Problema Solution
The quantity demanded of a certain brand of DVD player is 3000/wk when the unit price 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 $181 or lower. But at a unit price of $406, they are willing to make available 2500 units in the market. The supply equation is also known to be linear.
Answer provided by our tutors
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)
Supply =S(x)
point (0,300) and (2500,525) are points of the line
slope = (525-300)/2500 = 0.09
S(x) - 300 = 0.09x
S(x) = 300 + 0.09x
to get the equilibrium
725 - 0.08x = 300 + 0.09x
425 = 0.17x
x = 2500 = quantity demanded at price = $525