Question

Given the demand equation 6x+p-50=0 and the supply equation 6x-p+14=0 where p is the unit price in dollars and x represents the quanity demanded in units of a thousand, determine the equilibrium quanity and equilibrium price

Answer 1

Answer:

The equilibrium quanity and equilibrium price is 3 Thousand units and 32 dollars respectively.

Step-by-step explanation:

Market equilibrium occurs in those markets in which the quantity demanded by consumers equals the quantity supplied by firms. In this state, the equilibrium point has its corresponding equilibrium quantity and price. That is, the equilibrium point is that point where, for a given price, the quantity supplied is equal to the quantity demanded.

The supply and demand curves represent the quantities that consumers are willing to buy and producers are willing to sell at that price respectively.

Being:

• demand equation: 6x+p-50=0 ⇒ 6x= 50 - p ⇒ $x=\frac{50 - p}{6}$

• the supply equation 6x-p+14=0 ⇒ 6x= p - 14 ⇒ $x=\frac{p-14}{6}$

Since when the market reaches equilibrium, the quantity demanded equals the quantity supplied and x representing the quantity demanded in units of thousand, then:

$\frac{50 - p}{6}=\frac{p-14}{6}$

Solving, you get:

$6*\frac{50 - p}{6}=p-14$

50 - p= p -14

50 - p +14 = p

50 +14= p + p

64= 2*p

$p=\frac{64}{2}$

P=32 dollars

This value is the equilibrium price. Replacing this value in the demand and supply equation, the equilibrium quantity is obtained, which should be the same for both cases:

• demand equation:  $x=\frac{50 - 32}{6}$ ⇒ x= 3 Thousand units

• the supply equation  $x=\frac{32-14}{6}$ ⇒ x=3 Thousand units

So, the equilibrium quanity and equilibrium price is 3 Thousand units and 32 dollars respectively.

In its graphical representation, the equilibrium point can be seen as that point where the supply and demand curves intersect. You can see this in the attached image, where the blue line represents the supply and the red line the demand.