Random sampling within the framework of a multivariate principal-agent approach

In this paper, we analyze a specific class of principal-agent models which seems to be sufficiently general to cover applications in environmental economics with upstream-downstream problems as an example. In our basic model, the observation outcome is ann-dimensional random vectorx and only the first and second moments ofx are common knowledge. We study the effects of random sampling in the presence of costly signals. For this purpose, we assume that the principal and the agent use a simple statistical procedure, i.e. their contract will be based on the mean of a random sample with sampling costs dependent on the sample size. It is shown that there exists an optimal sample size. We investigate the relationship between the optimal sample size, the marginal sampling costs, and the agent's risk aversion.