Consider a simple economy with search and unemployment. The matching function is given by

M = em(Q, A) = eQ^2/5A^3/5,

where the government supplied employment insurance is b = 0.5, the worker productivity is z = 1.3, firms' cost of posting a vacancy is k = 0.1, the matching efficiency parameter is e = 0.4191 and the worker's bargaining power factor is a = 0.5. The working age population is N = 1000 and we denote by Q the labour force. As standard in DMP model, we assume that consumers make their job search decisions based on the current level of the expected payoff from the job search?. Furthermore, we assume that the relationship between Q and?, which can be derived by maximizing the consumer's utility, is given by:

Q= N (