Please answer these questions. It is about Urban Econ.

Exercise 1.2 Consider four cities. A. B. C. and D, located as follows: A D B C Suppose that the residents of these cities consume widgets. with consumption in each city equaling lI] widgets {see the map below). The rm that produces widgets must deice how to arranges its production. It could set up four factories. one in each city. with each factory producing 100 1 widgets. In this case. the rm incurs no cost for shipping its output. Or the rm could locate its factory in the centrally located city. D. The single factory must then produce 400 widgets. 300 of which are shipped to cities A, B, and C. The shipping cost per widget is $2. A nal assumption is that widget production exhibits economies of scale. with the cost per widget production exhibits economies of scale. with the cost per widget in a factory falling as output rises. {a} Suppose that the cost per widget varies with output as follows: cost is $4 if factory output is 100 widgets; cost is $1 if factory output is 4m widgets. In this situation, nd the bets arrangement of production for the rm {i.e.. one central factory or four separate factories). THe best arrangement leads to the lowest total cost for the rm, where the total cost is the sum of production and shipping cost. {h} Repeat {a} if the cost per widget varies with output as follows: cost is 34 if factory output is llll] widgets; cost is $3 if factory output is 400 widgets. (c) Explain intuitively any difference in the answers to (a) and {b}. {d} Suppose production costs are those given in (a). and let shipping cost per widget be given by t. Although i 2 in {a}, what value of t would make the two arrangements for production {centralized vs. separate factories) equivalent in terms of cost