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 500 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 2000 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) price. equilibrium quantity units equilibrium price

Explanation / Answer

demand equation

we have two points ( 3000 , 485 ) and ( 3500 , 465 )

slope m = -20 / 500 = - 1/25

y - 485 = -1/25 ( x - 3000)

demand equation p(x) = -1/25 x + 605

for supply equation we have two points

(0,350 ) and ( 2000, 525)

slope = (525 - 350 ) / 2000

slope = 7/80

equation of supply is

p(x) = 7/80 x + 350

c) set both equations equal to each other to find equilibrium quantity and price

7/80 x + 350 = -1/25 x + 605

x = 2000

equilibrium quantity = 2000 units

equilibrium price = $ 525

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