Y_e = x (a -bT + I_g + X_n + G) where b is the MPC. From this relationship, we determined that the "multiplier" for government expenditures is equal to = . Likewise, the "multiplier" for lump-sum taxes is equal to = . More generally, we see from the formula for Y_e that D Y_e = x (-bD T + D G). What happens if there is a balanced-budget change in government spending and taxes? Substituting D T = D G to find D Y_e, we see that D Y_e = x (-bD G + D G). Factoring out the common D G from the term in parentheses and rearranging, we find that D Y_e = x (1 -b) x D g = D G. That is, the change in equilibrium GDP from an equal change in government spending and taxes is equal to the change in spending. Alternatively, the multiplier for a balanced-budget change in G and T is equal to = x (1 -b) = 1.