In: Math
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 | $ |
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 |