causes higher rents at those locations, as in the no-substitution case. But firms then use less land and more capital, temporarily earning economic profit as a result. That economic profit leads to even higher rent, as wannabe firms compete for already occupied land. That higher rent in turn leads to another round of factor substitution, and so on. Fortunately, this process does not go on forever but converges to equilibrium values for rent and factor inputs. We have already seen earlier in these notes how these equilibrium rents and factor inputs can be determined, for any given values of the exogenous variables. Observers looking at high land rent and high buildings at certain city locations often question the direction of causality. Are the high buildings the result of high land rent or is it the other way around? In the adjustment process described two paragraphs above, both directions were operative. However, in equilibrium land rent and building height alike are endogenous variables – determined by exogenous variables in the model and the production function for buildings. The cost advantage attached to these prime locations remains a significant influence, as it was in the case of no factor substitution. Factor substitution adds another influence. In the example of Fig. 6-5, it can be seen that land rent at x = 1 is $1600 / hectare / day given the ability to construct a 25-floor building at that location, but only $856 if limited to 4 floors. The cost advantage of being at 1 block (as opposed to farther out) is the same either way, so it is factor substitution that accounts for the difference. At least in this model, we will never see tall buildings constructed on cheap land. This point is illustrated in Table 6-6 in the text. It is possible to build a 25-floor building on the lowest cost land in that table ($40 / hectare / day rent), but the resulting building cost is far higher (at $251.60 / day) than the building cost associated with lower buildings on larger sites ($110 / day or $90 / day). A firm that did construct a 25-floor building at that location would soon go out of business, since it would have to compete with firms constructing low-rise buildings with only $90 / day in building cost. Likewise Table 6-6 illustrates the rule that low buildings will not be built on expensive land. When considering high land rents – typically near the city centre – the question may arise: does the limited supply of land at these central locations have anything to do with the high rents there? The geometry of circles does imply that a limited land supply is available closer to the centre – for example in a ring approximating a one-block radius compared with a ring farther out (say at 5 blocks). However, in this model the land supply does not affect rent. This point can be illustrated with Figure 2 in these notes. In Figure 2, it is assumed that the land supply at x = 1 block is 20 hectares. This might correspond to the number of hectares in a ring-shaped area of land (referred to in
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