Equilibrium search model with endogenous growth rate of human capital

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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.