Explain why the tax multiplier is different from the government purchases multiplier, in both sign and relative magnitude

What will be an ideal response?

A dollar change in government purchases has the opposite impact of a dollar change in taxes. For example, an increase in government purchases increases income, spending, and GDP in the economy. In contrast, an increase in taxes lowers income, spending, and GDP in the economy. As a result, the government purchases multiplier is positive, and the tax multiplier is negative.
A dollar change in government purchases will have a larger affect on GDP as compared to a dollar change in the tax multiplier. A change in government purchases affects overall spending directly. The first round GDP change in the multiplier process will be equal to this change in spending. In contrast, a change in taxes affects income first and then spending. For example, a tax cut will increase income, but not all of that income will be spent; some of it is saved. The fraction of income that is spent is the MPC times the income change. The first round GDP change in the multiplier process will be equal to this smaller change in spending. Hence, a decrease in taxes will have a smaller impact on equilibrium than would an increase in government purchases.