Question 1: Consider a model in which agglomeration is driven by forward and backward linkages between firms. As in our standard model, the world is composed of manufacturing workers, who can move between locations, and agricultural workers who cannot. Suppose that transport costs are such that the economy is at the sustain point.

(a) Draw the correct relative wage curve describing the economy. Mark any stable equi¬librium with filled circles and unstable equilibrium with an open circle.

(b) What is the dispersion force in this model?

(c) Suppose that there is a -Green Revolution" which makes agriculture more productive. This allows half of the agricultural workers to switch into manufacturing. Show *graphically* how this changes the graph you drew for the economy.

Question 2: In the U.S. in the early 20th century, damming rivers provided an important source of electricity. Cities grew up in locations were dams could be constructed because firms could take advantage of cheaper electricity, since it was expensive to transport elec¬tricity over long distances before the introduction of high-voltage lines.

What type of agglomeration economy is responsible for these cities?

After 1950, new high voltage lines made it dump to transport electricity, eliminating the advantage of being near a dam. Based on the results of Bleakley and Lin, what would we expect to happen to cities near the dams?

What do the results of Bleakley and Lin tell us about the roll of different agglomeration economies in generating cities?

Suppose that even after the advantage of cheap local electricity disappears, cities near the dams are able to take advantage of reservoirs that people enjoy being close to. Under these circumstances, could we draw similar conclusions about the role of different agglomeration forces to those found by Bleakley and Lin by studying dams?

Question 3 - A recent paper by Michaels, Rauch and Redding (2013) shows that in 1880, most of the work done in American cities was characterized by production in low-skilled and routing manufacturing tasks, such as sewing garments or spinning yarn. These tasks were done by relatively low skilled, often immigrant, workforces.

Consider each of the labor market pooling theories discussed in class. Which of these are consistent with the pattern described above, and which are not?

What implications does the pattern described above have for Moretti's theory of agglomeration driven by human capital spillovers? In contrast, Michaels, Rauch and Redding show that today the work done in American cities is characterized by production in high-skill interactive tasks, such as analysis and planning. Their hypothesis is that the fall in transportation and communication costs has allowed firms to concentrate headquarter and research tasks in cities while moving routine work to less expensive locations. If they are correct, would this pattern be more consistent with the theory of external increasing returns through input-output linkages or technology spillovers? Why?

Question 4: Consider the model with human capital spillovers (Moretti's model) that we studied in class. Some reminders about the model: the production function for an individual firm in the model is y = AlicHLaLK0 where y is output. A is technology, H is high-skilled workers employed, L is low-skilled workers employed, and K is land. The firm's cost of production in c = WHH + WLL + rK. Firms are identical and perfectly competitive. The city is endowed with some initial supply of land Ko, the land market is competitive, so rent adjusts until all land is used in production by firms or for housing by workers. There are human capital spillovers so the technology level A is an increasing function of the number of skilled workers in the city.

Draw two graphs, one for high skilled workers and another for low skilled workers, showing how equilibrium is determined in the model.

Suppose that the city starts with land Ko, but then a state reclamation program drains a swamp surrounding the city so that the supply of land increases to K1 > Ko. Does this shift the worker's indifference curves in your graphs in part 2a? If so, how?

How is the population of the city affected by the increase in available land?

How is the firm's cost curve c(wL, wH, r) affected by the increase in available land? Draw two graphs showing, for high-skilled and low-skilled workers, the new equilib¬rium in the city.

Now suppose that there are no human capital spillovers in the model. Show graph¬ically how the firm's cost curve c(wL, um, r) is affected by the increase in available land? Draw separate graphs showing, for high-skilled and low-skilled workers, the new equilibrium in the city.