This article studies an equilibrium search problem when jobs provided by firms can be either unskilled or skilled and when workers differing in their education level can be either low-educated or high-educated. The structure proportion of jobs affects the equilibrium which indicates a threshold that can distinguish whether the equilibrium is separating or cross-skill. In addition, the cross-skill equilibrium solution implies the high-educated workers are more likely to obtain higher pay rates than the low-educated workers with same tenure. Moreover, the profits of the firms decrease as the number of the low-educated workers increases. The most interesting conclusion is that the growth rate of the human capital is an endogenous variable which is different from previous work.
dynamic programming, contracts, job search, market equilibrium, human capital
49L20, 90C39, 91B40, 97M40