Question

Locational Indifference There are two cities, Springfield and Eugene, and 100 identical workers who can choose to live in either city. Suppose the indirect utility of living in either city is given by 4. Where Wy is the wage of living in either city j and R is the rent in city Wages in Eugene are $210 and wages in Springfield are $180. Rents in Eugene, Re are given by: RE-10+LE, where Ls is the number of workers in Eugene, and rents in Springfield, Rs are given by: Rs-20+2Ls, where Lsis the number of workers in Springfield. a. If half the workers live in Springfield, and half the workers live in Eugene, what is the indirect utility of living in each city? b. Would this allocation, with half the workers in each city, be a locational equilibrium? Why or why not? In locational equilibrium, how many workers will live in each city? c.

Answer 1

1) wage in Eugene = $210

rent in Eugene = Re = 10 + 50 = 60

indirect utility = wages (Eugene ) - rent (Eugene )

= 210 - 60

= 150

wage in Springfield  = $180

rent in Springfield = Re = 20 + 50 = 70

indirect utility = wages (Springfield ) - rent (Springfield )

= 180 - 70

= 110

2) This would not be an locational equilibrium as the indirect utility for both the cities are not equal if workers are dived into half half.

3) For locational equilibrium , The indirect utility in both cities must be same

indirect utility (Eugene ) = indirect utility (Springfield )

= wages(Eugene )- rent (Eugene ) = wages (Springfield ) - rent (Springfield )

= 210 - 10 - Le = 180 - 20 - Ls

200 - Le = 160 - Ls

200 - Le = 160 - (100- Le ) ( Ls + Le = 100 )

200 - Le = 60 + Le

140 = 2 Le

Le = 70 workers

so Ls = 100 - 70 = 30 workers .