Supply & Demand: Finding the Equilibrium price and quantity

Question

At a price of $150 there is demand for 1920 items and supply of 1050 items. I had a price of 270 there is demand for 960 items in supply for 1890 items. Assuming supply and demand or linear, find the equilibrium price and quantity..

Answer 1

for demand: (1920, 150), for supply: (1050, 150)

for demand: (960, 270), for supply (1890, 270)

supply curve is upward sloping

demand curve is downward sloping

it helps to do a rough

sketch plot the points and lines

the demand curve has slope = (150-270)/(1920-960) = -120/960=-1/8

supply curve has slope = (270-150)/(1890-1050) = 120/840 = 1/7

in slope intercept form

demand curve is: y = (-1/8)(x-960) +270

supply curve is y = (1/7)(x-1050)+ 150

set them equal, solve for x and y

then y= the equilibrium price and x =equilibrium amount bought and sold

-x/8+ 120 +270 = x/7 - 1050/7 +150

(1/7 +1/8)x = 390-150+150

15x/56= 390

x = 390(56)/15= 26(56)= 1456 items = equilibrium amount bought & sold

y= (1/7)(1456-1050)+150= 406/7+150= $208= equilibrium price