Answer to Question #150008 in Math for enny

Question

The demand and supply functions of a goods are given by:
p=-4QD+120
p=1/2QS+28
where P, QD, and QS denote the price, quantity demanded and quantity supplied respectively. Find the equilibrium price and quantity.

Answer 1

$$p=-4QD+120=>4QD=120-p$$

$$=>QD=30-\dfrac{1}{4}p$$

$$p=\dfrac{1}{2}QS+28=>\dfrac{1}{2}QS=p-28$$

$$=>QS=2p-5$$

In equilibrium Qd = Qs

$$30-\dfrac{1}{4}p=2p-56$$

$$\dfrac{9}{4}p=86$$

$$p=38.22$$

$$QD=QS=22$$