Final answer:
The deadweight loss associated with a $1 per unit tax on travel mugs will be $1.23.
Step-by-step explanation:
The deadweight loss associated with a $1 per unit tax can be calculated by finding the difference between the quantity of mugs exchanged before and after the tax is imposed. To do this, we need to compare the quantities at the original equilibrium price and the new price after the tax. The original equilibrium price can be found by setting the demand and supply equations equal to each other:
50 - 0.5Q = 0.33Q
Solving for Q gives Q = 19.23. The original equilibrium price can be found by substituting this value into either the demand or supply equation.
Plugging Q = 19.23 in the demand equation gives P = 40.77. After the tax is imposed, the new price for buyers would be P + tax = 40.77 + 1 = $41.77.
The new price for sellers would be P - tax = 40.77 - 1 = $39.77.
The new equilibrium quantity can be found by setting the new demand and supply equations equal to each other:
50 - 0.5Q = 39.77
Solving for Q gives Q = 20.46. The deadweight loss is the difference between the original equilibrium quantity and the new equilibrium quantity, which is 19.23 - 20.46 = 1.23.
Since the tax is $1 per unit, the deadweight loss associated with the tax will be $1.23.