Search intensity, wage dispersion and the minimum wage

We study a labor market where employers post wages and workers simultaneously choose the number of applications they send out. Firms offer the job to a worker at random; workers with multiple offers pick the best one. If the application costs are sufficiently low, workers contact multiple firms and there is wage dispersion in equilibrium. The number of applications workers send out is excessive from a welfare perspective due to a rent seeking externality. A mandatory minimum wage increases the mean and reduces the variance of the wage distribution. The net effect on welfare is ambiguous.