Urban Economics Problem Set#2 Due Date: Feb/ 19/ 2019 Note: But1 you are responsible for your idea of solving the problems. TA oice hours: Fridays…
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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.
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