休閒外部性與經濟成長：兩部門模型

Abstract

本文探討休閒外部性和經濟成長的關係。本文採用兩部門內生成長模型，並將休閒外部性引入效用函數中。本文分別探討三種不同的情形：(1)兩部門模型、但休閒未引入效用函數；(2)休閒引入效用函數中，但實體資本未用為人力資本部門的生產要素，且休閒外部性不存在；(3)休閒外部性存在。本文的發現如下： (1)將休閒引入效用函數後，我們無法排除多重均衡的可能，且當休閒的跨期替代彈性夠大時，商品部門以及教育部門的技術進步，均會使分配到商品部門的實體資本以及人力資本比例下降，並使經濟成長率上升。 (2)當代表性個人對休閒的偏好上升時，會使分配到商品部門的實體資本以及人力資本比例上升，並使經濟成長率下降。 (3)休閒的跨期替代彈性上升時，代表性個人會選擇較低的休閒水準，從而使經濟成長率上升。 (4)休閒外部性上升時，代表性個人會選擇較低水準的休閒而使經濟成長率上升。 (5)當經濟成長率夠高時，即經濟成長率越接近時間偏好率，休閒外部性的增加有可能使代表性個人的終身福利增加。

This paper adopts a general two-sector endogenous growth model with leisure externalities incorporated in the utility function. Three cases are discussed: (1) leisure is not incorporated in the utility function; (2) leisure is in the utility function but without leisure externalities in the utility function and physical capital is not hired in the production of human capital; (3) leisure externality is added in the utility function and physical capital is used in the educational sector. When leisure is not incorporated in the utility function, the economy has a unique steady state given a set of parameters, while we cannot exclude the possibility of multiple equilibria when leisure is in the utility function. This paper finds that, when the intertemporal leisure elasticity of substitution is large enough and when physical capital is used as an input in the educational sector, the technology advancement in the goods and the educational sectors will raise the steady-state economic growth rate. Increases in the intertemporal leisure elasticity of substitution will increase the steady-state economic growth rate and lower the leisure level chosen by the agent. Increases in leisure externality will decrease the leisure level and raise the steady-state economic growth rate, but increases in the preference intensity for leisure will raise the fraction of human capital allocated to the goods sector, and reduce the steady-state growth rate. This paper also finds that changes in the intensity of leisure externalities might raise the life-time welfare of the representative agent if the growth rate is high enough.