User Cost Dissipation Under Open Access
We can illustrate the situation of absence of scarcity capture using a simple example adapted from Baland and Platteau (1996). Suppose we have a forest that is an open access, and assume the entire stock of timber is given by S. Let us consider an input called man-with-a-saw, n. The total amount extracted of timber Y depends on the amount of n employed represented by the function F(n). Using as an example a quadratic production function, 
, and normalising the price of timber to one, we can characterise the equilibrium situation. Under open access, the average product Y/n, is equal to w, the price of the input.51Therefore the open access situation is characterised by:
The rent from this activity is 
. Using the previous result in the rent equation, we can observe that under open access the rent is completely dissipated,
.
If the extraction activity was privately owned, the necessary condition for profit maximization would be the equality between the price of the input, w, and the marginal product (not the average product as in the open access situation). This equilibrium condition will lead to:
Substituting this condition in the rent equation, it can be noted that we will have a positive rent:
.
