Transition rates
Production opportunities arrive to the unemployed at the rate a as a Poisson process. If undertaken, each production opportunity yields a unit of output with cost c. Only production with cost c' or less will be undertaken.
The transition rate from k to k + 1 is given by (n - k)aG(c*), where c' is the reservation cost in the sense that only production with cost c ≤ c' is undertaken. Since this reservation cost is a choice variable and depends on k/n, we write it as c' (k/n), or as c+(k) for short, in the following.For an employed agent, trading opportunities arrive as a Poisson process at the rate β(k/n). His probability for being one of the random pair is 1 - Ck-1j2/Ck>2 = 2/k. We define the arrival rate of trading opportunity for an agent to be b(k/n) := (2/k)β(k/n). While an employed agent waits for a trading partner, the probability is [Ck-1j2/Ck>2]β = [(k - 2)√2]β that a pair involving other employed agents trade, thus decreasing k to k - 2. In aggregate, then, the transition rate from state k to k - 2 is given by {k/2)b(k/n).
9.3