Question

In: Economics

There are two cities, San Fran and Eugene, and 100 identical workers who can choose to live in either city.

There are two cities, San Fran 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: V_j=W_j -R_j where W_j is the wage of living in either city j and R_j is the rent in city j. Wages in Eugene are $200 and wages in San F. are $400. Rents in Eugene, R_e are given by: R_e = 30 + L_e, where L_e is the number of workers in Eugene, and rents in San Fran., R_s are given by: R_s = 60 + 2L_s, where L_s is the number of workers in San Fran.

Assume indirect utility in Eugene is 120 and indirect utility in San Fran is 240.

a. Suppose we introduce a lump sum tax, such that workers pay $12 in taxes, regardless of where they live. How many workers will live in each city?

b. What is the total tax revenue given the lump sum tax?

Solutions

Expert Solution

(a)

City Eugene

Indirect utility of worker living in Eugene (Ve) = We - Re.

Wage in Eugene (We) = $200.

Workers pays $12 in taxes.

So, the Net Wage in Eugene is $188 (i.e., $200 - $12)

Now, Wage in Eugene (We) = $188.

Rent in Eugene (Re) = 30 + Le.

Ve = We - Re

Ve = 188 - (30 + Le)

Ve = 188 - 30 - Le

Ve = 158 - Le. ----------------- (1)

City San Francisco

Indirect utility of worker living in San Francisco (Vs) = Ws - Rs.

Wage in San Francisco (Ws) = $400.

Workers pays $12 in taxes.

So, the Net Wage in San Francisco is $388 (i.e., $400 - $12)

Now, Wage in San Francisco (Ws) = $388.

Rent in San Francisco (Rs) = 60 + 2Ls.

Vs = Ws - Rs

Vs = 388 - (60 + 2Ls)

Vs = 388 - 60 - 2Ls

Vs = 328 - 2Ls. ----------------- (2)

At Spatial equilibrium point Ve = Vs

188 - Le = 328 - 2Ls

Note: Le + Ls = 100

Le = 100 - Ls

So, 188 - (100 - Ls) = 328 - 2Ls

188 - 100 + Ls = 328 - 2Ls

88 + Ls = 328 - 2Ls

Ls + 2Ls = 328 - 88

3Ls = 240

Ls = 240 / 3

Ls = 80

And, Le = 100 - Ls

Le = 100 - 80

Le = 20

Hence, 20 workers lives in Eugene and 80 workers lives in San Francisco.

(b) There are total 100 workers (80 lives in San Francisco and 20 lives in Eugene).

Each workers pays a lump sum tax of $12.

Total tax revenue = 100 * ($12)

Total tax revenue = $1200.

Rahul Sunny answered 1 year ago

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