1. Assume that the central business district is the most desirable location because firms located at the urban center have maximum access to goods and services.

2. To further strengthen the pull of the metropolitan center, assume that wherever a commodity is produced it must be shipped to the urban center for export.

3. For greater simplification assume that market access is the only relevant location factor, so that spatial variation in labor costs, taxes, public services, and so forth are equal everywhere in the area.

4. Profits depend upon land costs and access to the metropolitan center.

1. Total industry demand is the sum of local demand plus export demand.

2. Higher export demand (exogenous) will ultimately increase the demand for local goods and services produced and the bid-rent value of land.

3. Total demand and supply determines the price of the product produced. Each competitive firm in the area is a "price taker" that is too small to have an effect on market price.

1. The net price (price less transportation cost) will be the greatest at the metropolitan center because it is the minimum transport-cost point for the area as a whole. Thus total revenue will be greatest for the metropolitan center for each quantity sold.

2. With a uniform transport surface, the net price per unit will fall the farther the firm is from the CBD. Hence, the firm’s total revenue curve will rotate downward.

3. The firm will maximize profits where the slope of the TR and the slope of the TC curve are the same. Rent is the amount of "excess profits" at each location that is used to pay for access to that point.

4. The bid-rent curve is the highest for TR (1) at the center of the CBD and falls to zero for TR (3) at the city’s edge.

5. The bid-rent curve can be thought of as a location/rent indifference curve between high rent central locations and low rent peripheral locations.

1. If transport costs are the only savings associated with a location at the center of the city and transport cost increase linearly with distance, then one might assume that the bid-rent curve would be linear, reflecting transport cost savings.

2. However, firms located near the center will employ land more intensively than firms located further out because input substitution is possible. In general, the relatively more valuable a resource, the more intensively it is used.

3. With more capital (and labor) used at the central business district, the marginal productivity of land is higher as is its rent.

4. Long-haul economies of transportation will also affect the shape of the bid-rent curve. A 5-mile trip to the urban core cost more than one-half of a 10-mile trip because of fixed costs associated with both trips and higher congestion costs nearer the CBD that increase time costs.

1. Rates of Costs Change. Activities that face rapid increases in costs as they move from the CBD will have steeper bid-rent curves.

2. Ability to Substitute. Activities that cannot subsitute other inputs for access afforded by the CBD have steeper rent gradients. (The effect of technology?)

1. The bid-rent curve for households is determined by preference for location near jobs (similar to firm location near resources).

2. But, households seek to maximize utility rather than profits, so that the demand for space offsets the demand for transport cost savings.

3. Households can have more than one bid-rent curve based upon their preferences for location versus other goods and services (including housing services.)

4. Each bid-rent curve can be viewed as a utility function for existing homeowners.

5. There is only one bid-rent curve for existing homeowners that equates the demand for labor with the supply of labor in the area.

6. Higher demand and supply for labor will shift the bid-rent curve for existing homeowners upward, lowering the utility received by original households.

1. Von Thunen and the Concentric-Zone Model (1926) explained the allocation of land among competiting uses based upon the slopes of their bid-rent curves.

2. Roads and axial developments recognize the concentric zone model be are adapted to reflect differences in transportation costs.

3. Agglomeration and multiple-nuclear cities recognize the possibility of agglomeration clustering of groups of firms and the effect of transport arteries in a city.

1. An increase in population growth will shift the rent gradient upward, reflecting higher transport costs at every location and greater benefits from agglomeration in the CBD.

2. An reduction in transport costs will flatten the rent gradient (substitution effect) and shift the rent gradient upward (income effect). However, the net effect will be a flatter rent gradient and lower rent in the CBD, although higher in the suburbs.

3. A change in income will flatten the rent gradient if the income elasticity of the demand for space is greater than the income elasticity of the demand for transport cost savings. Also, with higher income, the fixed cost of commuting is a smaller percentage of total income, which may lower the income barrier to commuting by upper income groups.

4. Agglomeration economies in the suburbs result in other peaks and mountains that affect the general shape of the rent gradient originating in the CBD1. The spreading of the metropolist due to increase in the economic base, employment and population. (invasion-succession model)