To illustrate the nature of the solution, we now make the simplifying assumptions that there are only two sectors (K =2), which we call sector A and sector B, and that the shocks to each sector (εA and εB) are uncorrelated. We also assume that αA and αB are both nonnegative. Appendix 2 derives the solution to this special case. The conclusion is the following equation for the optimal weight on sector A: