A region\'s population of consists of two million living entirely within two cit
ID: 1189171 • Letter: A
Question
A region's population of consists of two million living entirely within two cities. Initially, migration between the two cities is prohibited. The relationships between population (in millions), daily labor income, and daily commuting costs in each city are given by the two following tables.
City A
City B
Population
Income
Cost
Population
Income
Cost
0
1
0
0
5
0
1
6
1
1
12
2
2
12
2
2
19
4
3
23
3
3
25
7
4
35
5
4
30
10
5
45
20
5
35
13
6
55
35
6
40
20
7
60
50
7
45
27
8
65
60
8
50
35
9
68
65
9
54
42
10
70
68
10
58
50
Suppose that, initially, City A's population is 4 million and City B's population is 6 million. Then, the national government allows free migration between the two cities. You can assume people move in increments of one million.
a. After migration, what will be the equilibrium population of City A and City B?
b. Will this equilibrium be stable, and why?
c. Instead of allowing free migration between the two cities, is there a way to assign populations to the two cities in way that raises both cities' utility above the equilibrium level? If so, what would be the population of City A and City B in that case?
d. The first fundamental theorem of welfare economics is that a competitive equilibrium leads to a Pareto-optimal allocation of resources. Does the theorem hold in this case? If not, why not?
City A
City B
Population
Income
Cost
Population
Income
Cost
0
1
0
0
5
0
1
6
1
1
12
2
2
12
2
2
19
4
3
23
3
3
25
7
4
35
5
4
30
10
5
45
20
5
35
13
6
55
35
6
40
20
7
60
50
7
45
27
8
65
60
8
50
35
9
68
65
9
54
42
10
70
68
10
58
50
Explanation / Answer
80
a) After migration the equilibrium population will be City A = 5 million & City B = 5 Million as people will migrate till the time they individually get the highest return.
b) Yes this equilibrium will be stable because now individually people are earning is the best possible outcome with no government control.
c) as per answer (a) combined benefit of both the cities is 125 + 110 = 235 but from the table we can see that the maximum benefit earned by the economy is 120 + 120 = 240 which is possible when population of City A is 4 million and population of City B is 6 million. So this will be the population assigned by the government.
d) Yes the theorem holds in this case as it can be seen in the table that when populatoin of City A was 4 million people were earning 30 units each but people of city B wanted to earn more i.e. from 20 unit to 25 units they dragged down the people of City A from 30 units to 25 units.
City A City B Population (a) Income Cost Income-cost (b) a*b Population Income Cost Income-cost (b) a*b 0 1 0 1 0 0 5 0 5 0 1 6 1 5 5 1 12 2 10 10 2 12 2 10 20 2 19 4 15 30 3 23 3 20 60 3 25 7 18 54 4 35 5 30 120 4 30 10 20 80 5 45 20 25 125 5 35 13 22 110 6 55 35 20 120 6 40 20 20 120 7 60 50 10 70 7 45 27 18 126 8 65 60 5 40 8 50 35 15 120 9 68 65 3 27 9 54 42 12 108 10 70 68 2 20 10 58 50 880
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