Question

Rural vs. Urban Development: In the initial equilibrium, a nation’s workforce of 24 million is divided equally between a city and a rural area. The initial common utility level is $50. The urban utility curve has the conventional hump shape, with a peak at 8 million workers. In the workforce range 8–12 million, the slope of the utility curve is –$3 per million workers. The rural utility curve is subject to mild increasing returns to scale. In the workforce range 12–16 million, the slope is $2 per million workers. Suppose the nation invests in rural infrastructure, increasing rural productivity and shifting the rural utility curve upward by $2.
a) Workers will migrate from _____ to _____ because ..................
b) Migration [increases, decreases] utility in the rural area and [increases, de- creases] utility in the city, with a [larger, smaller] change in the [city, rural area].
c). Show the new equilibrium distribution of the workforce between the rural area and the city. In the new equilibrium, the workforce of the city is _____; the workforce of the rural area is _____; the common utility level is _____.

Answer 1

Initially the workers in rural and urban areas are distributed equally, so in the total workforce of 24 million the workers in rural and urban areas must be 12 millions each.

(a) Due to shift in the utility curve by $2 and positive slope of utility curve in rural area of $2 per million between 12 million and 16 million. And given that slope of utility curve in rural area is -$3 per million between 8 million and 12 million, Which means for every 1 million decrease in workers in urban areas the utility for rest of the workers in urban area will increase by $3. So when the workers migrate from urban area to rural area and the utility of workers in rural areas increases. And for every million workers migration the utility of workers in rural area will increase by $2 and the utility of workers in urban areas will increase by $3.

So the workers will migrate from urban areas to rural areas.

(b) As discussed in part a, migration increases utility in rural area and increases utility in city, with a larger change in the city.

(C) Again as discussed in part a, the migration of workers will take place from urban area to rural area. The workforce in urban area will be reduced by 2 million from 12 million to 10 million. And the workforce in rural area will increase from 12 million to 14 million in rural areas. That's the new equilibrium distribution of workforce.

The workforce in rural area will be 14 million and the workforce in urban area will be 10 million.

The new common utility level will be, the initial common utility level was $50 and every million workers migration increases the utility in urban area by $3. And 2 million workers so the new utility level in urban area will be,

= 50 + 2×3

= $56.

Similarly we can check whether the common utility level in rural area is $56 or not.

So the new utility level in rural area before migration was $52 (+$2 due to infrastructure building) after the migration of 2 million workers in rural area will be,

= 52 + 2×2

Since every million workers added in rural area increases the utility by $2 in rural area. So the migration of 2 million workers in rural area will add 2×2 = $4 of utility in rural area.

= 52 + 4

= $56.

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