Consider a model where the intensity of the job search is designated by the scalar formula_39, which can be interpreted as the amount of time and/or intensity of the effort devoted to search. Assume that the arrival rate of job offers is formula_40 and that the wage distribution is degenerated to a single wage formula_5. Denote formula_42 to be the cost arising from the search effort, with formula_43. Then the discounted utilities are given by:formula_44Therefore, the optimal search effort is such that the marginal cost of performing the search is equation to the marginal return:formula_45This implies that the optimal search effort increases as the difference between the expected utility of the job holder and the expected utility of the job seeker grows. In fact, this difference actually grows with the wage. To see this, take the difference of the two discounted utilities to find:formula_46Then differentiating with respect to formula_5 and rearranging gives us:formula_48where formula_49 is the optimal search effort. This implies that a wage increase drives up job search effort and, therefore, the job finding rate. Additionally, the unemployment rate formula_50 at equilibrium is given by:formula_51A hike in the wage, which increases the search effort and the job finding rate, decreases the unemployment rate. So it is possible that a hike in the minimum wage "may", by boosting the search effort of job seekers, boost employment. Taken in sum with the previous section, the minimum wage in labor markets with frictions can improve employment and decrease the unemployment rate when it is sufficiently low. However, a high minimum wage is detrimental to employment and increases the unemployment rate.