A decrease in the cost of production for a good will always result in a leftward shift of the supply curve.

A drop in production costs makes it cheaper to make each unit of the good, so producers can supply more at every price level. This increased ability to produce shifts the supply curve to the right, not left. The logic is that higher cost would restrict supply, causing a leftward shift, but a lower cost expands supply. For example, if a new machine reduces the cost of producing widgets, a farmer can produce more widgets at the same price, shifting supply to the right. Thus the statement is incorrect.