Ricardian rent as one of the three components of the urban rent:

K: transportation cost in $ per mile

D: distance in miles from a house to the city center

Q: parcel of land in acres

x: all expenditures and savings other than expenditures for real estate

r(a): rent per acre in the agricultural land

b: the distance of the edge of a city from the center of it.

C: annualized cost of construction

Y: household income

At the edge of a city, there is no Ricardian, differential rent.

Housing rent consists of agricultural rent and annualized construction cost.

R(b) = r(a) q + c

Inside the city housing rent is composed of three parts:

(3.1) R(d) = ( r(a) q + c) + k( b – d)

In (3.1) the distance d is the only variable. The closer the house is to the center, the higher is the rent.

Let’s convert the housing rent into the land rent. First, subtract the structure rent (construction cost). Second, the unit of measurement should change from a housing unit to an acre of land.

(3.4) r(d) = r(a) + k (b – d)/ q

π ν

Population, land supply and Ricandian rent:

The degree of circularity: ν

If it is equal to 1, the city is fully circular; if 0.1, the tip of pennysla.

The number of households in the city: n

The acres of land used by a household: q

Then n q equals the area of the city measured in acres

The size of a fully circular city: π b²

The size of a city with the degree of circularity ν : ν π b²

^{Equating the two, n q =} ν π b²

Then the radius, the distance from the edge to the center, is determined as

(3.5) b = ( n q / π ν )^1/2

The numerical example:

housing density q: 4 households for each acre of land. One square mile equals 640 acres. Therefore, 2,560 households per sq. m. Each household occupies 0.0004 sq. m. of land.

The number of families n: two million households

Assume a fully circular city. In the United States, the residential land is only 60 percent of the whole city area. Thus ν is equal to 0.6.

From (3.5) b = 20.606

If the city is semi-circular, then b = 29.142