The quantity demanded x each month of Russo Espresso Makers

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $140; the quantity demanded each month is 500 when the unit price is $130. The suppliers will market 750 espresso makers if the unit price is $40. At a unit price of $70, they are willing to market 3000 units. Both the demand and supply equations are known to be linear (a) Find the demand equation (b) Find the supply equation (c) tind he Find the equilibrium equilibrium quantity equilibrium price (c) Find the equilibrium quantity and the equilibrium price Xunits

Solution

(a) The typical linear demand equation is as follows -

Q = a - bP

Where,

Q = quantity demanded

P = Price

b = Slope

a = Y-intercept

In the given case, two price and quantity points are given.

Quantity is taken on X-axis and price is taken on Y-axis.

So, points can be written as follows -

(250, $140) and (500, $130)

Calculating Slope -

b = (y₂ - y₁)/(x₂ - x₁) = (130 - 140)/(500 - 250) = -0.04

Using point - slope equation,

y - 140 = -0.04(q - 250)

y = -0.04q + 10 + 140

y = -0.04q + 150

Replacing y with p as y represent price in given case.

p = -0.04q + 150

The demand equation is -: p = -0.04q + 150

(b) The typical linear supply equation is as follows -

Q = a + bP

Where,

Q = quantity supplied

P = Price

b = Slope

a = Y-intercept

In the given case, two price and quantity points are given.

Quantity is taken on X-axis and price is taken on Y-axis.

So, points can be written as follows -

(750, $40) and (3,000, $70)

Calculating Slope -

b = (y₂ - y₁)/(x₂ - x₁) = (70 - 40)/(3,000 - 750) = 0.01

using the point-slope formula for a line -

y - 40 = 0.01(q - 70)

y - 40 = 0.01q - 0.7

y = 0.01q + 39.3

Replacing y with p as y represent price in given case.

p = 0.01q + 39.3

The supply equation is -: p = 0.01q + 39.3

(c) Equilibrium is attained when supply equals demand.

Equating demand and supply equations to ascertain equilibrium quantity -

-0.04q + 150 = 0.01q + 39.3

-0.05q = -110.7

q = 2,214

The equilibrium quantity is 2,214 units.

Calculating equilibirum price -

p = -0.04q + 150 = (-0.04*2,214) + 150 = -88.56 + 150 = 61.44

The equilibrium price is $61.44.