WHERE DO FIRMS LOCATE?

• Location decision of firms are based on profit maximization.• A firm’s potential profit varies accross space for several

reasons:1. It is costly to transport inputs and outputs. Hence, locations with relatively

low transport costs will generate higher profits, ceteris paribus.2. Some inputs cannot be transported at all. Locations with nontransferrable

inputs will generate higher profits , ceteris paribus.3. Some firms benefit from proximity to other firms in the same industry

(localization economies) and other firms may benefit from being in a large diverse city (urbanization economies).

4. Public sector levies taxes and provides public goods and services. Hence locations with relatively efficient public sector will generate higher profits, ceteris paribus.

• If transportation cost is the dominant factor in location decision: We call such firms as “transfer-oriented firms”.

• If a firm has relatively high costs for transporting its input, it is called a “resource oriented firm”.

• In general, when a firm’s input is relatively bulky, perishable, fragile or hazardous, the firm will prefer to locate near input resource.

• Such firms are usually involved in “weight-losing” activities.

• Consider a firm canning fruits. The input is perishable, hence should be transported by refrigrated trucks. This makes cost of production high. To lower these costs, firm will locate near its input source, a fruit farm.

• Monetary weight of input is greater than the monetary weight of the output.

Monetary weight of the input= Physical weight of the input x Transportation rate (USD/mile)

Monetary weight of the output= Physical weight of the output x Transportation rate (USD/mile)

• If a firm has relatively high costs for transporting its output to the market, it is called a “market-oriented firm”.

• Such firms are involved in weight-gaining activities.

• E.g. Automobile assembly firm: Output is more bulky than inputs.

Monetary weight of output is greater than monetary weight of inputs.

The Principle of Median Location• When we have multiple markets or inputs, we

have to use another tool to predict the location choice of a firm.

• Optimum location for a firm is the median transport location.

• This is the location that splits total monetary weight of the firm into two halves.

• At the median location, half the monetary weight comes from one direction and half from the other direction.

E.g. Let’s consider the location decision of a sawmill

There are two input suppliers: A & BSawmill buys the harvests from suppliers A & B, processes them

and sells the product (lumber) to an overseas market at point M.

Sawmill is a weight losing activity. This means, the sawmill is a resource-oriented or a transfer

oriented firm. Where will the firm locate the sawmill?

MMW=10

PORT

Input source A (MW=15)

Input source B(MW=15)

MARKET AREAS AND

CENTRAL PLACE THEORY

•Until now we have dealt with urban development in the framework of single city.•Now, we will analyze urban development in the regional perspective.•There are also interactions between cities in a regional economy.•Our key concepts:1.Equilibrium in spatial competition2.Determinants of market areas3.Central place theory

• Market area: A firm’s market area is defined as the area over which the firm can underprice its competitors.

• Remember that, firm’s net price is equal to: Price charged by the store

+ travel costs incurred by the customers

• Consider a region where consumers buy CDs from music stores. Characteristics of this region are as follows:

1.All music stores have the same technology and face the same input prices: Common store price.

2.In each trip each customer buys 1 CD. Travel cost is 50 cents per round trip-mile.

3.Region is rectangular: 60 miles long and 120 miles wide.

• Analysis of:

• 1 CD store• New entries• Equilibrium

Determinants of market areas:Assumptions:1.There are 3 stores in equilibrium.2.Each sell CDs and each has a price of $6.3.They have different locations.

• Can we set up an algebraic model to determine the market areas of market oriented firms?

• Let’s define:d: Per capita demand (number of CDs)e: Population density (per square mile)q: Output of the typical firm (CDs sold per month)

M= q/(d.e) M: Market area of the firm (in square miles) is the

territory required for the firm to sell its target quantity, q.

(d.e)= Demand density

• E.g.

Per capita demand d 4 CDs

Population density e 50 people/sq. mile

Demand density d.e 50 x 4 =200 (CD/sq mile)

Output per store q 1000 (CDs per month)

Market area M=q/(d.e) 1000/200=5 sq mile

This firm needs 5 sq miles to sell its targeted output.

• When demand for CDs (d) increases: • Market area of each firm becomes smaller. This means,

the firm needs a smaller area to exploit scale economies.

• For example, if demand (d) increases to 8 CDs, market area decreases to 2.5 square miles.

• When population density (e) increases:• It has a similar effect. Market area decreses since firm

now needs a smaller area to exploit scale economies.• For example, if (e) increases to 125, market area

decreases to 2 square miles.

• If scale economies increase, what is its effect on the market area? • If scale economies increase, this means average production costs continue

to fall over a larger range of output. This motivates firm to produce more, since there are greater scale economies to exploit.

• The effect of increase in scale economies on market area depends on the price elasticity of demand for CDs:

If demand is elastic If demand is inelastic

Increase in scale economies leads to increase in the production (q). Increse in scale economies also means that production costs decrease ; hence price of CDs decreses. Since CD has an elastic demand, demand for CDs (d)increases. This may offset the effect of increase in production. The more elastic is the demand, the less will be the effect of increase in scale economies on market area.

Increse in scale economies will lead to increase in output, decrease in production costs and prices. However, since demand for CDs is inelastic, demand will not increase due to decrease in price level. Hence there will not be any offsetting effect. Consequently, market area will increse.

• Suppose that in this region, a faster and cheaper travel mode is in use. This means, monetary and time costs of travel decline. What is its effect on the market area?

• Due to travel costs, a firm cannot move to the minimum point of its AC curve. The higher is the travel cost, the further away is the firm from the minimum point of the AC curve. This also ends up with a smaller production amount.

• If travel costs decline, firm will move down along the AC curve and produce more. The final effect depends on the price elasticity of demand for CDs.

• The final effect depends on the price elasticity of demand for CDs.

• How do differences in income affect the size of market areas?•Assumptions: 1.There are two cities in a region but one is poor and the other is wealthy.2.CD and land are normal goods (Positive income elasticity).3.Each firm in this region produces a common output (q).

Under these circumstances, city with the larger demand density (d.e) will have a smaller market area, since larger demand means that a firm needs a smaller area to exploit its scale economies.

• Since land is a normal good, wealthy citizens prefer to live in single-family homes but poor in apartment buildings. Hence, in the wealthy city, population density (e) will be lower .

• Since CD is a normal good, per capita demand for CD, (d),will be higher in the wealthy region.

• Hence, in the wealthy city, e is low and d is high: What will be the size of the market area? Larger or smaller than the poor region?

• Answer depends on the relative income elasticities of demand for land and CDs.

• If income elasticity of land is higher than the income elasticity of CDs: Density effect will dominate the demand effect: Market area will be larger in the wealthy region.

Central Place Theory• This theory was developed by Christaller (1966) and Losch

(1954).• It is an extension to our market area analysis.• It shows how the location pattern of different industries are

merged to form a regional system of cities.• This theory answers two questions:1. How many cities will develop?2. Why are some cities larger than others?

• Consider a region with 3 consumer products: CDs, pizzas and jewelry.

• Region has the following characteristics:1. Total population is 80000 and it is uniformly distributed.2. There are no shopping externalities.3. All inputs are available at all locations at the same prices.4. Uniform demand: Per capita demand for each product is

same throughout the region.5. Three goods have different per capita demands and scale

economies.

Products Per capita demand and scale economies

Jewelry Scale economies are large relative to per capita demand. Each jewelry store needs a population of 80000. Hence, 1 jewelry store is enough for this region.

CDs Scale economies are moderate relative to per capita demand. Each music store needs a population of 20000. Hence, 4 music stores are enough for this region.

Pizzas Scale economies are small relative to per capita demand. Each pizza parlor needs a population of 5000. Hence, 16 pizza parlors are available for this region.

Since all inputs are available at same price at all input locations, firms base their location decisions only on access to their customers, they ignore input costs.

• Since the jewelry has a larger scale economies and requires a population of 80000, it will locate at the center of the region. Remember the principle of median location!!!

• Jewelry workers will locate around the store to economize on commuting costs. Population density near the store increases and a city develops (L).

• Each music store requires a population of 20000. In the city (L), there will be enough demand for CDs. Two music stores will split the rest of the region into two market areas. Then, two more cities will develop around them (M).

• Suppose that L supports 4 pizza parlors and M supports 2. Then, around L 8, and around each M 4 pizza parlors will be established. As a result, we have 8 new cities (S).

• Total cities: 11

• Central place model generates a hierarchical system of cities. • 3 types of cities have developed:

Large Medium Small

Jewelry CD Pizza

CD Pizza

Pizza

•The larger is the city, the greater the variability of goods sold.

•Each city imports goods form the higher-order cities and exports to lower order cities.

• Some of the assumptions of the CPT are unrealistic. Let’s analyze and relax them:

1. The model assumes that the products from different stores are identical (No shopping externalities). This means there is no need for comparison shopping, hence no tendency for music stores to cluster. But, if the commodities were clothes, for instance, then the customers would likely to make comparison shopping. This would encourage clothing stores to cluster rather than disperse like music stores. If optimum cluster is 4 stores, all music stores would cluster in the center. Then there will be only two types of cities:

This would decrease the number of cities to 9 (1 large 8 small).

Large Small

Jewelry Pizza

CD

Pizza

2. Another assumption which may be unrealistic is that: “Three products are not complements”. However, some products may be complements. For instance, CDs and pizzas may be complmentary and pizza parlors and music stores will locate close to each other. Then there would be 2 types of cities:

Large Medium

Jewelry CD

CD Pizza

Pizza

In this case there will be 1 large city and 2 medium cities; totally 3 cities.

Although number of cities change, urban hierarchy is still present.

3. Another assumption about the central place model is that per capita demand does not vary with city size. Let’s replace pizzas with horseshoes, a good for which per capita demand is high in smaller cities and nearly zero in large cities. Due to this, urban hierarchy will be disrupted since there will be no horseshoe stores in the large city. The medium and small sized cities supply goods that are not available in large city.

An empirical approach to size distribution of cities: Rank-size ruleGeographers and economists have estimated the relationship between city size and rank. This relation is approximated by the rank-size rule.

Rank x Size = Constant Product of rank and size is same in all cities in a region. E.g. If the largest metropolitan area has a population of 16 million, second largest should have a population of 8 million, third largest 5.33 million, etc.