where pMt
is the current market price of button mushroom. Bt is cost of building for button mushroom,
Ct is other costs of button mushroom production, such as management fee, labor fee, etc., M is the yield
of button mushroom per year, Lt is the sum of the cost of managing the trees and land rent between
time t and t + 1, and r is the interest rate.
Conceptually, the decision (2) implies that the optimal decision on mushroom growing at time t
depends on both the market price of mushroom at time t and the mushroom growing history before
time t. The benefits of growing mushroom in year t consist of the revenue from mushroom sales, which
depends on the market price of mushroom, and the increase in the value of the stand at age t + 1. The
latter revenue equals W(t
+
1; df . . . dt−1, 1)
−
W(t
+
1; df . . . dt−1, 0). Growing mushrooms at
time t will, ceteris paribus, lead to a greater timber stock at time t + 1 and perhaps also faster growth
of the stand thereafter.