The quantity demanded x of a certain brand of DVD player is

The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485. For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is $350 or lower. But at a unit price of $525, they are willing to make available 2500 units in the market. The supply equation is also known to be linear. (a) Find the demand equation P(x)- (b) Find the supply equation p(x)- (c) Find the equilibrium quantity and the equilibrium price (c) Find the eqium quantity and the equibrium price. units equilibrium quantity equilibrium price

Solution

a. Demand Equation can be calculated as follows:

Demand = D(x) with x = quantity demanded
point (3000,485) is a point of the line and slope of the line = - 20 /250
D(x) - 485 = -20/250(x - 3000)
D(x) = 485 + 240 - 0.08x
D(x) = 725 - 0.08x (it is the weekly price-demand)

b. Supply equataion can be calculated as follows:
Supply =S(x)
point (0,350) and (2500,525) are points of the line
slope = (525-350)/2500 = 0.07
S(x) - 350 = 0.07x
S(x) = 350 + 0.07x

c. To find the equilibrium price and demand:

725 - 0.08x = 350 + 0.07x
375 = 0.15x
x = 2500

Equilibrium Quantity = 2500

Equilibrium quantity demanded = 0.07*2500+350 = $525