Zero Inventory (ZI) is a new and powerful concept to improve production efficiency. Underpinning ZI is set up reduction and this paper examines what eventuates when set up costs are cut. The folklore is that set up reduction lowers inventory and costs. We obtain results contrary to that. Reducing set up costs need not reduce inventory, for example. Likewise lowering set up costs need not necessarily lower total production and inventory costs. Furthermore, most investments produce marginally decreasing returns. Set up cost reduction prompts the opposite; it produces marginally increasing (not decreasing) returns. A parametric algorithm that calculates the benefit of set up cost reduction is provided. Most presentations of ZI have been descriptive with very few mathematical models of it yet untaken. By modeling certain ZI concepts mathematically, we scrutinize their validity and sometimes invalidity.