Question

Suppose the supply and demand for a certain textbook are given by supply: p = 1/3 q2 , demand: p = -- 1/3 q2 + 30, 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

Answer:

1) 8

2) 3

Step-by-step explanation:

The supply and demand functions are, respectively:

$p=\frac{1}{3}q^2\\p=30-\frac{1}{3}q^2$

Applying p=$5 gives us the supplied and demanded quantities (q).

For the supply function:

$5=\frac{1}{3}q^2\\q=3.87$

For the demand function:

$5=30-\frac{1}{3}q^2\\q=8.66$

Rounding down to the next whole unit:

1) The number of books that are demanded at a price of $5 is 8

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