So if they sell it back they do so before next fall?
So, let an, bn, cn and dn be the number of new, second-hand, third-hand and fourth-hand books sold during fall in year n.
a0 = 5 million; b0 = c0 = d0 = 0.
a1 = 5 million - b1; b1 = 0.9 a0; c1 = d1 = 0.
a2 = 5 million - b2 - c2; b2 = 0.9 a1; c2 = 0.8 b1; d2 = 0.
a3 = 5 million - b3 - c3 - d3; b3 = 0.9 a2; c3 = 0.8 b2; d3 = 0.6 c2.
Or eliminate b, c and d to get an in terms of an-1, an-2 and an-3.
Make a spreadsheet from either to see it stabilise at a60.
Homogenise the second as directed here Recurrence relation - Wikipedia, the free encyclopedia, and you can make a transition matrix,