Question

3. Suppose we had an economy summarized by the following equations: Expenditure equation: Y = C +1:+G + NX, Closed economy: NX: = 0 Consumption equation: C = Co + mpc * Y:-1 Investment equation: 1: = 10 +a (C-C-1) Government spending: G = G Where the variables and parameters of the model are as follows: Y,: output at timet Y: natural level of output Ce: consumption at timet Co: exogenous consumption (occurs every period) 1: investment at timet 10: exogenous investment (occurs every period) a: sensitivity of investment to consumption changes G: government spending at timet G: exogenous government spending occurs every period) NX,: net exports What is the natural level of output of this economy in which Y, = Y:-1 = Y-2 = Y? Please provide your answer in terms of Colo G, and mpc. You don't need to provide an exact numerical value as we are not setting the values of these parameters. (10 points)

Answer 1

Y eqt Itt G q + NXt where; NX=0 CE Co to mpc yeri It lota (et-Ca-1) Ge= From the consumption function et we can find eta, .. Ce-i = Cot mpe.Ye-z Thus we have; Ye Cotmpe Ye-, & Iota (Cotmpe-7 - - Co-mbe. Ye-2) + G +0. It is given that Y+= Ye_p? Ye-g? Y >> T- Cot mbe. + Iot a(mpc. 7 - mbe 7)+G- a) 7 - Cot mbe. 7+ 1+ a) 7 (1-mpe) = Cottot Ğ s) To Let Iot G To-mpc) The natural level of output for this economy is; - % Cot Io + G Trumpe)