Question

The demand for commodity X is represented by the equation P = 100 - 2Q and supply by the equation P = 10 + 4Q. If demand changes from P = 100 - 2Q to P = 130 - Q, the new equilibrium quantity is:

Answer 1

Answer:

The new equilibrium quantity is 24 units of the commodity X.

Explanation:

In order to calculate the equilibrium quantity we must solve the system of equations. The system will be composed of the supply equation and the new demand equation:

$\left \{ {{P=10+4Q} \atop {P=130-Q}} \right.$

There are several ways to solve the system. Here'll we'll use substitution. We substitutute P in the supply equation for the new demand equation. So we have:

$130-Q=10+4Q$

We group terms on the same side of the equation:

$4Q+Q= 130-10$ ⇒ $5Q=120$

We divide each member of the equation by 5:

$Q=120/5=24$

So the new equilibrium quantity is 24 units of the commodity X.

Answer 2

The new equilibrium quantity is 24.

Important information:

The demand for commodity X is represented by the equation P = 100 - 2Q and supply by the equation P = 10 + 4Q. If demand changes from P = 100 - 2Q to P = 130 - Q,

The calculation  of new equilibrium quantity is:

130- Q = 10 + 4Q

130 - 10 = 4Q + Q

120 = 5Q

Q = 24

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