13
In the spirit of traditional public finance literature we assume that the policy maker
credibly commits to a future policy (see e.g. Atkinson and Stiglitz 1980). Technically
this means that before any private harvest decisions are made the Forest Service
announces its harvest policy and thereby acts as a Stackelberg dominant player by
taking into account the response of private forest owners when choosing the public
rotation age.13 We start by analyzing the case when there is free access not only to
public but also to private forests.
4.1. Free access to private forests
The government chooses the optimal rotation age τ* so as to maximize the social
welfare function when citizens have free access to both public and private forests. The
quasi-linear social welfare function consists now of the present value of the indirect
utility function of the representative forest owner ( W * (τ, p, r, c)),14 the present value
of the utility of recreators from private forests ((n - 1)E ), the present value of the
utility of all citizens (n) from public forests (nEg ), and of the net present value of the
public harvest revenue over an infinite series of rotations (V g ).
In formulating the social welfare maximization problem we have to take into account
that the private rotation age T H may depend on the public rotation age, such that
T H = T H (τ,...) . Hence public harvesting will affect social welfare both directly and
indirectly by changing private harvesting behavior. While only the direct effect
matters to the representative forest owner because he has optimized with respect to T,
both the direct and indirect effects are relevant for the other agents. Therefore, the
social welfare function can be written as
13 If government cannot enter into binding commitments regarding its future harvesting
policy, then it re-optimizes at the beginning of each period. The representative landowner
decides about harvesting given his (or her) expectations concerning government policy.
Government in turn sets its harvesting policy, taking the behavior of the landowner as given.
Equilibrium in this non-commitment environment is the Nash equilibrium (see. e.g. Persson
and Tabellini (1990) for an introduction).
14 The indirect utility function W*(τ,p,r,c) can be obtained by substituting the optimal
private rotation age T H (τ, p, r, c) , implicitly defined by equation [6], for T in equation [5].
Here we are interested in the effect of τ on the components of social welfare defined in
equation [11].