Scale of Local Production and City Size
指出，人口增长不仅增加本地差异化产品的种类，还会扩大现有产品的生产规模，这一被忽视的“第二维度”有助于解释某些行业本地生产与人口之间的凸性关系。
In recent years there has been great interest in economic geography (e.g., Paul Krugman, 1991). A central theoretical result from this literature is that if the population increases at a location, there will be an increase in the variety of differentiated goods produced at the location. In these analyses, the number of different varieties at a location is the key margin. This paper (which summarizes work in Holmes [1998]) highlights a second margin that the previous literature has ignored. It argues that this second margin should be incorporated into the analysis because it will help to explain an empirical relationship. This second margin is the scale of local production of particular differentiated goods. An increase in population will increase the scale of production of existing locally produced goods, in addition to increasing the variety of such goods. The empirical relationship that holds for certain industries is a convexity in the relationship between local production and population. The existing literature has ignored this second margin because it has focused on the Dixit-Stiglitz model of monopolistic competition (Avinash K. Dixit and Joseph E. Stiglitz, 1977). In the way this model is usually implemented, the equilibrium output of any particular locally produced differentiated product is independent of local population. As population increases, total local production expands by adding new varieties; the scale of production of any existing product remains fixed. This is an implausible implication. It is reasonable to expect that the output of existing products would increase. This paper departs from the Dixit-Stiglitz formulation to incorporate this second margin. A general requirement of the Dixit-Stiglitz formulation is that the elasticity of substitution between differentiated inputs exceed 1. A key feature of my formulation is a low elasticity of substitution; in fact, I look at a special case where it is zero (Leontief). This limits the tendency to substitute variety for quantity of particular differentiated inputs. To see the basic idea, suppose output in a particular industry (e.g., grocery wholesaling), is a composite of 10 different specialized inputs (e.g., vegetable wholesaling, fish wholesaling, etc.). The technology is Leontief so that to make one unit of the wholesaling composite, one unit of each of the 10 differentiated inputs is required. In a small town, there may be local production of perhaps only two specialist inputs. For example, the small town may have a local vegetable wholesaler and a packaged-goods wholesaler, but not a fish wholesaler, not a candy wholesaler, and so on. For this town, required vegetable and required packaged-goods wholesaling services will be acquired locally, while the needed fishwholesaling services will be imported from somewhere else. In contrast, a large city may be of sufficient scale to have many different inputs produced locally. For the purpose of later discussion, I will assume that a particular large city has seven out of the 10 different inputs provided locally. Adding people to a location increases the variety of locally produced goods, as in the standard model. But there is also a second effect: adding people increases the scale of production of the existing products. If the vegetable-wholesaling product is initially provided locally, then adding an additional person will increase the output of local vegetable wholesaling because this new person will want vegetables! The reason why adding this second margin is an interesting thing to do is that it provides a nice explanation for why there might exist a convex relationship between local industry production and population (I discuss the empirical basis for this relationship below). * Department of Economics, University of Minnesota, Minneapolis, MN 55455, and Federal Reserve Bank of Minneapolis. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.