6.3. The multiplier-accelerator. (Samuelson, 1939.) Consider the following model of income determination. (1) Consumption depends on the previous period's income: C = a + bY-1. (2) The desired capital stock (or inventory stock) is proportional to the previous period's output: K; = CY-1. (3) Investment equals the difference between the desired capital stock and the stock inherited from the previous period: 11 = K - K-1 = K; - CY-2. (4) Government purchases are constant: Gz = G. (5) Y = (1 +11+ Gt. (a) Express Y, in terms of Y-1, Y-2, and the parameters of the model