Question

28. Suppose, yt = -3yt-1 + 8 and y0 = 16, Solve for yt.

Comment on the time path.

you must show how you Check your answer

Answer 1

yt = -3yt-1 + 8

=-3*(-3yt-2 + 8)+8

= 3^2*yt-2+8(1-3)

=3^2*(-3yt-3 + 8)+8(1-3)

=(-1)^3*3^3*yt-3+8(1-3+3^2)

........

= (-1)^t*3^t*y0+8(1-3+3^2-...+(-1)^t-1*3)

= (-1)^t*16*3^t+8(1-(-3)^t)/(1-3)

=(-1)^t*16*3^t+4((-3)^t-1)

So, if t is even, yt=16*3^t+4*3^t-4 = 20*3^t-4

So, if t is odd, yt=-16*3^t-4*3^t-4 = -20*3^t-4

The time path will be a fluctuating ever increaing(in magnitude) number. Thus, the absolute value of the number will increase at an exponential rate but the value will fluctuate between positve and negative.