Revision history [back]
 | 1 | initial version |
By a couple of substitutions: $$C_t = c(C_{t-1} + I_0 + \gamma(C_{t-1} - C_{t-2})) + C_0$$ $$=c(1+\gamma)C_{t-1} - c\gamma C_{t-2} + cI_0 + C_0,$$ which then translation into that of $Y$: $$Y_t = c(1+\gamma)Y_{t-1} - c\gamma Y_{t-2} + C_0+I_0.$$ Is this what you want?
| | 2 | No.2 Revision |
By a couple of substitutions:
$$C_t = c(C_{t-1} + I_0 + \gamma(C_{t-1} - C_{t-2})) + C_0$$
$$=c(1+\gamma)C_{t-1} - c\gamma C_{t-2} + cI_0 + C_0,$$
which then translation translates into that of $Y$:
$$Y_t = c(1+\gamma)Y_{t-1} - c\gamma Y_{t-2} + C_0+I_0.$$
Is this what you want?
| | 3 | No.3 Revision |
By a couple of substitutions:
$$C_t = c(C_{t-1} + I_0 + \gamma(C_{t-1} - C_{t-2})) + C_0$$
$$=c(1+\gamma)C_{t-1} - c\gamma C_{t-2} + cI_0 + C_0,$$
which then translates into that of for $Y$:
$$Y_t = c(1+\gamma)Y_{t-1} - c\gamma Y_{t-2} + C_0+I_0.$$
Is this what you want?
