GAMS — The Solver Manuals - Available Software

PATH 4.6 499
Note that the variable y M represents “maintenance labour” and g represents the amount of “maintained land”
produced, an intermediate good. The process of generating maintained land uses a Leontieff production function,
namely
min(λ r y r , λ M y M ) ≥ g.
Here λ M = 1 ɛ , ɛ small, corresponds to small amounts of maintenance labour, while λ 1
r =
1−β c−ɛ
is chosen to
calibrate the model correctly. A simple calculus exercise then generates appropriate demand and cost expressions.
The resulting complementarity problem comprises (28.14), (28.17), (28.18) and
0 ≤ w L ⊥ e L ≥ ∑ r,c
0 ≤ w r ⊥ a r ≥ ∑ c
( ) 1−βc
γ c,r = wβc L wL ɛ + w r (1 − β c − ɛ)
φ c 1 − β c
(
βc ɛ(1 − β c )
x c,r γ c,r +
w L w L ɛ + w r (1 − β c − ɛ)
x c,r γ c,r (1 − β c )(1 − β c − ɛ)
w L ɛ + w r (1 − β c − ɛ)
After making the appropriate modifications to the model file, PATH 4.x solved the problem on defaults without
any difficulties. All indicators showed the problem and solution found to be well-posed.
)