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

The “self-sufficiency-principle” would imply production in A at a cost corresponding to the line M’M’
(with a slope equal to - NCH2 γ2 /NCCH 1 γ₁ ). The Guldbrandsen-Lindbeckprinciple says that in
normal years the most efficient way to guarantee the provision of L^M is to produce in the point marked
as B, corresponding to the dotted line M’’M’’ going through this point.

Assume that we choose a level of food security equal to λ¹, 0<λ¹<1, which corresponds to a
level of land use equal to L¹< L^M. Given our assumptions, the minimal governmental cost, NC, for
providing such a level of food security equals:

(4)           NC=NC(L¹) =[NCH2]L¹.

For complete food security the net cost is NC^M=NC(L^M).

2.2 Landscape preservation

An additional argument for agricultural support is the amenity value of the landscape. This is
grounded in the value of an open and varied landscape, sustained by agricultural production. We
follow Lopez (1994) and assume the following willingness to pay function for landscape preservation:

(5)          WTP = E[LP]^ε

where E (>0) is a constant, LP is an index of amenity enhancing agricultural land which we in this
section assume is equal to the use of land for agricultural production, L. ε reflects the marginal
willingness to pay for landscape preservation and since we assume ε<1, the function in (5) conforms to
the standard assumption of being increasing and concave in LP.

If the amenity value of the landscape is the only external effect, the optimality condition is that
agricultural production should expand as long as the marginal willingness to pay exceeds net cost per
hectare, i.e.

NCH₂ = MWTP ≡ εEL^ε-1.

Figure 2 illustrates the optimal solution. The necessary rate of subsidy is marked as NCH2. Since the
available production techniques are Leontief, NCH2 is a straight horizontal line. The marginal
willingness to pay for landscape preservation, MWTP, is given by the convex curve. Marginal
willingness to pay is large when the agricultural activity is low, and diminishes with increased
agricultural activity. The optimal land use equals L^LP.

2.3 Cost complementarities

Assume now that in addition to landscape preservation, complete food security shall be provided. This
means that L^M must be used in production of agricultural commodities. L^M is marked into figure 2,
where it is assumed that L^M >L^LP. In this case food security dominates landscape preservation, and it is
not optimal to use more land than L^M. The reason is that MWTP is less than the per hectare cost in
production in L^M.

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