The quantity demanded of a certain brand of DVD player is 3,300/wk when the unit price is $455.00. For each decrease in unit price of $5.00 below $455.00, the quantity demanded increases by 100 units. The suppliers will not market any DVD players if the unit price is $350.00 or lower. But at a unit price of $374.00, they are willing to make available 2,400 units in the market. The supply equation is also known to be linear. Find the equilibrium quantity and price.

Question

Quizplus · Accepted Answer

To find the equilibrium quantity and price, we need to set the quantity demanded equal to the quantity supplied:
Quantity demanded = Quantity supplied
3300 - 100(P-455) = S
where S is the supply equation.
We know that S = 2400 when P = $374, so we can substitute in to solve for the slope:
2400 = 3300 - 100(P-455)
-900 = -100(P-455)
9 = P-455
P = $464
Now we can use either the demand or supply equation to find the equilibrium quantity. Using the demand equation:
3300 - 100(P-455) = S
3300 - 100(464-455) = S
3200 = S
Therefore, the equilibrium price is $464 and the equilibrium quantity is 3200.

The Quantity Demanded of a Certain Brand of DVD Player