Final answer:
A reduction in the soda tax would lead to an increase in the supply of sodas, a decrease in the equilibrium price, and an increase in the equilibrium quantity, represented by a rightward shift in the supply curve.
Step-by-step explanation:
The initial statement that when a sales tax of 20¢ per soda is imposed the supply curve for soda shifts down by precisely 20¢ per soda is false. Typically, a tax imposed on a good like soda, collected from sellers, causes the supply curve to shift up or to the left in a supply-demand diagram, since the tax is a cost to producers.
In a scenario where there is a soda tax aimed to curb obesity, a reduction in the soda tax should increase the supply of sodas. This is because the tax reduction decreases the cost of producing and selling soda. Graphically, the supply curve would shift to the right, signaling an increase in quantity supplied at every price level. The equilibrium price would generally fall, and the equilibrium quantity would rise.