Factor substitution

3.6.1 Factor substitution

Suppose we let the production function of a nation be represented by the simple relationship

where Q is output; N is an input of natural resources expressed in some standard unit; K, often referred to as capital, is a composite factor of production representing all other inputs; and T represents the current techniques of production. Given this representation of an aggregate production function, factor substitution possibilities can be portrayed by using the concept of an isoquant. An isoquant represents the locus of all technically efficient combinations of two inputs that can be used to produce a given level of output, assuming no change in the current techniques of production (i.e. the variable T is held constant). Figure 3.9 shows three isoquant graphs which each represent a different degree of factor substitution.

Given that the isoquants are negatively sloped, in Figures 3.9a and 3.9b it is possible to substitute other factors of production (K) for natural resources (N) and still produce the same level of output. However, although both cases allow factor substitution possibilities, the nature of the substitution possibilities differs markedly. In Figure 3.9a , the straight-line isoquant implies a constant rate of factor substitution possibilities between natural resources and capital. This constant rate of factor substitution is measured by the slope of the isoquant curve. For example, if the constant slope of this isoquant in Figure 3.9a is −2.0, it implies that if natural resource (N) is reduced by 1 unit, capital (K) has to increase by 2 units in order to maintain the same level of production. This means that it takes 2 units of K to substitute for 1 unit of natural resources (N).

MARKETS, EFFICIENCY, TECHNOLOGY 45

Figure 3.9 Factor substitution possibilities

Furthermore, this can be interpreted as saying that the opportunity cost of 1 unit of natural resource is twice that of capital. That is, 2 units of capital would have to be sacrificed in order to compensate for the loss of just a unit of natural resource. Note also that in this special case where the isoquant has a constant slope, the use of natural resources can be reduced to zero without raising the opportunity cost (in terms of the other inputs sacrificed). Hence, the implication is that the increasing scarcity of natural resources will not be reflected in increased opportunity cost. Although conceptually interesting, however, this case is rather unrealistic.

In the case of the isoquant shown in Figure 3.9b , natural resources can still be substituted by other factors of production but not at a constant rate. In this specific case, as natural resources are progressively substituted by other factors of production, the slope of isoquant increases monotonically. For example, as is evident from Figure 3.9b , the slope increases as we move from point C to B, and from point B to point A. Since, as discussed above, this slope is a measure of opportunity cost in terms of forgone capital (K), it can

be seen that each incremental reduction in natural resource requires a progressively increasing amount of other factors of production (K) in order to maintain the same level of production, Q 0 . In other words, the opportunity cost of using natural resources, in terms of other inputs sacrificed, increases at an increasing rate as natural resources become scarce. According to standard microeconomic theory, this situation is viewed as being the most plausible scenario.

Finally, the isoquant shown in Figure 3.9c represents an extreme case where factor substitution possibilities are totally absent. In this situation, natural resources, N, and other factors of production, K, are used in a predetermined fixed proportion to produce a given level of output. For example, as shown in

Figure 3.9c , to produce Q 0 level of output, amount N 0 of natural resource and amount K 0 of other inputs are needed. Along the given right-angled isoquant, an increase in K alone would not precipitate a decline in the use of natural resources. That is, to produce the given level of output, Q 0 , amount N 0 of natural resource is needed regardless of the level of the other inputs, K, being utilized. Therefore, one important implication of this situation is that to produce a given level of output a certain minimum level of natural resource input is

needed. In our example above, to produce level Q 0 of output, at a minimum, amount N 0 of natural resources is needed. Given the current state of production technology (no change in T), any reduction in the amount of natural resources usage from this minimum will cause a decline in output, and this will be the case regardless of the amount of the other factor input used.

From the discussion thus far, we can generalize that the concern about the availability of natural resources very much depends on the assumption one makes about the nature of the rate of substitution possibilities between natural resources and other factors of production. If a natural resource is viewed as

46 MARKET SIGNALS OF SCARCITY

being perfectly substitutable with other factors of production, then its availability should be of little or no concern. This is the situation depicted by Figure 3.9a . On the other hand, if the substitution possibility between a natural resource and other factors of production is zero, the case demonstrated by Figure 3.9c , then a certain critical minimum of this resource will be needed to produce a given level of output. In this case, availability of natural resources would be a major concern since a decline of natural resources below this minimum would entail an automatic lowering of living standards or output.

As stated earlier, the case that is most realistic in depicting the nature of the substitution possibilities between a natural resource and other factors of production would have an isoquant with a general shape similar to the one shown in Figure 3.9b . In this situation, natural resources can always be substituted by other factors of production, but at an increasing opportunity cost. That is, successive reduction in natural resources requires an incrementally larger increase in other factors in order to maintain the production of a constant level of output. It is in this sense, therefore, that the scarcity (availability) of natural resources would become a concern.