The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $136. The quantity demanded each month is 1000 when the unit price is $106. The suppliers will market 750 espresso makers when the unit price is $72 or higher. At a unit price of $92, they are willing to market 2250 units. Both the supply and demand equations are known to be linear. Find the equilibrium quantity and the equilibrium price.

Question

The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $136. The quantity demanded each month is 1000 when the unit price is $106. The suppliers will market 750 espresso makers when the unit price is $72 or higher. At a unit price of $92, they are willing to market 2250 units. Both the supply and demand equations are known to be linear. Find the equilibrium quantity and the equilibrium price.

Answer 1

To find the equilibrium quantity and price, we need to determine the point where the demand and supply curves intersect. Since both the demand and supply equations are linear, we can derive their equations using the given information.

Let's start with the demand equation. Given that the quantity demanded is 250 at a unit price of $136 and 1000 at a unit price of $106, we can calculate the demand equation as follows:

Slope (m) = (change in quantity) / (change in price)
= (1000 - 250) / ($106 - $136)
= 750 / -$30
= -25

Using the point-slope form of a linear equation (y - y1) = m(x - x1), we can use either of the two points (250, $136) or (1000, $106) to find the demand equation. Let's use the first point:

Quantity demanded (Qd) - 250 = -25(Unit price - $136)

Simplifying:
Qd = -25(Unit price) + 3400

Next, let's calculate the supply equation. We know that the suppliers will market 750 espresso makers when the unit price is $72 or higher, and 2250 units at a unit price of $92. Using similar calculations, we can find the supply equation:

Slope (m) = (change in quantity) / (change in price)
= (2250 - 750) / ($92 - $72)
= 1500 / $20
= 75

Using the point-slope form and using the point (750, $72):

Quantity supplied (Qs) - 750 = 75(Unit price - $72)

Simplifying:
Qs = 75(Unit price) - 4950

Now that we have both the demand and supply equations, we can set them equal to each other to find the equilibrium quantity and price:

-25(Unit price) + 3400 = 75(Unit price) - 4950

Rearranging the equation:
100(Unit price) = 8350

Dividing both sides by 100:
Unit price = $83.50

To find the equilibrium quantity, we can substitute the unit price back into either the demand or supply equation. Let's use the demand equation:

Qd = -25(Unit price) + 3400
= -25($83.50) + 3400
= -2087.50 + 3400
= 1312.50

Therefore, the equilibrium quantity is 1312.50 espresso makers per month, and the equilibrium price is $83.50 per unit.

r+e3

To find the equilibrium quantity and price, we need to determine the point where the demand and supply curves intersect. Since both the demand and supply equations are linear, we can derive their equations using the given information.