Question

22 question (4 points) suppose that the demand for a concert is represented by the following equation, where p is the price of concert tickets and $q_d$ is the quantity of tickets demanded. $q_d = 2200 - 24p$. the supply of tickets is represented by the equation where p is the price of the tickets and $q_s$ is the quantity of tickets supplied. $q_s=-500 + 77p$. in the questions below, give all answers to two decimals. 1st attempt part 1 (2 points) find the equilibrium price and quantity of tickets sold. price: $ quantity: part 2 (2 points) calculate the consumer surplus and producer surplus at the equilibrium price and quantity. use the formula for the area of a triangle (1/2 * base * height) to calculate each value. cs: $ ps: $

Explanation:

Step1: Set demand equal to supply

Set $Q_D = Q_S$. So, $2200 - 24P=- 500+77P$.

Step2: Solve for equilibrium price $P$

First, combine like - terms:
$2200 + 500=77P + 24P$.
$2700 = 101P$.
Then, $P=\frac{2700}{101}\approx26.73$.

Step3: Solve for equilibrium quantity $Q$

Substitute $P = 26.73$ into the demand function $Q_D=2200 - 24P$.
$Q=2200-24\times26.73=2200 - 641.52 = 1558.48$.

Step4: Find the price - intercept of the demand curve

Set $Q_D = 0$ in $Q_D=2200 - 24P$. Then $24P = 2200$, and $P_D=\frac{2200}{24}\approx91.67$.

Step5: Find the price - intercept of the supply curve

Set $Q_S = 0$ in $Q_S=-500 + 77P$. Then $77P = 500$, and $P_S=\frac{500}{77}\approx6.49$.

Step6: Calculate consumer surplus (CS)

$CS=\frac{1}{2}\times(91.67 - 26.73)\times1558.48=\frac{1}{2}\times64.94\times1558.48\approx50791.97$.

Step7: Calculate producer surplus (PS)

$PS=\frac{1}{2}\times(26.73 - 6.49)\times1558.48=\frac{1}{2}\times20.24\times1558.48\approx15763.73$.

Answer:

Part 1:
Price: $\$26.73$
Quantity: $1558.48$
Part 2:
CS: $\$50791.97$
PS: $\$15763.73$