3. Monopoly Power, Endogenous Entry, and Macroeconomic (In)Stability
3.3 Macroeconomic Indeterminacy
3.3.2 Economic intuition for indeterminacy
We first discuss the linkage between the possibility of local indeterminacy and the extent of monopoly power. In an earlier paper, Benhabib and Farmer (1994) incorporate internal increasing returns at the level of the intermediate firm in a monopolistic competition market structure without free entry. Their analysis indicates that the condition for local indeterminacy crucially depends upon the extent of the monopoly power. In addition, Chang et al. (2011) consider an endogenous entry under monopolistic competition and conclude that local indeterminacy can occur with an empirically plausible degree of increasing returns provided that the degree of monopoly power is large. Departing from their analysis, our study allows for endogenous entry and distinguishes returns to specialization from monopoly power. With this specification, we find that the necessary condition for local indeterminacy is independent of monopoly power.46
The independent result between monopoly power and local indeterminacy can be explained intuitively. It is well known in the literature on imperfect competition, see e.g., Coto-Martínez (2006), that a higher degree of monopoly power tends to generate more monopoly profits for firms and hence increases the lifetime income of households.47 By way of this so-called feedback effect from monopoly profits to the household’s behavior, the degree of monopoly power can govern the transitional dynamics of the economy. Once a firm’s free entry is allowed, it will result in a zero-profit condition in equilibrium. Zero monopoly profits imply that the feedback effect from monopoly profits on the household’s behavior is cut off. As a consequence, the condition for local indeterminacy is independent of the monopoly power.48
45 In what follows, to satisfy both the necessary and sufficient condition for local indeterminacy we impose the constraint for a relatively smaller absolute congestion, i.e., Aa2/x. Obviously, when we exclude absolute congestion from our model (i.e., A0), the constraint is automatically satisfied.
46 By differentiating the necessary condition for local indeterminacy with respect to , we have:
(1 ) [1 (1 )]0
a
x
R .
47 In their static model with imperfect competition, Dixon (1987) and Startz (1989) also show that a higher degree of monopoly power is associated with more monopoly profits for firms, thereby leading to a rise in the disposable income for households.
48 This is also the reason why Startz (1989) concluded that the long-run output effect is independent of
The above discussion leads to the following proposition:
Proposition 3. In a one-sector RBC model with monopolistic competition and free entry, the necessary condition for equilibrium indeterminacy is independent of the monopoly power.
We then deal with the interrelation between the possibility of local indeterminacy and the extent of production externalities from the public sector. In their recent paper, to highlight the role of production externalities from the public sector, Guo and Harrison (2008) assume that all internal returns to scale and relative congestion are absent (i.e., 1 and R0). Substituting 1 and R0 into the necessary condition for local indeterminacy yields:
a x R
( 1, 0) . (41)
Equation (41) reveals the main finding in Guo and Harrison (2008): when government spending is financed with a fixed tax rate, the economy displays equilibrium indeterminacy if production externalities from the public sector are large enough.
However, if public services available to the individual are subject to proportional relative congestion (i.e., R1), the necessary condition for local indeterminacy will change to:
( 1,R 1) a0. (42)
Equation (42) indicates that the economy displays equilibrium determinacy even if production externalities from the public sector are brought into the picture. This reveals the fact that the introduction of productive government spending no longer provides a vehicle for the occurrence of local indeterminacy if public services available to the individual are subject to proportional relative congestion.49 The intuition for this result is easy to understand. By incorporating useful government spending into the private production function, the possibility for the emergence of local indeterminacy will increase when public expenditures generate sufficiently strong production externalities. With proportional relative congestion, public services provided by the government are equally shared by all firms. The feature of
the monopoly power. Similarly, Bénassy (1996) derived the conclusion that output persistence is independent of the monopoly power.
49 Domenech and Garcia (2002) consider the case of proportional congestion for public goods, while they adopt the specification in the utility function when public expenditures provide a positive
a firm’s free entry would make the production externalities available to each firm become of trifling importance, and hence the economy always displays equilibrium determinacy even if production externalities from the public sector are present.
The above discussion leads to the following proposition:
Proposition 4. In the presence of proportional relative congestion, the equilibrium indeterminacy disappears even if productive government expenditures are incorporated.
Finally, we would like to deal with how the possibility of local indeterminacy is related to the internal increasing returns to scale . In their pioneering paper, by excluding the possibility of firm entry and exit, Benhabib and Farmer (1994) propose that indeterminacy can easily occur provided that internal increasing returns are large enough. Running in sharp contrast to the Benhabib and Farmer (1994) result, this chapter allows for endogenous entry, and finds that a higher degree of internal increasing returns ( ) is more unlikely to result in local indeterminacy when production externalities from the public sector are present.
In the presence of productive government spending (i.e., x0), from the necessary condition for local indeterminacy we have:
Our intuitive explanation for the indeterminacy results in equation (43) is borrowed from Guo and Harrison (2004). For ease of presentation, the Keynes-Ramsey rule reported in equation (36) can be expressed in the following discrete-time form:
When the households generate optimistic expectations regarding having a higher future return on physical capital, i.e., the marginal productivity of capital (denoted by MPK) is expected to increase in the future, they will tend to reduce consumption and raise investment today. This in turn will induce a rise of the capital stock in the next period (Kt1). Given that labor and physical capital are complements in production, labor supply in the next period (Ht1) will increase, too. As a result, future consumption Ct1 will rise in response. A higher value of future consumption
(Ct1) together with a lower value of current consumption (C ) will cause the t left-hand side of equation (44) to increase.
With a rise in Ct1 and a fall in C , it is clear from equation (44) that a t self-fulfilling equilibrium driven by the agents’ optimistic expectations can emerge when the right-hand side of equation (44) increases. As described above, when agents become optimistic, Ht1 will rise in response. As such, when faced with a higher degree of internal increasing returns ( ), two conflicting effects will be at work. First, a higher value of increases the labor productivity, which is reflected by the term (1a) on the right-hand side of equation (44). Second, due to the fact that agents’ optimistic expectations create more future consumption demand (Ct1), the number of firms in the next period (Nt1) will increase in response. An increase in the number of firms will cut down factor inputs in production and intensify the relative congestion, thereby leading to a lower degree of a positive effect stemming from productive government spending. This negative induced effect arising from free entry is reflected by the term 1[ (1R)x] on the right-hand side of equation (44). In equilibrium, the second effect due to free entry dominates the first effect and, as a result, a higher value of is more likely to lead to a fall in the right-hand side of equation (44). As a consequence, a higher value of is less likely to result in local indeterminacy.
It should be noted that in Benhabib and Farmer (1994) the number of firms is exogenous, and hence the second effect is excluded. Accordingly, their analysis proposes that a higher value of more easily results in local indeterminacy. This is the reason why our result runs in sharp contrast to the Benhabib and Farmer (1994) assertion.
Summing up the above discussion, we can establish the following proposition: Proposition 5. When the production technology of a private firm possesses the feature of internal increasing returns, the possibility for the emergence of local indeterminacy is negatively related to the extent of the internal increasing returns to scale.
3.4 Conclusion
By allowing for the endogenous entry of producers, this chapter sets up a monopolistically competitive model with productive government expenditure that is subject to the congestion effect. Then, this chapter focuses on the linkage between endogenous entry and the possibility of indeterminacy. Several main results are obtained from the analysis.
First, some existing RBC studies, e.g., Bernanke and Parkinson (1991) and Burnside et al. (1995), find a puzzling fact: the estimated output elasticity of capital is close to zero and the estimated output elasticity of labor is close to or greater than one.
By resorting to endogenous entry, this chapter endogenizes the output elasticity of both inputs and provides a plausible way to solve the puzzle. Second, by making a distinction between returns to production specialization and monopoly power, this chapter finds that the necessary condition for equilibrium indeterminacy is independent of the monopoly power. Third, the introduction of productive government spending no longer provides a vehicle for the occurrence of local indeterminacy if public services available to the individual are subject to proportional (relative) congestion. Finally, by allowing for endogenous entry, this chapter asserts that a higher degree of internal increasing returns is associated with a lower possibility for the emergence of indeterminacy when production externalities from the public sector are present. If a firm’s endogenous entry and exit is excluded, the reverse result is true.
Chapter 4
What Determines Optimal Fiscal Policies under Imperfect Competition? A Comprehensive
Analysis
4.1 Introduction
Recently, externalities have been an important subject of extensive discussion in the field of economic growth. The majority of extant studies concerning market externalities can be classified generally into two aspects, consumption externalities and production externalities. With regard to consumption externalities, Abel (1990) first explores the effect of consumption externalities on asset prices and shows further that consumption habit formation plays an important role in explaining equity premium puzzle. Gali (1994) shows that asset prices and returns in an economy with a keeping-up-with-the-Joneses preference are equivalent to those of an economy with a properly adjusted degree of risk aversion. Garcia-Penalosa and Turnovsky (2008) find that, in a growing economy with heterogeneous agents, the “keeping up with the Joneses” preference results in less inequality than that in an economy without consumption externalities. With regard to production externalities, Romer (1986) proposes production externalities arising from learning by doing and analyzes the effect of production externalities on long-run economic growth. By considering government infrastructure in private production activities, Barro (1990) shows that the economy is able to sustain a balanced growth rate in the presence of productive government spending.
Subsequent studies on externalities pay their attention to the normative analysis, and turn to examine the optimal fiscal policies from the viewpoint of welfare maximization. With respect to consumption externalities, Ljungqvist and Uhlig (2000) show that, if households’ preference specification embodies a “keeping up with the Joneses” effect, equilibrium consumption is more likely to result in over-consumption, and as a result, the optimal income tax rate is positive. Similarly,
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Dupor and Liu (2003) show that an optimal tax rate is positive or negative depending upon a preference exhibiting jealousy or admiration. In contrast to Ljungqvist and Uhlig (2000), Liu and Turnovsky (2005) and Liu and Chang (2011) find that the government uses a consumption tax to correct for the consumption externalities once the consumption tax is an alternative.
With respect to production externalities, by incorporating the congestion effect of productive government spending into the Barro (1990) model, Eicher and Turnovsky (2000) show that the optimal tax rate on capital increases with the degree of the congestion effect. Later on, Gómez (2004) shows that an optimal income tax rate in the first-best optimal equilibrium depends on not only upon the extent of production externalities arising from productive government expenditures, but also the congestion effect. Liu and Turnovsky (2005) introduce learning-by-doing externalities based on the cumulative aggregate capital stock, and show that the optimal tax rate on capital is negative. More recently, by separating government spending into federal and local government spending, Gong and Zou (2011) derive an optimal tax rate (on both federal and local government taxes) is just the sum of the production externalities arising from the federal and local government expenditures.
By extending the Barro (1990) model from linear income taxation to nonlinear income taxation, Lai and Liao (2012) show that the Pareto optimality can be achieved in the Barro model if policy instruments for the tax scalar and the extent of the tax progressness/repressiveness are set optimally.
The results of all of above studies are derived in a perfect competition environment. However, by examining U.S. industry data, some empirical studies including Hall (1988, 1991) find that the estimated markup ratio is greater than one.
Accordingly, the hypothesis of perfect competition can be treated as a first approximation, but does not reflect reality.
Many recent studies in macroeconomics have focused on macroeconomic policies in the presence of imperfect competition. Till now, to the best of our knowledge, three familiar but distinct types of adjustment mechanisms are now discussed in the literature concerning imperfect competition. The first type allows imperfectly competitive firms to earn positive profits in equilibrium, and hence allows mechanism to highlight the importance of monopoly profits in affecting the relevant macro variables in the economy (e.g., Dixon, 1987; Benhabib and Farmer,
1994; Guo and Lansing, 1999; Chang et al., 2009). The second type emphasizes the role of endogenous monopoly firms, and focuses on the situation where monopolistically competitive firms make zero profits in equilibrium via the channel of free entry and exit of firms (Dixon and Lawler, 1996; Devereux et al., 2000; Chang et al., 2011; Bilbiie et al., 2012). The third type instead highlights the importance of endogenous overhead costs, and pays attention to the situation where monopolistically competitive firms make zero profits in equilibrium via the channel of adjusting overhead costs (Rotemberg and Woodford, 1992; Hornstein, 1993; Kim, 2000).50
Compared with existing literature on the normative analysis under imperfect competition, our analysis has the following three distinctive traits. The first trait is the introduction of internal increasing returns to scale stemming from diminishing marginal costs. To the best of our knowledge, until now the linkage between optimal fiscal policies and the extent of internal returns to scale is all but absent in the existing literature. This chapter thus turns the focus and examines what the role played by the extent of internal returns to scale is in determining optimal fiscal policies. The second trait is the simultaneous presence of consumption and production externalities. As such, once the consumption tax and income taxes (on both labor income and capital income) are available to the government, we are able to compare the relative efficiency of these two taxations in correcting both consumption externalities and production externalities. As we will show in this chapter, there exists an appropriate use of consumption tax and income tax for remedying consumption and production distortions. The third trait is the distinct types of adjustment mechanism. The existing imperfect competition studies on optimal fiscal policies either are characterized by a zero-profit condition due to free entry, or alternatively, adopt a constant number of firms in which there exists a positive profit (Guo and Lansing, 1999; Judd, 2002; Coto-Martinez, 2006; Chang et al., 2007). As mentioned above, three different types of adjustment mechanisms (fixed monopoly firms, endogenous monopoly firms, and endogenous overhead costs) are the topics of discussion in the imperfect competition literature debate. This chapter thus tries to create a comprehensive analysis on the interrelation between the optimal fiscal policies and market distortions under three different types of adjustment mechanisms.
50 See Hornstein (1993) for a detailed discussion.
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This chapter is organized as follows. Section 2 describes the model economy.
Section 3 examines optimal fiscal policies with an endogenous number of firms.
Section 4 examines optimal fiscal policies with endogenous overhead costs. Section 5 examines optimal fiscal policies within the existence of monopoly profits. Section 6 concludes our discussion.
4.2 The Model
The economy under consideration consists of three types of agents: households, firms, and a government. The production environment consists of two sectors: the perfectly competitive final good sector and the monopolistically competitive intermediate goods sector. Suppose that this final good is produced through the use of a range of differentiated intermediate inputs.51 The households derive utility from consuming the final good and enjoying leisure. Savings are held in the form of physical capital. The balanced-budget government provides infrastructure service that enhances private productivity but is subject to congestion effect.
4.2.1 Firms
Following Bénassy (1998), final output is produced by a perfectly competitive firm with the following technology:
1
0 1
1 (
)N N yi di
Y , 01, 0, (1) where y represents the quantity of input i used in the production of the final good i and N is the total number of intermediate goods. As we will explain later, the parameter measures the degree of monopoly of the intermediate good firms, and the parameter measures the extent of the increasing returns due to production specialization.
If all intermediate goods are hired in the same quantity, namely y , then output is given by Y N1y. As a consequence, an expansion in the number of intermediate inputs raises the final goods production if 0. Thus, the parameter
51 As stated by Kim (2004), heterogeneous outputs need to be aggregated from a macroeconomic point of view. A conventional specification is introducing an aggregator, such as a firm producing a final good, in the economy.
reflects the extent of the increasing returns due to production specialization. In their previous studies, Devereux et al. (1996) and Chang et al. (2007) specify that the production function of final output has the following form: 1
0 )
(
Nyi di
Y , where
monopoly power and increasing returns to production specialization (an expansion in variety) are characterized by the same parameter . As stressed by Bénassy (1998), the specification of Eq. (1) allows us to incontrovertibly separate returns to production specialization from monopoly power, so that both effects can be fully disentangled.
Assuming that the final good is the numéraire, the profit-maximization problem for the final good firm can be expressed as:
N i i
f
y Y py di
Max
i 0 ,
where p is the relative price of the intermediate good i . Accordingly, the i corresponding first-order condition is given by:
N ( 11 )y 1Y1
pi i . (2) Eq. (2) is the demand function for the i th intermediate good which is characterized by a constant price elasticity 1/(1).
Intermediate good firms operating in a monopolistic market use the capital stock, labor input, and public services provided by the government to produce their product and sell it to the final good firm at the profit-maximizing price. To be more specific, the production technology for the i th intermediate good i can be expressed as:
( i i1 ) ( S)
i k h G
y , 10 , 1, 0, (3) where k and i h respectively represent the capital stock and labor input hired by i the i th intermediate good producer, G refers to the public services available to S each firm, (1 ) measures the capital (labor) share in the sector of the intermediate good output, captures the degree of the production efficiency stemming from diminishing marginal costs, captures the extent of the production externalities resulting from the public services, is an overhead cost.
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It should be noted that there are two kinds of internal economies of scale in our model. The first kind of economies of scale stems from the presence of the overhead cost . Production technology is said to feature increasing returns to scale if 0 and constant returns to scale if 0.52 More specifically, this kind
It should be noted that there are two kinds of internal economies of scale in our model. The first kind of economies of scale stems from the presence of the overhead cost . Production technology is said to feature increasing returns to scale if 0 and constant returns to scale if 0.52 More specifically, this kind