find the demand and supply equation

Question

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $160; the quantity demanded each month is 750 when the unit price is $140. The suppliers will market 750 espresso makers if the unit price is $100. At a unit price of $130, they are willing to market 3000 units. Both the demand and supply equations are known to be linear.

 

Find the demand equation.

p=?

 

Find the supply equation.

p=?

 

Find the equilibrium quantity and the equilibrium price.
equilibrium quantity is      ?      units
equilibrium price      ?       

Answer 1

With the information provided we're going to have to work on the basis that the S&D curves are linear.

 

We're given 2 points for both the supply curve and the demand curve.  Quantity (Q) is the X-axis and Price (P) is the Y-axis.

 

Supply Curve Points: (750, $100) & (3000, $130)

Demand Curve Points: (250, $160) & (750, $140)

 

We can use the standard linear equation formula y=m*x+b where m is slope and b is intercept.

 

m(Supply Curve) = ($130-$100) / (3000-750) = 0.01333 $/unit

b(Supply Curve) = $100-(0.013333$/unit)*750units = $90

 

Linear Supply Curve Formula: QS(Quantity Supplied) = -6750 + 75P

 

m(Demand Curve) = ($140-$160) / (750-250) = -0.04$/unit

b(Demand Curve) = $160-(-0.04$/unit)*250units = $170

 

Linear Demand Curve Formula: QD(Quantity Demanded) = 4250 - 25P

 

Since the equilibrium quantity (Q) and Price (P) in an ideal micro-econ market is determined by the point of intersection of the supply and demand curves we simply have to substitute one equation into the other.

 

-6750+75P = 4250 - 25P simplifying this yields 100P=11000 so Equilibrium Price is P = $110

 

We can now substitute the equilibrium price into either our supply or demand equation to determine the equilibrium quantity.

 

Q(Equilibrium)=4250-25*(110) = 1500 units