RDP 2016-07: The Efficiency of Central Clearing: A Segmented Markets Approach Appendix B: Solving the Constrained-efficient Problem

As described in Section 3.6.2, the planner maximises all traders' utility, taking into account all traders' budget constraints, and the CCP's budget constraint. The Lagrangian for the problem is:

This equation is maximised by choice of and for all m ϵ [0,1].

The first-order conditions for market m give two pricing equations, one for the long trader and one for the short trader:

The solution method for finding the stationary equilibrium is identical to that used for the decentralised equilibrium.