After one step, all the particles each decide its next state, according to the transition probabilities. 2.5% of those in Bull state would change to Recession, while 90% of them would remain in Bull.

0.025 U + 0.05 E + 0.5 R = R ..... one of 3 equations. 3 equations and 3 unknowns. U is found to be 6250, E = 3125 and R = 625

But why the " ... = R" part? Answer is the steady state. After one step, if 0.025 U + 0.05 E + 0.5 R is 0.000001% more than R, then this is not steady state and the R population will increase at every step and it would capture all 10000 particles.

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