Question

1. The market demand for butter beer is Q = 480 − 4P, and the government intends to place a $3 sales tax per butter beer purchased. Calculate the deadweight loss of this tax when:

a. Supply of butter beer is Q = 300.

b. Supply of butter beer is Q = 8P.

c. Explain why the deadweight loss calculations differ between (a) and (b).

Answer 1

a) Q is fixed at 300. Then tax will not effect the quantity because it is perfectly inelastic for any price.

We then have QD = QS or 480 - 4P = 300. P = $45. Price received by sellers is unchanged at $45. Price paid by buyers is 45 + 3 = $48. Entire tax is paid by consumers.

At P = 48, QD = 480 - 4*48 = 288 units

DWL = 0.5*tax rate*(300 - 288) or 0.5*3*12 = $18.

b) Before tax QD = QS gives 480 - 4P = 8P or P = 480/12 = 40 and Q = 40*8 = 320 units

Supply is decreased to Q = 8(P - 3). This implies at new equilibrium we have QD = QS

480 - 4P = 8P - 24

P = 504/12 = $42 (paid by buyers)

Q = 480 - 4*42 = 312 units

DWL = 0.5*3*(320 - 312) = $12

c) The difference arises because when demand or supply is perfectly inelastic or elastic, tax burden increases. This raises the deadweight loss. When demand or supply are fairly elastic, deadweight loss is smaller.