Question

Suppose the supply and demand for a certain textbook are given by ​supply: p equals one half q squared comma ​demand: p equals negative one half q squared plus 20 comma where p is the price and q is the quantity. Find the demand quantity and the supply quantity at a price of ​$5.

1) The number of books that are demanded at a price of $5 is? ____2) The number of books supplied at a price of $5 is? ____

Answer 1

1) The number of books that are demanded at a price of $5 is 6

2) The number of books supplied at a price of $5 is 3

Explanation:

We are given the following in the question:

Supply function:

`p =\displaystyle(1)/(2)q^2`

Demand function:

`p = -\displaystyle(1)/(2)q^2 + 20`

where p is the price and q is the quantity.

1) The number of books that are demanded at a price of $5

Putting p = 5 in the demand function we get,

`5 = -\displaystyle(1)/(2)q^2 + 20\\\\(1)/(2)q^2 = 15\\\\ q^2 = 30\\q = √(30) = 5.477 \approx 6`

2) The number of books supplied at a price of $5

Putting p = 5 in the supply function we get,

`5 =\displaystyle(1)/(2)q^2\\\\q^2 = 10\\q = √(10)\\q = 3.162 \approx 3`