Why do we have a min wage when economist agree that it causes unemployment?

A firm will higher up to the point where MRP (marginal revenue product...also called the demand for labor) = the wage. MRP continuously decreases. For every factor of production added to a production process, it's revenue generating capacity decreases, in general. In some cases, this does not happen at the beginning. However, there's no denying diminishing marginal product for factors of production. A min wage is a price floor...and when binding (i.e, that is when set above what the market determined) a surplus is created, the quantity of labor supplied > the quantity of labor demanded. Price controls, and this is what the min wage is, cause surplus and shortages. In effect, prices induce the country to utilize its scarce resources less efficiently than can be. This situation is called government failure. Government failure is a situation in which the government intervenes in the market mechanism and creates sub-optimal outcomes. I.e., outcomes that are less efficient than what the market would create.