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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.

x 3440BE 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 class=

Respuesta :

MrRoyal

Answer:

(d) is correct

Equilibrium quantity is 4.5

Equilibrium price is 5

Step-by-step explanation:

Given

[tex]p = \frac{1}{4}q^2[/tex] -- supply

[tex]p = -\frac{1}{4}q^2 + 10[/tex] -- demand

Required

Find the equilibrium price

Equilibrium price is when:

[tex]Demand = Supply[/tex]

This means that (d) is correct

So, we have:

[tex]p =p[/tex]

[tex]\frac{1}{4}q^2 = -\frac{1}{4}q^2 + 10[/tex]

Collect Like Terms

[tex]\frac{1}{4}q^2 +\frac{1}{4}q^2= + 10[/tex]

[tex]\frac{1}{2}q^2 = 10[/tex]

Multiply both sides by 2

[tex]2*\frac{1}{2}q^2 = 2*10[/tex]

[tex]q^2 = 20[/tex]

Take the square root of both sides

[tex]q = \sqrt{20[/tex]

[tex]q = 4.47[/tex]

[tex]q = 4.5[/tex] -- approximated

The equilibrium price is:

[tex]p = \frac{1}{4}q^2[/tex]

Substitute value for q^2

[tex]p= \frac{1}{4}*20[/tex]

[tex]p = 5[/tex]

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