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

a) Demand equation :
`y=-(2)/(25)x+725`

b) Supply equation :
`y=(7)/(100)x+350`

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

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 =
`(-20)/(250)=(-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=(-2)/(25)(x-3000)\\y=-(2)/(25)x+725`

a)So, Demand equation :
`y=-(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=(y_2-y_1)/(x_2-x_1)(x-x_1)\\y-350=(525-350)/(2500-0)(x-0)\\y-350=(7)/(100)x\\y=(7)/(100)x+350`

b) So, Supply equation :
`y=(7)/(100)x+350`

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

`-(2)/(25)x+725=(7)/(100)x+350\\725-350=(7)/(100)x+(2)/(25)x\\x=2500`

So, equilibrium quantity = 2500

To find equilibrium price substitute equilibrium quantity in any equation

`y=(7)/(100)x+350\\y=(7)/(100)(2500)+350\\y=525`

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