Suppose that consumption at the aggregate level follows the following expression: C_t=20+.6Y_t-1, the investment is given by I_t=20+.1Y_t and the income is determined by the expression Y_t= C_t+I_t.

_i) use the expressions for consumption and investment in the expression that determines income to find an equation in first differences

ii) Find the solution to the equation

iii) Say whether as time progresses to infinity the income converges to a constant. If convergent, what is the constant?