Figure 2. Optimal solution with public goods
The figure brings us to the concept of jointness in production. In general, joint production exists if the
production of two or more outputs is interlinked in some way, e.g. through technical interdependences
or non-allocable inputs (see Peterson et al, 2002). Jointness gives rise to cost complementarities, also
referred to as economies of scope, which means that it is more expensive to produce the outputs
separately than together.
For agricultural public goods, jointness is mainly related to the existence of non-allocable
inputs. By definition it is difficulty to determine a non-allocable input’s contribution to each output. In
agriculture, land is the most obvious non-allocable input since land enters into the production of both
landscape preservation and food security, as well as private goods. But also labor and animal material
have such characteristics. Besides being key inputs in production of food, these inputs contribute to food
security and they affect the amenity value of the landscape.
If we return to our simplified framework with land as the only input, (4) gives the net stand
alone costs of providing food security. This relationship is drawn into figure 3a. Due to our simple
production technology, the net stand alone cost of producing landscape preservation coincides with the
drawn cost curve. If we use LM in the production of food security and LLP in the production of
landscape preservation, the sum of the net stand alone costs are: NC(LM ) + NC(LLP) . In this case
the cost from joint production is: NC(LM ) . The percentage increase in costs if the production of the
two goods is split into separate processes compared to joint production is then:
(6)
_ 100 NC (LM ) + NC(Llp ) — NC(LM ) _ 100 NC(Llp )
С ɪ ʊ'-' H ʃ -- ɪ ʊ`-' H ʃ
NC(LM ) NC(LM )
Thus, c is a measure of the degree of cost complementarities between food security and landscape
preservation, for given prices of private goods. If c=0, there is no cost complementarities.
The existence of cost complementarities can also be visualized by reference to the incremental
cost concept. The solid line in figure 3b illustrates the incremental cost of increasing the supply of
landscape amenity values (ICLp) if we have complete food security (LM). Up to LM, landscape values
are produced freely. However, if the society demands more landscape values, an incremental cost
incurs. Visa versa, the dotted line in figure 3b is the incremental cost of producing food security (ICM)
for a given minimum level of landscape preservation, LLp.