Demand Surface with External Economies: Derivation from Two Utility Functions(I)

With understanding that the study of the external agglomeration economies is increasingly significant in both theoretical and applied analyses in the field of spatial economics, this paper attempts to investigate the influence of the T-external economies (i.e., the external agglomeration economies stemming from "the total number of consumers who actually purchase a specific type of service") upon the utility level of those who consume the service. Our analysis is based on the assumption that there exists a market where one kind of composite goods and one kind of service are transacted, and that an individual consumer in this market may, if s/he can afford to do so, purchase any non-negative amount of the composite goods and either zero or one unit of the service. In this setting, we first obtain the demand surface by use of the following curves and surface as the basis: (i) a utility curve for the consumption of the non-negative amount of the composite goods, (ii) a utility surface for the simultaneous consumption of the non-negative composite goods and one unit of the service, and (iii) the income-density distribution curve. We also assume that the utility surface reflects the existence of external agglomeration economies stemming from "the total number of consumers who actually purchase the service" (i.e., the equilibrium demand level for the service). The shape of the obtained demand surface resembles a platypus' upper bill with its right-hand side vertically trimmed to a degree. Secondly, from the demand surface, we obtain the derived demand curve which serves as the actual market demand curve. This curve has upward convexity and forms a bell-shaped curve. Thirdly, we briefly discuss the research agenda to follow the investigation in this paper.