Final answer:
To calculate the deadweight loss of a tax in the automotive oil market, we need to evaluate the changes in supply and demand curves, but the question does not provide enough information to quantify the deadweight loss. More data, such as supply and demand elasticities, are required.
Step-by-step explanation:
The deadweight loss from a tax on automotive oil can be understood by analyzing how the tax affects the supply and demand curves in the market. The imposition of a $1.50 tax per liter shifts the supply curve vertically upwards by the amount of the tax. This results in a new equilibrium where the quantity of automotive oil sold is reduced because the tax makes it more expensive for consumers and less profitable for producers. The deadweight loss is the loss of economic efficiency when the equilibrium outcome is not achieved due to the tax. It is represented graphically by the area between the supply and demand curves over the range of quantities by which the tax reduces the quantity traded in the market. To calculate the actual deadweight loss, we need more information such as the elasticities of supply and demand or the specific supply and demand schedules.