At a price of S70 there is demand for 942 items and a supply

At a price of S70 there is demand for 942 items and a supply of 630 items. At a price of $120 there is demand for 792 items and a supply of 1080 items. Assuming supply and demand are linear, find the equilibrium price and quantity

Solution

Let Demand Equation

D = aP+b

942 = 70a+b

792 = 120a+b

a = -3 and b = 1152

D = -3P+1152

Similarly let supply equation be

S = cP + d

630 = 70c+d

1080 = 120c+d

b = 0 and a = 9

So, S = 9P

At Equilibrium

S = D

9P = -3P+1152

12P = 1152

P = 96

At P = 96

S = 9*96 = 864

So, Equilibrium price is $96 and Quantity is 864