Ferrying Inputs and Outputs
A firm is considering where to locate a factory. The firm employs a given technology to make its product. The firm incurs a cost to ship product to a customer place. The firm uses two non-ubiquitous inputs—each available only at a specified location—that it then ships to the production site. All shipping costs are proportional to distance. All other inputs are ubiquitous. What location for the factory will maximize the firm’s unit profit? In Model 6B, geography takes the form of a rectangular plane. Model 6A (location on a line) is a simplification of Model 6B that illustrates important ideas about localization (here, clustering with a customer or supplier). Model 6A is also helpful in thinking about location on a network (Model 6F). Model 6C introduces substitutability of inputs and the possibility of economies of scale. Model 6D makes the prices of output and inputs endogenous. Model 6E expands on the number of inputs and the number of customer places. This chapter builds on Chapter 3 through 5. In Chapter 4 and 5, a local supply curve was assumed at each place that could have a different intercept. Chapter 3 made a similar assumption about unit production cost varying by location. Chapter 6 explains such differences in part as a result of the variation in the effective prices of non-ubiquitous inputs from place to place.