**regional and urban growth**(or decline) is a function of the expansion (or contraction) of the

**basic sector**. This employment is in turn having impacts on the employment of two other sectors; retail and residential.

Basic sector. Employment that meets non-local demand. It produces good and services, which are exported outside the urban area. It generates a centripetal capital flows into the city, which results in economic growth and surpluses. Most industrial sector employment is within this category. This sector is usually less constrained by urban market accessibility considerations since the local market is not the main outlet of the output. The basic sector is anexogenous elementof the Lowry model andmust be provided.

Retail sector(non-basic sector). This employment is to service the local demand such as retailing, food and construction. It does not export any finished goods and services and use the region as its main market area. Since this sector strictly serves the local / regional demand, location is an important consideration. Employment levels are also assumed to be linked with the local population through a multiplier effect. The retail sector is anendogenous elementof the Lowry model.

Residential sector. The number of residents is related to the number of basic and retail jobs available. The choice of a residential area is also closely linked to the place of work, so the model tries to minimize commuting distances. This consideration is anendogenous elementof the Lowry model.

**transport costs**, or the friction of distance. The higher the friction of distance, the closer places of employment (basic and non-basic) and residential areas are. Overall, the Lowry model has three assumptions:

- The residential sector, and thus urban land use, is a
**function of employment**. This function is calculated assuming the multiplier effects of basic and non-basic employment. Each job is thus linked to a number of people. - The total employment is a function of the employment in the
basic sector and retail employment the result of
**multiplier effects of basic sector employment**. - The location of the population is a function of the costs involved
to go to their place of work, commonly taking the form of a
**gravity-based friction of distance function**.

**exogenous spatial distribution of the basic sector employment**and a set of transport costs between zones, the model calculates total population and employment by zone. It is composed of an economic sub-model and a spatial allocation sub-model, which are subject to constraints.

- The economic sub-model provides the
**impacts of basic employment**on non-basic employment and the total population. - The spatial allocation sub-model provides the
**distribution of the population**in function of attractiveness and transport costs. This is done by a gravity-type**spatial interaction model**.

- The spatial distribution of basic employment is considered given.
- The location of the basic sector workers is determined according to a location-probability matrix, itself the result of a least friction of distance function.
- Calculation of the residential popualtion per zone according to the population per worker multiplier.
- Calculation of the number of non-basic workers per zone to service the population. This is the result of a non-basic worker per capita multiplier.
- The location of non-basic workers is determined according to a location-probability matrix.
- Recalculation of the total population according to the population per worker multiplier.
- Calculation of the total number of workers and the total population. This is the summation of the basic and non-basic employment and of the basic and non-basic related population.
- Steps 4 to 7 are repeated until a convergence is reached, that is an optimization of the equation system of the model following a set of constrains such as density limitations.

**singly constrained**, that is the only constraint is the fixed location of basic employment. It can also be

**doubly constrained**, where the location of basic employment and housing are fixed. The singly constrained Lowry model is solved according to these equations:

- Tij = Interaction from residential zone i to work zone j (work-related travel).
- Sij = Interaction from residential zone i to service zone j (service-related travel).
- Pi = Total population of a zone i.
- Ei, EBi and ESi = Total employment, employment in the basic (B) and service (S) sectors for zone i.
- dij = Euclidean distance between zone i and j (in km).
- Alpha = population over basic employment multiplier.
- Beta = service employment over population multiplier.
- Lambda: Friction factor for residential interactions.
- Micron: Friction factor for services interactions.
- WTTRij and WTTSij = Willingness to travel for Residential (R) or Services (S) between zone i and j.
- LPRij and LPSij = Locational probability for Residential (R) or Services (S) between zone i and j.

**static model**, which does not tell anything about the evolution of the transportation / land use system. Furthermore, recent economic changes are in the service (non-basic) sectors, forming the foundation of urban productivity and dynamics in many metropolitan areas, cannot be effectively represented. Under such circumstances the model is likely to be inaccurate in major service-oriented metropolitan areas. A way to overcome this issue is to consider some non-basic service employment as basic. Further, the Lowry model does not consider movements of freight in urban areas, which are very significant and have impacts on the friction of distance.

- Click here to download an operational basic Lowry model (MS Excel format).