Question

A baseball team plays in a stadium that holds 58,000 spectators. With ticket prices at $10, the average attendance had been 27,000. When ticket prices were lowered to $8, the average attendance rose to 33,000. (a) Find the demand function (price p as a function of attendance x), assuming it to be linear.

Answer 1

Answer: The demand function is:

`P = 19 - (1)/(3000) Q`

Step-by-step explanation:

The linear demand function is as follows:

P = a - bQ ⇒ (1)

Where,

p - price

Q - Quantity

a - intercept value

b - slope coefficient

From the given data, we have the following two equations:

10 = a - b(27,000) ⇒ (2)

8 = a - b(33,000) ⇒ (3)

By solving the equations (2) and (3), we get

a = 19 and b =
`(1)/(3000)`

So, the demand function is as follows:

putting the values of 'a' and 'b' in equation (1), we get

`P = 19 - (1)/(3000) Q`

Answer 2

Answer:P(x) = -3000
`*`(x) + 57000

Explanation:

Let the demand function be given by p(x)

Let P(x) be the demand for the match at price x

P(x) = a
`*`(x) + b

27000 = a
`*`(10) + b

33000 = a
`*`(8) + b

Solving we get a = -3000 and b = 57000

Thus P(x) = -3000
`*`(x) + 57000