Question

Suppose that the demand for a concert is represented by the following equation, where P is the price of concert tickets and QD is the quantity of tickets demanded:

QD = 2200 –20P
The supply of tickets is represented by the equation where P is the price of the tickets and QS is the quantity of tickets supplied:
QS = –500 +75P
Find the equilibrium price and quantity of tickets sold.

Answer 1

The equilibrium price for the concert tickets is approximately $28.42, and the equilibrium quantity is approximately 1631 tickets, determined by setting the demand equation equal to the supply equation and solving for P and Q.

Step-by-step explanation:

To find the equilibrium price and quantity for the concert tickets, we need to set the demand equation equal to the supply equation because at equilibrium, the quantity demanded (QD) is equal to the quantity supplied (QS). Given that the demand is QD = 2200 – 20P and the supply is QS = –500 + 75P:

2200 – 20P = –500 + 75P

Adding 20P to both sides and adding 500 to both sides gives:

2700 = 95P

Dividing both sides by 95, we get the equilibrium price (P):

P = 2700/95

P = 28.42 (approx)

Now we substitute the value of P back into either the demand or supply equation to get the equilibrium quantity (Q):

QD = QD = 2200 – 20(28.42)

QD = 2200 - 568.4

QD = 1631.6 (approx)

So, the equilibrium price is approximately $28.42, and the equilibrium quantity of tickets is approximately 1631 tickets.