Figure A: Conditions Before a Minimum Wage Increase
Assume that initially the wage-setting (WS0) and vacancy-supply (VS0) curves intersect at point A determining both the equilibrium market wage w* and equilibrium labor market tightness, θ*. The job creation curve (whose slope is θ*) intersects our Beveridge curve at point A1 which determines that our equilibrium vacancy rate is V* and equilibrium unemployment rate is U*. These are represented graphically in Figure A.
Figure B: After a Mandated Increase in the Minimum Wage
Then out of the blue the government introduces a minimum wage w1 that exceeds the market wage w*.
The wage-setting curve now has a "floor" and this is represented by its vertical portion at the minimum wage. As higher wages cut into business profits, firms open fewer vacancies. We move from point A to B in Figure B. Since labor market tightness has now decreased from θ* to θ1, the job creation curve (with its new slope θ1) rotates downward. The rotation of the job creation curve from JC0 to JC1 increases the unemployment rate from U* to U1. We moved from our original position at A1 to B1 and the job openings rate has decreased from V* to V1. In this situation a binding minimum wage raises both wages and unemployment.
Incorporating Workers Job-Search EffortLet's assume now that workers can choose the intensity with which they search for a job- how much time they spend searching the internet for a job, how many job applications they fill out, ect. Under this assumption, a higher wage has two simultaneously opposing effects:
a) A higher expected wage increases the payoff for workers when they finally do find a job. A worker with this in mind will be motivated to look harder and "more intensely." This increase in work intensity would shift our Beveridge curve inwards.
b) It weakens firms' incentives to create jobs because it cuts into their profit and thus making workers less likely to succeed and so depressing their search efforts. Less intense search effort by the firm would correspond to an outward shift of the Beveridge curve.
The net effect of these countering forces depends on where the wage stood before the increase. To visualize this, consider two extreme cases where wages are initially really high or really low, depending on the extent of the workers bargaining power. First, suppose that workers are powerless and have no bargaining power, firms post wages unilaterally, and workers search until they find an acceptable wage offer. Since employers appropriate the entire surplus from their relationship with labor, unemployed people have very little incentive to search actively for a job and the result is high unemployment. Now consider the other extreme, where workers have all the bargaining power to set wages. Firms make no profit from hiring more workers. Since opening and advertising job vacancies is costly, firms rather not do so, and unemployment increases.
Figure C: Increased Search Intensity by Workers
Markets that tend to be dominated by employers or equivalently where workers' bargaining power is pretty low, a compulsory increase in the wage can lead to higher search intensity and higher employment. If the market wage is low, then a binding minimum wage can make employment more attractive to workers which strengthens their search efforts and reduces unemployment. Figure C graphs this result. The increase in workers search intensity would shift the Beveridge curve inward from BC0 to BC1 and the unemployment rate would go from U1 to U2, before the shift we were at point B1 and after the shift we settle at point C1. In this respect the search model's results are consistent with the monopsony model as it explains how, in theory, a minimum wage can reduce unemployment. If the the market wage is high, a binding minimum wage may discourage workers from looking for a job because there are fewer vacancies. It can also be shown that worker's search effort and social welfare move together. The wage that maximizes search effort also maximizes social welfare. If the minimum wage is small enough, it can improve labor market conditions and increase social welfare.
Another interesting result of this model is that the minimum level of unemployment occurs when the market wage is below the one maximizes workers search effort. This means that a minimum wage can make workers better off even if it increases unemployment.
Adding Labor Force Participation
If we focus our attention on the workers' decision to participate in the labor force we can use logic that mirrors that from our search intensity example. If the market wage is very low because workers have little bargaining power, they might decide to not even look for a job at all. They have no incentive to enter the market because non market activities, like home production and leisure, are more valuable than working and thus employment is low. Conversely if the market wage is very high, firms are not hiring, unemployment durations are long, and workers stay out of the labor force. In general, employment is a hump-shaped function of the wage. However, unlike the model with workers' search effort, unemployment always decreases with the wage.
Although participation is weaker when wages are low, firms still create jobs because their profits are high. This has the effect of swelling the number of vacancies relative to the number of job seekers, making it more probable that they will find employment. If the market wage is too low and workers lack bargaining power, the introduction of a binding minimum wage strengthens labor force participation even though the duration of unemployment increases. In contrast, if the market wage is high, a minimum wage reduces the supply of vacancies and increases unemployment duration, which has the balancing effect of discouraging workers from entering the labor force.