Exercise 10.7 Consider a corporate firm that is influenced by an economic condition, and suppose that there are two states, good (state 1) and bad

(state 2), for the condition. If the state is good, the hazard rate for default of the firm is λ, while it is given by μ, μ > λ, when the state is bad. Suppose that the economic condition is currently good, and it evolves according to a homogeneous Markov chain with transition probabilities p11 = a and p22 = b, where 0 <

a, b < 1. Determine the survival probability of the firm. Hint: The state probabilities at time t of the two-state Markov chain can be obtained in closed form by using the spectral decomposition of the transition matrix.