The quantity demanded x each month of Russo Espresso Makers

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $138. The quantity demanded each month is 1000 when the unit price is $108. The suppliers will market 700 espresso makers when the unit price is $66. At a unit price of $96, they are willing to market 2200 units. Both the supply and demand equations are known to be linear.

(a) Find the demand equation.
p =

(b) Find the supply equation.
p =

(c) Find the equilibrium quantity and the equilibrium price.

Solution

supply curve points are ( 66,700) (96,2200)

demand curve points are ( 138,250) ( 108,1000)

finding equation of each curve

slope of supply curve is (2200 - 700 ) / (96 - 66 )

m = 50

b) supply equation is S(p) = -2600 +50p

finding equation of demand curve

slope = (1000- 250 ) / (108-138)

m = -25

a) D(p) = 3700 - 25p

c) equillibrium occurs when demand = supple

setting both equatiosn equal to each other

3700 - 25p =  -2600 +50p

3700 + 2600 = 50p + 25p

p = 84

equillibrium price is $ 84

equillibrium quantity is 3700 - 25(84)

= 1600 units