization in a perfectly competitive industry. In contrast, government consumptive expenditure should be less than would be provided in a perfectly competitive industry. Such policies would help to offset part of the aggregate consequences of market power. Section V concludes.

2. The Long and Plosser Model with Monopolistically Competitive Firms

   The purpose of this section is to present a version of a neoclassical growth model that can be amended to incorporate elements of monopolistic competition. The model of Long and Plosser [18] is chosen here because it is tractable, known to most macroeconomists, and general enough to allow incorporation of a variety of different sectors. Note that the intent is not to develop a real business cycle model and obtain positive implications; rather the emphasis is on generating normative results concerning the optimal size and composition of government expenditure, for which the Long and Plosser model seems an appropriate vehicle.

   In adapting the Long and Plosser Model (henceforth LP) two basic changes must be implemented. First, since in monopolistic competition the outcome is not generally Pareto optimal, the social planner approach cannot be used and a decentralized approach is employed in formulating and solving the model. Second, monopolistically competitive firms are embedded by assuming that some or all sectors consist of firms with monopoly power derived from the production of imperfect substitutes.

   The layout of this section is to first describe the model from the representative household's perspective and subsequently consider the decision problem for the different firms and the ensuing outcome at the sectoral level and lastly identify the equations relevant for solving the model. In this pursuit the original LP notation is maintained wherever possible.

   The Representative Household

   Given the information available at time t the household maximizes a standard time-additive utility function:

   [E.sub.t] [summation of] [[Beta].sup.s] u([C.sub.s], [Z.sub.s]) where s = t to [infinity], (1)

   with one-period utility a function of the consumption index [C.sub.t] and leisure [Z.sub.t]. Employing the same example as LP, further specify:

   u([C.sub.t], [Z.sub.t]) = [[Theta].sub.0] ln [Z.sub.t] + [summation of] [[Theta].sub.i] ln [C.sub.it] where i = 1 to n, (2)

   where [[Sigma].sub.i][[Theta].sub.i] = 1 (sum from 1 to n) by normalization. All [[Theta].sub.i] [greater than or equal to] 0 and n represents the number of different sectors (or industries) in the economy.

   As in Lucas [19], the representative household holds shares that represent claims to the dividends of the firms. Additionally the household receives labor income, implying the following budget constraint,

   [C.sub.t] + [summation of] [Q.sub.it][S.sub.it + 1] where i = 1 to n = [W.sub.t] [summation of] [L.sub.it] where i = 1 to n + [summation of]([Q.sub.it] + [D.sub.it])[S.sub.it] where i = 1 to n. (3)

   The [S.sub.it] indicates the proportion of the shares in sector i held by the household and [L.sub.it] denotes the household's labor supply to sector i. All prices (here the wage [W.sub.t] and share prices [Q.sub.it], as well as dividends [D.sub.it], are presented in real terms, that is, units of the consumption basket [C.sub.t]). The same applies to the output prices in the various industries [P.sub.it] so that

   [C.sub.t] = [summation of][P.sub.it][C.sub.it] where i = 1 to n. (4)

   An additional constraint sets leisure plus the sum of all labor inputs equal to H the number of hours available to the household,(2)

   [Z.sub.t] + [summation of][L.sub.it] where i = 1 to n = H. (5)

   The household chooses the [S.sub.it + 1], [C.sub.it], and [Z.sub.t] to maximize (1) subject to (3) and (5), yielding, respectively, for all i:

   [Beta][E.sub.t]([R.sub.it + 1][C.sub.t]/[C.sub.t + 1]) = 1, (6)

   with [R.sub.it + 1] [approximately equal to]([Q.sub.it + 1] + [D.sub.it + 1])/[Q.sub.it] denoting the realized shareholder return for holdings in sector i, and:

   [P.sub.it][C.sub.it]/[[Theta].sub.i] = [C.sub.t], (7)

   [W.sub.t] = [[Theta].sub.0][C.sub.t]/[Z.sub.t]. (8)

   In solving the model, equations (5) through (8) will represent the consumer side of the economy. First, however, the production side will be considered.

   The Monopolistic Firms and Sectoral Equilibrium

   In each sector a given fixed number of firms produces to maximize the expected present value of profits (dividends).(3) Firms are identical within each sector except that they produce different varieties of the sectoral good. These firms derive monopoly power from the fact that consumers and other firms value variety in their use of the sectoral output, as in the static models of Ethier [12], Weitzman [31], and Woglom [32]. Appendix A derives the market outcomes under the assumption of Cobb-Douglas production functions and CES sub-production and sub-utility functions (the latter two producing constant-elasticity demand functions). Given that in equilibrium all firms in a sector produce the same quantities, using the same inputs, output in sector i at time t + 1, [Y.sub.it + 1], is just the sum of the output of...