8. In Ch. 7 we discussed city size. Consider a region where there are 24 million workers. The urban/city utility curve reaches a maximum with 8 million workers. a. [10 points) Graph the urban/city utility curve for the region described above. Show which city sizes lie on the positively and the negatively sloped portion of the curve. Explain what the positive and negative slope indicates about a city. b. [10 points] Suppose there are four cities each with 6 million workers. Are these city sizes a stable equilibrium? Explain. If the answer is no, what city size will be a stable equilibrium. (You can use the graph from part a to help you explain.) c. [10 points) Suppose there are two cities each with 12 million workers. Are these city sizes a stable equilibrium? Explain. If the answer is no, what city size will be a stable equilibrium. (You can use the graph from part a to help you explain.) Consider our discussion of how cities develop from Chapter 3. a. [5 points) Provide one example of a city you think developed primarily as a trading city and one that developed as a factory city. Be sure to give a brief explanation for why you chose that city in each case. (This may require some brief research into the history of your city choice.) b. (5 points) Describe the general chain of events that take place in economic models when a city is formed. FIGURE 4-2 Labor Pooling Generates a Lower Wage 12 - - - - - b 11 a 10 - --- Utility (utils) Switch cost 100 121 144 Income ($)4. [10 points, Ch 4) Consider the model of labor pooling shown in Figure 4-2. As before the utility function is U\" [Lt-y = V wag 8. The isolated wage is $144 and the switching cost for the cluster is zero. Suppose the switching cost for the isolated site increases to $80. Illustrate the implications for the expected utility and certainty equivalent of the isolated job