The theory of optimal delegation with an application to tariff caps (Q2864826)

The authors consider a general representation of the delegation problem -- with and without money burning -- and provide conditions under which interval delegation is its optimal solution. They apply their results for trade agreements among privately informed governments, and they establish -- for both perfect and monopolistic competition settings -- conditions under which an optimal agreement takes the form of a tariff cap.NEWLINENEWLINEIn the authors' setting, there is a principal and an agent. The welfare functions of the principal and the agent are \(w(\gamma,\pi) - t\) and \(\gamma\pi +b(\pi) - t\), where \(\pi\) represents an action or allocation, \(\gamma\) represents a state or shock that is private information to the agent, and the value of \(t\) represents an action that reduces everyone's utility, i.e.\ money burning. It is assumed that \(\gamma\) has a continuous distribution \(F\) over a compact interval \(\Gamma = [g_{0},g_{1}]\), and \(\pi\) is chosen from an interval \(\Pi \subseteq \mathbb R\) with nonempty interior. The \textit{delegation problem} is to find \(p : \Gamma \rightarrow \Pi\) and \(\tau : \Gamma \rightarrow \mathbb R\) which maximize the principal's welfare function: NEWLINE\[NEWLINE \max \int_{\Gamma}(w(\gamma,p(\gamma)) - \tau(\gamma))d F(\gamma)NEWLINE\]NEWLINE subject to \(\displaystyle \gamma \in \arg \max _{\tilde \gamma \in \Gamma} \{\tilde \gamma p(\tilde \gamma) + b(p(\tilde \gamma)) - \tau(\tilde \gamma)\}\) and \(\tau(\gamma) \geq 0\) for all \(\gamma \in \Gamma\). Money burning may be excluded by imposing the additional constraint \(\tau(\gamma) = 0\) for all \(\gamma \in \Gamma\).NEWLINENEWLINEA \((p,\tau)\) is an \textit{interval allocation with bounds \(a,b\)} if \(a,b \in \Gamma\), \(a<b\), \(\tau(\gamma) = 0\) for all \(\gamma \in \Gamma\) and with \(\pi_{f}: \Gamma \rightarrow \Pi\) denoting the agent's preferred action, we have \(p(\gamma) = \pi_{f}(a)\) if \(\gamma \in [g_{0},a]\); \(p(\gamma) = \pi_{f}(\gamma)\) if \(\gamma \in (a,b)\); \(p(\gamma) = \pi_{f}(b)\) if \(\gamma \in [b,g_{1}]\). An interval allocation is a \textit{cap} if \(a = g_{0}\).NEWLINENEWLINEUnder relatively mild differentiability and convexity assumptions for \(w\) and \(b\), the authors characterize optimal interval allocations within the class of interval allocations; give sufficient conditions for an interval allocation to solve the delegation problem, with or without money burning; show that these sufficient conditions are also necessary if \(w\) is of special form; and give sufficient conditions for a cap to solve the delegation problem.NEWLINENEWLINEThe authors discuss two main applications of their results for trade policy. In the first one, they study optimal trade agreements under perfect competition: there are two countries which trade a single good with competitive supply functions in both countries. Concrete specifications for supply and welfare functions are given which imply that the optimal trade agreement takes the form of a tariff cap; moreover, these specifications allow for binding overhang. In the second application monopolistic competition is considered, and the optimality of tariff caps is established in a concrete setting. The authors also show that the derived optimality of tariff caps still holds if their assumption of ``no contingent transfer of resources'' is relaxed but such transfers remain ``sufficiently inefficient''.NEWLINENEWLINEFinally the authors outline how several results in the delegation literature, e.g.\ some in [\textit{R. Alonso} and \textit{N. Matouschek}, Rev. Econ. Stud. 75, No. 1, 259--293 (2008; Zbl 1141.91354)] or [\textit{M. Amador} et al., Econometrica 74, No. 2, 365--396 (2006; Zbl 1145.91367)], follow from their results.