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ANNALS OF ECONOMICS AND FINANCE 5, 61–77 (2004) Multiple Equilibria and Interfirm Macro-Externality: An Analysis of Sluggish Real Adjustment Yew-Kwang Ng Faculty of Business and Economics Monash University, Australia and Ying Wu Department of Economics and Finance Franklin P. Perdue School of Business Salisbury University, USA E-mail: [email protected] In an imperfectly competitive economy, a continuum of equilibria at the firm level exists under certain analytical conditions (Ng 1986). Extending the earlier analysis of a representative firm, this paper shows that even if the condition for a continuum of equilibria is not exactly satisfied, the factors of price-adjustment costs, interfirm heterogeneity, and macro-externality can cause the economy to be stuck at the quasi macroequilibria after aggregate demand experiences a contractionary shock. Although adjustment costs are small and gains from adjustment are potentially large, the adjustment tends to be sluggish due to the existence of interfirm macro-externality. c 2004 Peking University Press Key Words: Imperfect competition; Externality; Adjustment cost; Aggregate demand. JEL Classification Numbers: E32, E31, D62, D43. 1. INTRODUCTION Macroeconomists are currently dichotomized, to a large extent, between those who believe that Keynesian economics is irrelevant and those who want to resurrect or at least to reconstruct it. In endeavors to unite Key- nesian economics with monetarism and the new classical macroeconomics, Ng (1980, 1982, 1992) shows in a micro-macro analysis of the representative non-perfectly competitive firm that each of these academic camps as 61 1529-7373/2002 Copyright c 2004 by Peking University Press All rights of reproduction in any form reserved. 62 YEW-KWANG NG AND a special case is possibly applicable under certain conditions. The analysis focuses on the optimizing decision of a representative firm with interfirm interactions and repercussions via aggregate variables and suggests the pos- sibility of a continuum of real equilibria under non-perfect competition.1 Given the existence of multiple or even a continuum of equilibria, according to micro-macroeconomic analysis of the representative firm, it may take only very small adjustment costs to cause multiple quasi macroequilibria in the real world that accounts for interfirm differences. An economy is said to be at a quasi macroequilibrium if the economy experiences a shock to aggregate demand but fails, due to the existence of small adjustment costs, to restore its general zero-economic-profit equilibrium after the shock. In this paper, we argue that, even under the conditions where there is a unique real equilibrium according to a disaggregated general equilibrium analysis, the economy may yet possess multiple or even a continuum of real quasi macroeconomic equilibria as a result of adjustment costs facing the representative firm and interfirm macroeconomic externality. Although adjustment costs are small relative to the gain realizable if the adjustments to the profit-maximizing general equilibrium position are ef- fected, the existence of interfirm macroeconomic externality explains the failure to pay the small adjustment costs to obtain a gain of higher order of magnitude. The expansion towards the higher general equilibrium position involves an increase in the adjusting firm’s output and thus the resulting decrease in its price, which raises the demand for other firms’ products through an increase in real aggregate demand even before the familiar income multiplier takes effect. In contrast, according to Shleifer and Vishny (1988), an apparently similar study, the macroeconomic externality depends on the income multiplier effect: the distribution of profits back to consumers leads to an increase in aggregate demand and hence the profits of “monopolists” with decreasing average costs.2 Moreover, our externality result vanishes under perfect competition whereas the Shleifer- Vishny result depends on some uncertainty and only vanishes with perfect information. In addition, although our work also shares the same spirit 1Ng’s approach of analyzing the effects of economy-wide changes on aggregate output and the price level is credited as one that “effectively started the modern movement” in providing the imperfect-competition microfoundation of macroeconomics (see Marris 1991, p.215). Following Ng (1977, 1980, and 1982), academic interest in this area has continued later in the work of Benassy (1982), Hart (1982), Snower (1983), Solow (1986), Blanchard & Kiyotaki (1987), Dixon (1987), Mankiw (1988), Startz (1989), Ball and Romer (1990), Ng (1986, 1992), Naish (1993), Romer (1993), Anderson (1994), Dixon and Rankin (1994), and Rankin (1995). 2See also Bohn and Gorton (1993) on the role of nominal contracts and monetary policies to overcome the relevant coordination failure. Indeed, Cooper and John (1988) provide a survey of related literature and a general framework in terms of Nash equilibria and strategic complementarity. However, our analysis focuses more specifically on the interactions between representative firms. MULTIPLE EQUILIBRIA AND INTERFIRM MACRO-EXTERNALITY 63 with Ball and Romer (1991) in tackling the issues of coordination failure and menu cost, our paper depends upon the cost responsiveness to post- shock changes in output and price rather than conditional upon the size of aggregate demand shock as in their paper. The paper is organized as follows. Section 2 presents the theoretical model of a continuum of equilibria and interfirm macro-externality for the representative non-perfectly competitive firm. Section 3 provides graphical presentations of the theoretical results. Section 4 presents some real-world evidence based on the cases of the United Kingdom and Japan. Section 5 concludes. 2. MODEL In the analytical framework of a representative imperfectly-competitive firm, if the proportional changes in marginal cost caused by proportional changes in the firm’s output and aggregate output entirely offsets the cor- responding proportional change in marginal revenue and if marginal cost is unit elastic with respect to the general price level, a continuum of real equilibria exists whereby there is a multiplicity of possible equilibrium output levels for a given equilibrium price and the equilibrium output level is not uniquely determined.3 Along this line, we present a two-sector model in which both a unique real equilibrium and a continuum of real equilibria could occur respectively as aggregate demand changes. Suppose that there are two goods X and Z (their respective quantities are also denoted by the same symbols), and each of them is supplied by a given number of Cournot-Nash imperfect competitors. The utility maximization by a representative consumer with a Cobb-Douglas utility function yields the following demand functions (a) pX X = λα ;(b) pZ Z = βα (1) where pX and pZ are the nominal prices of X and Z, λ and β (with λ+β = 1) are the preference parameters associated with X and Z respectively, α is the nominal aggregate demand given by α = α(pX , pZ , X, Z, M), (2) satisfying that 0 < ηαpx, ηαpz, ηαX , ηαZ , ηαM < 1 (In general, ηuv is the elasticity of u with respect to v, defined as (∂u/∂v)(v/u), where u and v are any two variables.), and M is the money supply. If we write the pX X◦+pZ Z◦ X ◦ Z c price level (Laspeyres price index) P ≡ pX◦ X◦+pZ◦ Z◦ = p X + p Z irc 3See Ng’s pioneering work of mesoeconomics (1980, 1982, 1986). 64 YEW-KWANG NG AND (from normalization), we have (from the position X = X◦,Z = Z◦), ∂P/∂pX = X, ∂P/∂pZ = Z. Thus from α = α(P, Y, M) (where Y is the aggregate output or real income in equilibrium), we have ∂α/∂pX = X αpx αP αpz αP (∂α/∂P )(∂P/∂p ) and thus η = SX η and η = SZ η where X Z SX ≡ p X/α, SZ ≡ p Z/α are the shares of X and Z in the total expen- ◦ ◦ pX X+pZ Z diture. Similarly, with respect to Y ≡ pX◦ X◦+pZ◦ Z◦ (Laspeyres quantity index), we thus have αpZ αpX αZ αX SX η = SZ η ; SX η = SZ η (3) Each firm in the X industry assumes the output of other firms as given and maximizes its profit [noting that pX = λα/X from Eq.(1(a))], λα θ P xi − W xi (4) xi + j6=i xj where xi is the output level for firm i, W is the price of the only composite variable input and θ is a constant related to the slope of the marginal cost curve (θ is greater or less than one according to whether the marginal cost curve is upward or downward sloping). Taking firm i as the representative, P we then have j6=i xj = (NX − 1)xi, where NX is the number of firms in the X industry, which is given in our context so that the demand elasticity for X could be constant at any given level of the price as aggregate demand changes. Assuming that the no-shutdown and second-order conditions are satisfied, the first-order condition is, 1 θ λα NX − 1 xi = 2 (5) θW NX Multiplying both sides by NX produces 1 θ λα NX − 1 X = NX 2 (6) θW NX Similarly, for the Z industry, we have 1 φ βα NX − 1 Z = NZ 2 (7) φW NX where NZ = number of firms in the Z industry, and φ is the counterpart of θ in the Z industry. If we take the variable input to be labour only and denote the labour employed in the X industry by LX and the labour in the Z industry by MULTIPLE EQUILIBRIA AND INTERFIRM MACRO-EXTERNALITY 65 θ φ LZ , then we have LX = X and LZ = Z , which is consistent with the θ structure of variable cost W xi in (4). Thus, from (6) and (7) the total demand for labour L in the two-sector economy is θ λα NX − 1 φ βα NZ − 1 L = NX 2 + NZ 2 (8) θW NX φW NZ The expected utility of the average worker, EU, depends on the real wage-rate W /P , the probability of employment ρ, and the utility of un- employment benefit u (taken as given by unions).

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