Econ 144B: Urban Economics II Nilopa Shah Assignment 4 (based on textbook Chapters 10 and 11) Question 1 (Ch 10 - allocation of resources across rich and poor) Consider a city with two neighborhoods - one rich and one poor - both with equal-sized populations. Based on budgetary restrictions, the city employs a police force of 20 officers. Letting C denote the number of crimes and P the number of police in the neighborhood. The relationships between crime and police for each of the two neighborhoods are given by: and a) Graph the crime curves for each of the neighborhoods and interpret the differences between their slopes and intercepts in intuitive terms. b) Do you think the difference in "productivity" of an extra police officer between rich and poor neighborhoods is realistic? Provide a general explanation based on of your socio-economic understanding of the issue of crime. c) Derive and graph the city's transformation curve between and , subject to the constraint that and sum-up to 20. Also, note that because of the linear relationship between and for each group, the transformation curve is a straight line. (Hint: you should be able to find the transformation curve solely by locating its endpoints.) d) Find and graph the crime level if the city divided the police officers equally between the two neighborhoods. e) Find and graph the crime level that would result if the city divided the police officers to equalize crime across the two neighborhoods. f) Finally, consider the case where the city's goal is to minimize overall crime, which equals . How should the city divide its police officers across the two neighborhoods? Find the answer by using the iso-crime line approach described in the chapter. Provide an intuitive explanation for the answer that you have calculated. [Hint: Given the linear lines, tangency occurs at an end-point of the transformation curve; at which end-point will total crime in minimized?] g) Next consider if the coefficient of in the above formula were equal to 4 and the coefficient of were equal to 2. Without drawing any diagrams or doing any computations, use your economic intuition on police productivity (developed in part (b) above) to tell how the city would allocate the police force if its goal were to minimize total crime. What allocation would be chosen? Provide an intuitive explanation. Cpoor = 110 − 2Ppoor Crich = 120 − 4Prich Cpoor Crich Ppoor Prich C P (Cpoor + Crich)/2 Ppoor Prich Department of Economics of UC Irvine1 4 Econ 144B: Urban Economics II Nilopa Shah Question 2 (Ch 11 - Roback Model) Average-Joe, a representative college graduate, is facing a choice between two competing job offers (for the same position from equally reputable companies) in two different cities - H and L. If he chooses the job in City H then Joe’s monthly salary will be $10,000 thousand while the company in City L is offering him a competing monthly salary of $12,500 thousand. Joe looks for the best available rental apartment options in each city (he is not planning to buy a house). For renting similar one-bedroom apartments at a short-distance from his work place, Joe will have to pay a monthly rent of $6,000 thousand in City H and $5,000 thousand in City L. Though the cities are very similar in almost all crucial characteristics, there is one main difference. City H is designed to be a bike-friendly city, while City L has no such facilities like bike-paths and bike-racks that are easily available in City H. For this example, ignore the congestion and pollution-reducing effects of being bike-friendly. Also, Joe walks to work and hence transport to work is not important to this discussion. So, the value of biking is in it’s pleasure and convenience as a leisure activity. Further, assume that bike-friendliness has no impact of the production costs or profit margins of these firms. Joe’s indirect utility function is given by ; where is monthly salary, is monthly rent and takes value 100, if the ‘bike-path’ amenity is available and 0 otherwise. a) With the above information complete the following table with the correct numbers: b) Now, complete the table below for each value of , calculate Joe’s indirect utility in each city and, resultantly his choice of city for employment: V = Y − R + δA Y R A Amenity Level Income (Y) Monthly Rent (R) Amenity (A) City H Low / High YH = RH = AH = City L Low / High YL = RL = AL = VL = YL + RL + AL = δ Note: Continue to hold as a variable in this table. δ VH = YH + RH + AH = δ δ Department of Economics of UC Irvine2 4 Econ 144B: Urban Economics II Nilopa Shah c) Explain the economic intuition underlying the above choices, focusing on the effect of the different values on Joe’s choice. d) Note that according to the Roback Model, only one case where is the migration equilibrium. Briefly explain this claim. e) When there is a migration disequilibrium, people (just like Average-Joe) are attracted to the city which has an advantage. What is this advantage? f) For the cases below (where ) migration occurs between the two cities. Circle the correct responses in the following table to indicate the direction of migration and it’s effect on income and rents in the city of choice. (Recall that firm costs are not affected by the bike-path amenity.) g) Now focusing on the migration equilibrium case , draw a diagram to show the determination of equilibrium income and rent in the two cities via the interaction of indifference curves and iso-cost curves. Represent income ( ) on the x-axis, rent ( ) on the y-axis, clearly label all curves and equilibrium income and rent in both City H and City L. VA VB Choice 
 of City δ = 35δ = 20δ = 0 δ = 40 δ δ = 35 δ ≠ 35 City of Choice Direction of Migration From City H to City L OR
 From City L to City H From City H to City L OR From City L to City H Effect on Income in City of Choice Upward / Downward Pressure Upward / Downward Pressure Effect on Rent in City of Choice Upward / Downward Pressure Upward / Downward Pressure δ = 20 δ = 40 δ = 35 Y R Department of Economics of UC Irvine3 4

















































































































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