SOS please answer before 7pm Chicago time Urban Economics, problem set 1Urban Economics, problem set 12. (You may handwrite the answer to this question.) This question is an application which focuses onthe interaction of scale economies and transportation costs in the formation of cities (in the spirit ofKrugman, Geography and Trade (1992)).d. Now let's generalize the problem just a bit. Suppose production costs are those given inpart (a), and let shipping cost per widget be given by t. Although we assumed t= 2 in theabove, for what value of t would the two arrangements for production (centralized vs.separate factories) be equivalent in terms of total costA firm is considering where to locate its factories given that it serves four cities, A, B, C, and D,3. (You may handwrite the answer to this question.) Using Figure 3-3 and related discussionarranged as follows:from the O'Sullivan text (9e, p.38) as a starting point, consider the effect of introducinghoverboard on the market area of a given shoe factory.Aa. Suppose hoverboards decrease travel time for consumers from 1/10 hour per round-trip mile to 1/20 hour per round-trip mile. Draw a graph to illustrate the implicationsfor the radius of the market area of the factory. (hint: see discussion in OS pp.38-39).What is the value for the new radius? Show your calculations.b. Now suppose the hoxerboards also decrease the commuting cost for factory workers.As a result the cost of urban living decrease from 0.80 gallons of milk to 0.30 gallons(see the OS text discussion pp. 36-37)田BSuppose that the residents of these cities consume widgets, with consumption in each cityequaling 100 widgets. Assume one firm produces widgets and must decide how to arrange itsproduction. It could set up four factories, one in each city, with each factory producing 100widgets. In this case, the firm incurs no cost for shipping its output. Or the firm could locate itsfactory in the centrally located city, D. The single factory must then produce 400 widgets, 300 ofwhich are shipped to cities A, B, and C. There are no localized inputs for the firm; it only has toship its output to the markets. Further, assume the shipping cost (1) per widget is $2 (same toeach city; note: we are not using the Weber notation of transport rate per ton per mile here; weare expressing shipping cost with less detail). Also assume that widget production exhibitseconomies of scale with the average cost per widget in a factory falling as output rises.a. Suppose the average cost per widget varies with output as follows: AC(g) = $4 per widgetif factory output (9) is 100 widgets; AC(9) = $1 per widget if factory output is 400widgets (note: read the notation ACc(g) as "average cost as a function of output.") If thegoal of the firm is to minimize the sum of total production costs plus shipping costs,where should the firm locate its factories?b. Repeat part (a) if the AC curve rotates so that the AC(g) = $4 per widget if factory outputq is 100 widgets; AC(9) = $3 per widget if factory output is 400 widgets.c. Explain intuitively any differences that you find in the answers to parts (a) and (b).5

2. Average cost can be defined as a function of output (q) or it can be a constant depending on the…

Urban Economics, problem set 1 2. (You may handwrite the answer to this question.) This question is an application which focuses on the interaction of scale economies and transportation costs in the formation of cities (in the spirit of Krugman, Geography and Trade (1992)). A firm is considering where to locate its factories given that it serves four cities, A, B, C, and D, arranged as follows: Urban Economics, problem set 1 d. Now let's generalize the problem just a bit. Suppose production costs are those given in part (a), and let shipping cost per widget be given by t. Although we assumed t = 2 in the above, for what value of t would the two arrangements for production (centralized vs. separate factories) be equivalent in terms of total cost 3. (You may handwrite the answer to this question.) Using Figure 3-3 and related discussion from the O'Sullivan text (9e, p.38) as a starting point, consider the effect of introducing hoverboard on the market area of a given shoe factory. a. Suppose hoverboards decrease travel time for consumers from 1/10 hour per round- trip mile to 1/20 hour per round-trip mile. Draw a graph to illustrate the implications for the radius of the market area of the factory. (hint: see discussion in OS pp.38-39). What is the value for the new radius? Show your calculations. b. Now suppose the hoverboards also decrease the commuting cost for factory workers. As a result the cost of urban living decrease from 0.80 gallons of milk to 0.30 gallons (see the OS text discussion pp. 36-37) Suppose that the residents of these cities consume widgets, with consumption in each city equaling 100 widgets. Assume one firm produces widgets and must decide how to arrange its production. It could set up four factories, one in each city, with each factory producing 100 widgets. In this case, the firm incurs no cost for shipping its output. Or the firm 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. There are no localized inputs for the firm; it only has to ship its output to the markets. Further, assume the shipping cost (f) per widget is $2 (same to each city; note: we are not using the Weber notation of transport rate per ton per mile here; we are expressing shipping cost with less detail). Also assume that widget production exhibits economies of scale with the average cost per widget in a factory falling as output rises. a. Suppose the average cost per widget varies with output as follows: AC(q) = $4 per widget if factory output (q) is 100 widgets; AC(q) = $1 per widget if factory output is 400 widgets (note: read the notation AC(q) as "average cost as a function of output.") If the goal of the firm is to minimize the sum of total production costs plus shipping costs, where should the firm locate its factories? b. Repeat part (a) if the AC curve rotates so that the AC(q) = $4 per widget if factory output q is 100 widgets; AC(q) = $3 per widget if factory output is 400 widgets. c. Explain intuitively any differences that you find in the answers to parts (a) and (b).