The demand and supply of movie tickets are given by Q^D = 30 - 3P and Q^S = 4P - 19, where P is the price per ticket and Q is in thousands of tickets. If the government places a $1 tax on each ticket, the prices that consumers pay with and without the tax are _____ and _____, respectively. A) $8; $7 B) $7.57; $7 C) $7.50; $6.80 D) $4.30; $3.80

Question

Quizplus · Accepted Answer

Before the tax:
Demand: QS1U1P1DS1S1P0 = 30 - 3P
Supply: QS1U1P1SS1S1P0 = 4P - 19

Equilibrium price and quantity:
30 - 3P = 4P - 19
7P = 49
P = 7

Quantity: QS1U1P1DS1S1P0 = QS1U1P1SS1S1P0 = 30 - 3(7) = 9

After the tax:
Demand: QS1U1P1DS1S1P1 = 30 - 3(P+1) = 27 - 3P
Supply: QS1U1P1SS1S1P1 = 4P - 19

Equilibrium price and quantity:
27 - 3P = 4P - 20
7P = 47
P = 6.71

Quantity: QS1U1P1DS1S1P1 = QS1U1P1SS1S1P1 = 30 - 3(6.71) = 10.87

Without the tax, consumers pay $7 per ticket. With the tax, the price that consumers pay is the equilibrium price plus the tax, which is $6.71 + $1 = $7.71. Therefore, the answer is B.

The Demand and Supply of Movie Tickets Are Given by QD

The Demand and Supply of Movie Tickets Are Given by Q^D