The quantity demanded of a certain brand of DVD player is 3,500/wk when the unit price is $460. For each decrease in unit price of $20 below $460, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is $400 or lower. But at a unit price of $445, they are willing to make available 500 units in the market. The supply equation is also known to be linear. Find the equilibrium quantity and the equilibrium price.
A) equilibrium quantity 2,000 units; equilibrium price $585
B) equilibrium quantity 400 units; equilibrium price $585
C) equilibrium quantity 2,000 units; equilibrium price $580
D) equilibrium quantity 400 units; equilibrium price $580

Question

Quizplus · Accepted Answer

To find the equilibrium quantity and price, we need to find the point where the quantity demanded and quantity supplied are equal.

Let Q be the quantity and P be the price.

From the information given, we know that:

- Q = 3500 - 250(P-460) for P between $460 and $445
- Q = 500 for P = $445
- Q = 0 for P ≤ $400

We can write the supply equation as a linear equation. Let's call it S:

- S = mP + b

To find the slope (m), we use the two points ($445, 500) and ($460,3500). The slope is:

- m = (500 - 3500)/($445-$460) = 200/3

To find the y-intercept (b), we use the point ($445, 500). The equation becomes:

- S = (200/3)P - (5800/3)

Now we can set Q = S and solve for P and Q:

- 3500 - 250(P-460) = (200/3)P - (5800/3)

Solving for P, we get P = $580.17. Plugging this back into either Q = 3500 - 250(P-460) or Q = (200/3)P - (5800/3), we get Q = 1999.67 or Q = 2000 (rounded to the nearest whole number). Therefore, the equilibrium quantity is 2000 units and the equilibrium price is $580.

The correct answer is C.

The Quantity Demanded of a Certain Brand of DVD Player