Final answer:
The decrease in taxes with no change in government spending decreases public saving. Private saving may increase due to individuals saving the tax savings, though the Ricardian equivalence suggests an increase, but this effect is not always one-to-one and can differ based on various factors.
Step-by-step explanation:
In the context of the neoclassical model with fixed income, if taxes decrease without a change in government spending, it leads to an interesting dynamic concerning public and private saving. Public saving would decrease because the government is collecting less in taxes without reducing its expenditures, thus saving less. On the other side, private saving could either increase or decrease depending on whether the individual chooses to save the tax savings or spend it. However, according to the Ricardian equivalence, private saving changes to offset exactly any changes in the government budget, which could imply that private saving increases when taxes are decreased and government budget remains unchanged. Yet, the offset is not always one-to-one and depends on several factors including individual and business responses to the tax change.
The concept of Ricardian equivalence suggests that when the government deficit (G - T) increases, private saving (S) should increase correspondingly. But, in actual scenarios, this effect varies and is not always a direct offset, highlighting that economic behaviors and responses to policy can be quite complex and varying.