When calculating the incidence on producers and consumers using a demand and supply curve is dead weight loss a part of the incidence? I know that for example the producer's incidence is a rectangle with a height of the old supply curve price at the new equilibrium quantity minus the new equilibrium price. What I'm not sure about is the width of the rectangle. I know it should start at the y-axis, but I'm unsure of where to stop. The original equilibrium quantity? Or the new equilibrium quantity? If I were to extend the rectangle to the new equilibrium quantity then dead weight loss is included. Is this correct?
According to standard textbooks on public finance (e.g., Tresch, Public Finance, 3rd ed., p. 272) the tax incidence includes the deadweight loss. This is because we are interested in the burden of the tax on consumers and producers and the deadweight loss can be a large part of this. (However, see https://en.wikipedia.org/wiki/Tax_incidence which does not include the deadweight loss.)
There are some difficulties, however. First, the deadweight loss is only a meaningful concept in partial equilibrium settings. The incidence as you described it cannot be used in general equilibrium settings as supply and demand curves shift with the introduction of the tax. Thus, the more common approach in general equilibrium is to determine the welfare loss of different individuals.