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Urban Economics Problem Set#2 Due Date: Feb/19/2019

Note: If you encounter any issues with the mathematics needed in the problem set, please attend TA

office hours and ask him to help you. But, you are responsible for your idea of solving the problems.

Q1. Suppose there are eight workers in a town available for a firm. The firm is going to decide on

locating in an isolated site or a cluster.

a) Suppose the demand function for labor when demand is low is L

d = 24 − 2w, where w is the wage

rate. Using algebra and also a proper diagram, find the equilibrium wage and show it on your diagram, for

isolated site option.

b) When demand is high, the firm demands for four more labors in each wage, compared to low demand

case. As in the slides, find equilibrium wage and show it on the diagram (add this to the diagram you have

from part a)

c) Suppose the firm expects a high demand with 25% probability and a low demand with probability

75%. Find the cluster wage to achieve locational equilibrium, and show it with a diagram for cluster case.

d) Find the optimal locating policy for the firm by comparing expected profits.

Q2. Skill Matching Problem Suppose there are 8 workers with uniformly distrubuted skills on a unit

circle. Now suppose 4 firms enter the market with skill equirement of {

1

16 ,

5

16 ,

9

16 , and 13

16 }. Use appropriate

diagrams to show your work in this question.

a) What is the skill gap?

b) What is the net wage, if the gross wage is equal to 10, and unit training cost is equal to 32.

c) Now suppose, workers types increase to 10. How many firms will enter the market? What is the new

skill gap? Find the new net wage?

d) Discuss the effect of clustering on workers’ welfare

Urban Economics Problem Set#2 Due Date: Feb/ 19/ 2019 Note: if you encounter any issues with the mathematics needed in the problem set, please attend TAoﬁice hours and ask him to help you. But1 you are responsible for your idea of solving the problems. TAoﬁice hours: Fridays 12:15—1:45, 113 Keller; email: Q1. Suppose there are eight workers in a town available for a ﬁrm. The ﬁrm is going to decide onlocating in an isolated site or a cluster. a) Suppose the demand function for labor when demand is low is L‘i : 24 7 211;, where w is the wagerate. Using algebra and also a proper diagram, ﬁnd the equilibrium wage and show it on your diagram, forisolated site option. b] When demand is high, the firm demands for four more labors in each wage1 compared to low demandcase. As in the slides, ﬁnd equilibrium wage and show it on the diagram (add this to the diagram you havefrom part a) c) Suppose the ﬁrm expects a high demand with 25% probability and a low demand with probability75%. Find the cluster wage to achieve locational equilibrium, and show it with a diagram for cluster case. d] Find the optimal locating policy for the firm by comparing expected proﬁts. Q2. Skill Matching Problem Suppose there are 8 workers with uniformly distrubuted skills on a unitcircle. Now suppose 4 ﬁrms enter the market with skill equirement of {115, 1%, %,and%}. Use appropriatediagrams to show your work in this question. a) What is the skill gap? b) What is the net wage1 if the gross wage is equal to 10, and unit training cost is equal to 32. c) Now suppose, workers types increase to 10. How many ﬁrms will enter the market? What is the newskill gap? Find the new net wage? d) Discuss the effect of clustering on workers’ welfare.