The quantity demanded x of a certain brand of DVD player is 3000/week when the u

Question

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

Explanation / Answer

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

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