Question

X 3.4.40-BE

Quest
Suppose the supply for a certain textbook is given by P
Find the equilibrium quantity and the equilibrium price.
and demand is given by p= - +10, where p is the price and q is the quantity. The graph of these equations is shown to the right.

Answer 1

(d) is correct

Equilibrium quantity is 4.5

Equilibrium price is 5

Explanation:

Given

`p = (1)/(4)q^2` -- supply

`p = -(1)/(4)q^2 + 10` -- demand

Required

Find the equilibrium price

Equilibrium price is when:

`Demand = Supply`

This means that (d) is correct

So, we have:

`p =p`

`(1)/(4)q^2 = -(1)/(4)q^2 + 10`

Collect Like Terms

`(1)/(4)q^2 +(1)/(4)q^2= + 10`

`(1)/(2)q^2 = 10`

Multiply both sides by 2

`2*(1)/(2)q^2 = 2*10`

`q^2 = 20`

Take the square root of both sides

`q = \sqrt{20`

`q = 4.47`

`q = 4.5` -- approximated

The equilibrium price is:

`p = (1)/(4)q^2`

Substitute value for q^2

`p= (1)/(4)*20`

`p = 5`