18. Gruber 20.1
The market demand for super-sticky glue is Q = 240 – 6P and the Market supply is Q = –60 + 4P.
a. Calculate the deadweight loss of a tax of $4 per Unit levied on producers of supersticky
Per unit Tax - a tax that is defined as a fixed amount for each unit of A good or service sold, such as cents per kilogram. It is thus proportional to The particular quantity of a product sold, regardless of its price.
Tax wedge - difference between before-tax and after-tax Wages. The tax wedge measures how much the government receives as a result of Taxing the labor force; A measure of the market inefficiency that is created When a tax is imposed on a product or service
Deadweight loss is Calculated as the area of a triangle, the height of which is the dollar amount Of the tax and the base of which is the change in quantity purchased resulting From the tax.
Without the tax, equilibrium is 240 – 6P = –60 + 4P, or 300 = 10P.
Equilibrium price is $30, So equilibrium quantity is
–60 + (4 × 30) = 120 – 60 = 60.
A tax levied on producers Changes the supply function to Q = –60 + 4(P – 4) because the Price the producers can keep from any sale is reduced by $4.
Recalculating Equilibrium, 240 – 6P = –60 + 4P – 16, or 316 = 10P.
Equilibrium price is $31.60, so equilibrium quantity is 240 – 6(31.60) = 50.4.
The change in quantity is 60 – 50.4 = 9.6, so the area of the deadweight triangle is:
½(9.6)(4) = 19.2