SOLUTION: The demand equation for a computer desk is p = -2x + 180, and the supply equation is p = 3x + 30. Find the equilibrium quantity x and price p. (Round your answers to one decim

Question 1126693: The demand equation for a computer desk is p = -2x + 180, and the supply equation is p = 3x + 30.

Find the equilibrium quantity x and price p. (Round your answers to one decimal place.)

(c) Find the price at which the buyer stops buying.

(d) Find the price at which the supplier stops supplying.

(e) Is there a shortage or surplus when the price is $90? How much?

(f) Is there a shortage or surplus when the price is $198? How much?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The demand equation for a computer desk is p = -2x + 180 and the supply equation is p = 3x + 30.

x represents the quantity demanded or supplied.
y represents the price at which the quantity is demanded or supplied.

Find the equilibrium quantity x and price p. (Round your answers to one decimal place.)

the equilibrium quantity and price is when the demand quantity and price is equal to the supply quantity and price.

set the equations equal to each other to get -2x + 180 = 3x + 30.
add 2x to both sides of that equation and subtract 30 from both sides of that equation to get 150 = 5x.
solve for x to get x = 150 / 5 = 30.
when x = 30, the demand price equals 120 and the supply price equals 120.
that's the equilibrium point.
price is 120 and demand is 30.

(c) Find the price at which the buyer stops buying.

the demand equation is p = -2x + 180.
when the demand is 0, the buyer has stopped buying.
set x = 0 and p becomes 180.
that's the price when the buyer stops buying.

(d) Find the price at which the supplier stops supplying.

the supply equation is p = 3x + 30.
when the supply is 0, the supplier has stopped supplying.
set x = 0 and p becomes 30.
that's the price when the supplier stops supplying.

(e) Is there a shortage or surplus when the price is $90? How much?

the demand equation is p = -2x + 180
the supply equation is p = 3x + 30

solve for x in each equation to get:

demand equation becomes x = (180 - p) / 2
supply equation becomes x = (p - 30) / 3

when p = 90, .....

demand equation becomes x = (180 - 90) / 2 = 45
supply equation becomes x= (90 - 30) / 3 = 20

there are 45 - 20 = 25 more units demanded than supplied which means there is a shortage.

(f) Is there a shortage or surplus when the price is $198? How much?

when p = 198, .....

demand equation becomes x = (180 - 198) / 2 = -9
supply equation becomes x = (198 - 30) / 3 = 56

there are 56 - (-9) = 65 more units supplied than demanded which means there is a surplus.

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