The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $125.00. The quantity demanded each month is 1,100 when the unit price is $91.00. The suppliers will market 700 espresso makers if the unit price is $74.00 or lower. At a unit price of $109.00, they are willing to make available 2,450 units in the market. Both the demand and supply equations are known to be linear. Find the equilibrium quantity and the equilibrium price.
A) equilibrium quantity 1,250 units; equilibrium price $85.00
B) equilibrium quantity 1,250 units; equilibrium price $90.00
C) equilibrium quantity 1,140 units; equilibrium price $90.00
D) equilibrium quantity 1,140 units; equilibrium price $85.00

Question

Quizplus · Accepted Answer

To find the equilibrium quantity and price, we first determine the equations for demand and supply. For demand, using the points (125, 250) and (91, 1100), we find the slope: (1100-250)/(91-125) = 850/-34 = -25. The demand equation form is Qd = mP + b. Substituting one point into the equation gives 250 = -25(125) + b, solving for b gives b = 3375. Thus, the demand equation is Qd = -25P + 3375. For supply, using points (74, 700) and (109, 2450), the slope is (2450-700)/(109-74) = 1750/35 = 50. The supply equation form is Qs = mP + b. Substituting one point gives 700 = 50(74) + b, solving for b gives b = -300. Thus, the supply equation is Qs = 50P - 300. Setting Qd = Qs to find the equilibrium, we get -25P + 3375 = 50P - 300. Solving for P gives P = $85. Substituting P = $85 into either equation gives the equilibrium quantity of 1,250 units.

The Quantity Demanded Each Month of Russo Espresso Makers Is