Respuesta :
Answer:
a) Demand equation :[tex]y=-\frac{2}{25}x+725[/tex]
b) Supply equation : [tex]y=\frac{7}{100}x+350[/tex]
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 =[tex]\frac{-20}{250}=\frac{-2}{25}[/tex]
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 : [tex]y-y_1=m(x-x_1)[/tex]
So, [tex]y-485=\frac{-2}{25}(x-3000)\\y=-\frac{2}{25}x+725[/tex]
a)So, Demand equation : [tex]y=-\frac{2}{25}x+725[/tex]
Now to find supply equation
We have two points (0,350) and (2500,525)
[tex](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[/tex]
b) So, Supply equation : [tex]y=\frac{7}{100}x+350[/tex]
Now to find equilibrium quantity and price equate demand and supply equation
[tex]-\frac{2}{25}x+725=\frac{7}{100}x+350\\725-350=\frac{7}{100}x+\frac{2}{25}x\\x=2500[/tex]
So, equilibrium quantity = 2500
To find equilibrium price substitute equilibrium quantity in any equation
[tex]y=\frac{7}{100}x+350\\y=\frac{7}{100}(2500)+350\\y=525[/tex]
C) The equilibrium quantity and the equilibrium price are 2500 and $ 525 respectively
