I'm looking for a reference in the literature on monopolistic screening/mechanism design, where there are multiple allocative variables and these interact in the agent's utility function.
For example, suppose a principal is a buyer of labour and wants the agent (an employee) to produce two goods, $x_1$ and $x_2$. The principal's payoff is given by $R(x_1, x_2) - t(x_1, x_2)$ where $t$ is a quasi-linear transfer. Let $\theta$ denote the private information (e.g the employee's marginal cost). Then suppose the agent's utility function takes the form:
$$ u(\theta) = t(x_1, x_2) - C(\theta, x_1, x_2) $$
where crucially, we assume $C_{x_1, x_2} \neq 0$ (subscripts denote derivatives). For example, we might assume that as the agent is asked to produce more of $x_1$, their marginal cost of producing $x_2$ increases.
Does anyone have a good paper/textbook reference for something like this? Thanks!
