4. (Keynesian Economics) Consider the simple Keynesian model below. Equation 1 is an identity, Equation 2 is a behavioral equation for consumption. Equation 3 is the govern- ment budget constraint which requires budget balance. The government chooses government spending G and taxes T each model period. Exogenous model parameters: (i) parameters governing consumption are a = 10 and b = 0.8 and (ii) investment It at time t is (I1, I2, I3, I4, I5) = (5, 5, 2, 5, 5) over model periods 1 to 5. 1. C+I+G=Y 2. C=a+b(YT) 3. G=T (a) If the government wants to engineer a constant level Y of GDP equal to 100 in each model periods t = 1, ..., 5 taking investment as exogenous, then nd the path of government spending and taxes in theses ve periods that makes Yt = 100 in each model period. (b) In the model calculate the balanced budget government spending multi- plier