The quantity demanded x each month of Russo Espresso Makers is 250 when the unit

Question

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $144. The quantity demanded each month is 1000 when the unit price is $114. The suppliers will market 700 espresso makers when the unit price is $69. At a unit price of $99, they are willing to market 2200 units. Both the supply and demand 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.

Explanation / Answer

From the given question,

linear demand equation is x = a - bP

Here x=quantity, P=price per unit

250=a-144b

1000=a-114b

solving we get a=3850, b=25

Demand equation: x=3850-25P

b) Supply equation

x=c+dP

700=c+69d

2200=c+99d

solving we get

c=-2750, d=50

supply equation: x=-2750+50P

c) equilibrium is reached when demand=supply

3850-25P=-2750+50P

solving we get P=88

replacing P we get x=1650

equilibrium quantity is 1650 units, equilibrium price is $88

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