Question

The quantity demanded of a certain electronic device is 1000 units when the price is $665. At a unit price of $640, demand increases to 1200 units. The manufacturer will not market any of the device at a price of $90 or less. However for each $50 increase in price above $100, the manufacturer will market an additional 1000 units. Assume that both the supply equation and the demand equation are linear.

(a) Find the supply equation.

(b) Find the demand equation

(c) Find the equilibrium price.

(d) Find the equilibrium quantity

Answer 1

Given that manufacturer will not supply any device at a price of $90

And For $150 He would supply 1000 units

So we have given two points (0, 90) and (1000, 150)

Equation of Supply, y = mx + b

P = mx + b

m (slope of line) = change in y/ change in x

= 150 - 90/ 1000 - 0

= 60/1000 or 0.06

Putting the value of point (0, 90) and m in equation

90 = 0.06(0) + b

b = 90

Hence, the supply equation

P = 0.6x + 90

(b) Similiary, we have given two points for demand equation (1000, 665) and (1200, 640)

m (slope for demand equation) = (640 - 665)/ (1200 - 1000)

= - 25 / 200

= - 0.125

Putting values of point (1000, 665) and m in demand equation.

665 = - 0.125(1000) + b

665 + 125 = b

b = 790

Hence, the demand equation

P = - 0.125x + 790

C) At the Point of equilibrium Demand equation equals to Supply equation

-0.125x + 790 = 0.06x + 90

790 - 90 = 0.06x + 0.125x

700 = 0.185x

X = 3784 approx

Putting value of x in supply equation

We get P = $317

So, Equilibrium Quantity = 3784

Equilibrium Price = 317