Multifunctionality of Agriculture: An Inquiry Into the Complementarity Between Landscape Preservation and Food Security

WTP = E[LP]^ε

to the economic surplus as defined in the previous paragraph. The amenity value of tilled land, T, is
allowed to differ from that of arable land and pasture, G. The aggregate for landscape preservation is
postulated by the following CES function:

^κ
LP = A[aGG (^κ-¹)/^κ + αTT (^κ-¹)/^κ ]й).

Following Brunstad et al. (1999), the parameters E, A, αG and αT are calibrated to estimates of amenity
benefits taken from the research of Drake (1992). Based on the research of Lopez et al. (1994), the
elasticity of scale, ε, is set to 0.172. This means that the marginal willingness to pay is strongly decreasing
for rising levels of LP. Moreover, the elasticity of substitution between cultivated pasture and tilled land,
к, is assumed to be equal to 3.0, reflecting a relatively high degree of substitution.

3.3 Food security

Food security, FS, is represented in the model by the nested CES function:

(7)             fs=(βLL^σ-1)/^σ+β_ss (^σ-^ι)/^σ+βAA (^{σ-1)/ σ} )σ /(^σ-1),

where S is skilled labour and A is a CES aggregate of animal products, defined as:

(8)            A = XmM^(μ-1)/μ + XeE-^-1vμ + XcC^(μ-ц/μ)"'^μ-".

Here, M is meat products, E is egg and C is cow milk. βi > 0 (∀ i = L, S, A) and X_j > 0 (∀ j = M, E, C)
are distribution parameters. σand μ are the substitution elasticities in the first and second level of the
function, respectively.

The function says that a certain level of food security can be obtained if certain levels of
acreage, labour (i.e. agricultural skills) and animal production (i.e. animal material) are available.
Furthermore, animal production is split into meat, egg and milk. If we allow for positive substitution
elasticities, then the same level of food security can be provided by different combinations of the
various components. An important special case is when the substitution elasticities are set to 0. The
CES functions in (7)-(8) then collapse into Leontief types.

To calibrate the distribution parameters of this function, we need to know the cost share
(quantity and unit cost) of each of the components for a defined level of food security. In this respect,
we use the crisis menu in table 1, and normalize the level of food security that corresponds to the crisis
menu to FS = 1. The menu provides sufficient vitamins, minerals and proteins for the yearly
subsistence needs of the population. If we take into account that there exist ample quantities of sugar
through stock-piling, this menu also provides sufficient kcal for the population. Compared to normal
consumption the menu involves higher consumption of vegetable in proportion to animal products.

Note: Values are expressed in million kg per year.

Table 1: Crisis menu compared to actual consumption in base year 1998; (NOU, 1991, p. 142)

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