Suppose that the market for product X is characterized by a typical, downward-sloping, linear demand curve and a typical, upward-sloping, linear supply curve. If a $2 tax per unit results in a deadweight loss of $200, how large would be the deadweight loss from a $4 tax per unit?

The deadweight loss will be $800 because the deadweight loss rises by the square of the tax increase. Thus, if the tax doubles, the deadweight loss quadruples.