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. PLEASE help I am totally lost on this

Answer 1

Answer:

a) Demand equation :$y=-\frac{2}{25}x+725$

b) Supply equation : $y=\frac{7}{100}x+350$

C) The equilibrium quantity and the equilibrium price are 2500 and $ 525 respectively

Step-by-step explanation:

We are given that  For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units.

Since decrease in unit price of $20 increase demand by 250 units

So, Slope =$\frac{-20}{250}=\frac{-2}{25}$

We are given that The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485.

Now for demand equation:

Use point slope form : $y-y_1=m(x-x_1)$

So, $y-485=\frac{-2}{25}(x-3000)\\y=-\frac{2}{25}x+725$

a)So, Demand equation : $y=-\frac{2}{25}x+725$

Now to find supply equation

We have two points (0,350) and (2500,525)

$(x_1,y_1)=(0,350)\\(x_2,y_2)=(2500,525)\\y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-350=\frac{525-350}{2500-0}(x-0)\\y-350=\frac{7}{100}x\\y=\frac{7}{100}x+350$

b) So, Supply equation : $y=\frac{7}{100}x+350$

Now to find equilibrium quantity and price equate demand and supply equation

$-\frac{2}{25}x+725=\frac{7}{100}x+350\\725-350=\frac{7}{100}x+\frac{2}{25}x\\x=2500$

So, equilibrium quantity = 2500

To find equilibrium price substitute equilibrium quantity in any equation

$y=\frac{7}{100}x+350\\y=\frac{7}{100}(2500)+350\\y=525$

C) The equilibrium quantity and the equilibrium price are 2500 and $ 525 respectively