Question

In this problem, you will solve for the equilibrium population
of an idealized city experiencing rural-urban migration, following
the augmented Harris- Todaro model from Chapter 3. The incomes
earned in urban employment and in the rural area are *y* and
*y*A, respectively, and *t* is commuting cost per
mile. *J* is the number of available urban jobs.

a) Suppose the city is a rectangle 10 blocks wide with the
employment center at one end (it’s an island like Manhattan). The
city spreads out along the length of the island to accommodate its
population, with its edge located *x**̄* blocks from
the employment center. Compute the city’s land area in square
blocks as a function of *x**̄* . Assuming that each
urban resident consumes 0.001 square blocks of land, compute the
amount of land needed to house the city’s population *L*.
Set the resulting expression equal to the city’s land area, and
solve for x̄ in terms of *L*.

b) With *J* jobs in the city, the chance of a resident
getting one of the jobs is *J*/*L*, which makes the
expected income of a city resident equal to
*y*(*J*/*L*). The expected disposable income
net of a commuting cost for a resident living at the city’s
boundary is then *y*(*J*/*L*) –
*tx**̄* . The rural-urban migration equilibrium is
achieved when this disposable income equals the rural income as
explained in Chapter 3. Write down this equation, and substitute
your solution for *x**̄* in terms of *L* from
part (a). Then multiply through by *L* to get a quadratic
equation that determines *L*.

c) Suppose that *y* = 10,000, *y*A = 2000,
*t* = 100, and *J* = 30,000. Substitute these values
into your equation from part (b), and use the quadratic formula to
solve for *L* (it’s the positive root). The answer gives the
city’s equilibrium population.

d) In equilibrium, what is the chance of getting an urban job? What is the implied unemployment rate in the city?

e) What is the distance to the edge of the city? How much does a resident living at the edge spend on commuting?

f) Suppose that *y* rises to 12,000. Repeat the
calculations in parts (c), (d), and (e). Given an intuitive
explanation of the changes in your answers to (c) and (d).

Answer #1

The basic urban model we studied assumed a fixed population,
agricultural land, and no inter-city migration. According to the
model what happens to each of these measures if agricultural land
rents were to increase?
Options are Unchanged, Increase, Decrease,
Ambiguous
Dwelling size
Land rent per acre
Building height
Commuting cost per mile
Rent per square foot of floor space
Total rent
Income
Population density
Dwellings per acre
Distance to the edge of the city ...

In this exercise, you will analyze the supply-demand equilibrium
of a city under some special simplifying assumptions about land
use. The assumptions are: (i) all dwellings must contain exactly
1,500 square feet of floor space, regardless of location, and (ii)
apartment complexes must contain exactly 15,000 square feet of
floor space per square block of land area. These land-use
restrictions, which are imposed by a zoning authority, mean that
dwelling sizes and building heights do not vary with distance to...

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