In the example in the chapter, the balanced budget multiplier was equal to 1.0. Prove that this must always be the case in our model, regardless of the value of the MPC or the amount by which G and T change (as long as their changes are equal and in the same direction).
Follow the following steps in your proof:
(1) Suppose that G rises by $X. Write a general expression for the change this will cause in equilibrium GDP, for any value of the MPC.
(2) Suppose that T rises by $X. Write a general expression for the change this will cause in equilibrium GDP, for any value of the MPC.
(Don’t forget to use the proper sign.)
(3) Add the two changes in GDP together. (Your expressions should have a common denominator, so you can add the numerators.)
(4) Divide the change in GDP by the change in G (or T ) that caused GDP to change. What value do you get?