Supply & Demand

Question

In supply (and demand) problems, y is the number of items the supplier will produce (or the public will buy) if the price of the item is x. For a particular product:

The supply equation is:  y=8x+307 

The demand equation is:  y=-6x+741

Solve this system of equations to determine the point at which the two lines intersect. Give your answer as an ordered pair.

The two lines intersect at (first answer here)

What is the selling price when supply and demand are in equilibrium?

When supply and demand are in equilibrium, the selling price per item is $ (second answer here)

What is the number of items in the market when supply and demand are in equilibrium?

There are (third answer here) items in the market when supply and demand are in equilibrium.

Answer 1

y= 8x +307 is the supply curve

y = -6x +741 is the demand curve

set them equal

8x + 307 = -6x +741

14x = 741-307 = 434

x = 434/14 = 31

y =-6(31)+741 = 741-186

y = 555

(x,y) = (31, 555)

at the equilibrium price, $5.55, 31 units are bought and sold

8(31)+307

= 248+307

= 555