مصرف جانبی و عدم قطعیت تحت افزایش بازده به مقیاس و کاهش ارزش سرمایه درون زا

This paper incorporates negative consumption externality embodying “jealousy” and “running away from the Joneses” into Guo and Lansing (2007)'s model with production externality and endogenous depreciation, and examines how consumption externality helps to generate equilibrium indeterminacy together with production externality. Specifically, the existence of consumption externality reduces the upper and lower bounds of production externality for local indeterminacy, and when the degree of consumption externality increases, the upper and lower bounds of production externalities for local indeterminacy are both reduced.

Considerable progress has been made over the past two decades in understanding the conditions needed to generate equilibrium indeterminacy in real business cycle models with production externalities or monopolistic competition. In the original one-sector models of Benhabib and Farmer (1994) and Farmer and Guo (1994), local indeterminacy requires an implausible high degree of increasing returns-to-scale or externality in production. Subsequent research has shown that RBC models with multiple sectors of production (Benhabib and Farmer, 1996, Harrison, 2001, Perli, 1998 and Weder, 2000) or endogenous capital depreciation (Guo and Lansing, 2007 and Wen, 1998) can generate local indeterminacy with much lower degrees of increasing returns. Moreover, a combination model that incorporates both multiple production sectors and endogenous capital utilization may give rise to equilibrium indeterminacy only within an extremely narrow range of increasing returns (Guo and Harrison, 2001). Another research line relates equilibrium indeterminacy to consumption externality. It has been shown that consumption externalities do not generate indeterminacy of the equilibrium path (1) when the labor supply is exogenous (Liu and Turnovsky, 2005); or (2) when the utility function has the restricted homotheticity (RH) property1 (Guo, 1999 and Weder, 2000) even if the labor supply is endogenous. However, indeterminacy can arise when consumption externalities modify the Frisch labor supply, which requires that the utility function is nonseparable between consumption and leisure (Alonso-Carrera and Raurich, 2008). However, there is no work on the interactions between consumption externality and production externality in determining equilibrium indeterminacy in the literature. This paper develops a straightforward extension of the one-sector, increasing returns-to-scale, and endogenous capital depreciation model of Guo and Lansing (2007) by incorporating negative consumption externality in the sense of Dupor and Liu (2003) and Liu and Turnovsky (2005). The RH property exhibited by the utility function in Guo and Lansing (2007) due to the separability between consumption and leisure tells that consumption externality cannot generate indeterminacy alone without the existence of production externality. However, the paper shows that due to the existence of consumption externality, compared to Guo and Lansing (2007), the requirement for production externality to generate equilibrium indeterminacy can be further reduced. In our model, households have separable utility on consumption and leisure. And the utility on consumption depends not only on private consumption but also on the average consumption of the society. For our purpose, the dependence of an individual's utility on the average consumption captures negative consumption externalities that reduce the felicity that each individual obtains from his or her own consumption and decrease the marginal rate of substitution between an agent's own consumption and leisure. That is, the individuals exhibit “jealousy” and “running away from the Joneses”. Similar to Guo and Lansing (2007), firms make decisions about the amount of labor devoted to production, the level of expenditures devoted to investment and maintenance, and the utilization rate of the existing capital. The production technology employed by firms is subject to an external effect that depends on the economy-wide average levels of utilized capital and labor inputs. By utilizing the standard procedure of log-linearizing the equilibrium conditions around the steady state, we construct a two-dimension linearized system that depicts the stability properties of the steady state as a function of the externality parameters. It is shown that the existence of consumption externality reduces the upper and lower bounds of production externality for local indeterminacy; and when the degree of consumption externality increases, the upper and lower bounds of production externalities for local indeterminacy are both decreased. The intuition for why consumption externality can make equilibrium indeterminacy easier to obtain is that more effective adjustments of private consumption due to consumption externality promote agents' optimistic expectations as a self-fulfilling equilibrium driven by production externalities. The rest of this paper is organized as follows. Section 2 describes the model set-up including both consumption externality in households' behaviors and production externality in firms' behaviors. Section 3 solves competitive equilibrium and the two-dimension dynamic system. Section 4 discusses the relationship between externalities and local indeterminacy. And the concluding remarks are summarized in Section 5.