Clear[A,  P,  Initial]
A  =  {{0.80,  0.60},  {0.20,  0.40}}
Initial  =  {{2500},  {2500}}
P[n_]  :=  
      If[n  ==  1,  Initial,  A  .  P[n  -  1]]

P[10][[1, 1]]

P[20]

ListPlot[
Table[{P[n][[1,  1]],  P[
              n][[2,  1]]},  {n, 1,  10}],  
      PlotRange  ->  {{0,  5000},  {0,  
            5000}}, 
PlotStyle  ->  
        PointSize[0.015]]

TableForm[
      Table[{P[n][[1,  1]],  P[n][[2,  1]]},  {n, 1,  
          10}]]

Eigensystem[A]