Question

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $170; the quantity demanded each month is 750 when the unit price is $150. The suppliers will market 750espresso makers if the unit price is $110. At a unit price of $130, they are willing to market 2250 units. Both the demand and supply equations are known to be linear.

(a) Find the demand equation.
p =

(b) Find the supply equation.
p =

(c) Find the equilibrium quantity and the equilibrium price.

equilibrium quantity		units
equilibrium price	$

Answer 1

Given that,

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $170;

the quantity demanded each month is 750 when the unit price is $150.

The suppliers will market 750espresso makers if the unit price is $110.

At a unit price of $130, they are willing to market 2250 units.

Both the supply and demand equations are linear.

The general equation of linear form is ; where m is slope

(a) Demand Equation :

Let the general equation be

Here, x is the number of units ;

y is the price

So,

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $170

That is, when x=250 ; y=$ 170

Substitute x=250 and y=$ 170 in

Similarly, the quantity demanded each month is 750 when the unit price is $150.

That is , x=750 ; y=$ 150

Substitute in

Subtracting with

So, slope is

Substitute m in

Substitute b and m in

Therefore,

The demand curve is

(b) Supply Curve:

Let the general equation be

Here, x is the number of units ;

y is the price

So,

The suppliers will market 750espresso makers if the unit price is $110.

That is, when x=750 y=$ 110

Substitute x=750 and y=$110 in

Similarly,At a unit price of $130, they are willing to market 2250 units.

That is, when x=2250 ; y=$ 130

Substitute x=2250 and y=$ 130 in

Subtract with

So, substitute m=1/75 in

Substitute b and m in

Therefore,

The supply equation is

(c) Equilibrium Quantity and Equilibrium Price:

Equilibrium occurs when demand is equal to supply

Equating both the suppply and demand equations

and

Equilibrium Quantity = 1500

Substitute x=1500 in

Equilibrium Quantity = 120

Therefore,

Equilibrium Quantity	1500	Units
Equilibrium Price	$	120