Find the Demand Equation

Question

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 500 when the unit price is $160. The suppliers will market 750 espresso makers if the unit price is $110. At a unit price of $120, they are willing to market 1500 units. Both the demand and supply equations are known to be linear.

 

Find the Demand Equation

p=

 

Find the Supply Equation 

p=

 

Find the equilibrium quantity and the equilibrium price.

Equilibrium quantity:

Price:

 

Answer 1

NOTE:

We know that both supply and demand functions are linear. The equations will take the form of y=mx+b, where m = slope of the line and b = y-intercept of the line. This is called the "slope-intercept" form.

Keep in mind in economics, we usually set price (P) on the y-axis. Quantity (Q) is usually on the x-axis.


STEP 1: Turn the data into useful information.

The first sentence: The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $170.

Therefore, this is a point on the demand curve, where D1 and D2 are points on the demand function.

D1 (quantity demanded, price) = (250,170)

Repeat for the other point on the demand curve. You will get:

D1(Qd,P) = (250, 170)
D2(Qd,P) = (500, 160)


STEP 2: Determine the demand curve function.

You can find the slope (m) for each demand curve by using the following formula:

m = (y2-y1)/(x2-x1)

For the demand curve,
D1(Qd,P) = (250, 170)
D2(Qd,P) = (500, 160)

m = (170 - 160) / (250-500) = 10 / (-250) = -1/25

The y-intercept (b) for the demand curve comes from rearranging and solving for b in the slope-intercept form of a line: b = y-mx. Let's use point D1(250,170)

b = y - mb = 170 - (-1/25)*(250) = 170 - (-10) = 170 + 10 = 180

Demand curve will be:
D(x) = 180 - x/25


STEP 3: Repeat the above process for the supply curve.

S1(Qs,P) = (750, 110)
S2(Qs,P) = (1500, 120)

S(x) = 100 + x/75


STEP 4: Set D(x)=S(x). Find the equilibrium number of units (x). Plug x into either demand or supply. Determine price.

You should get:
Q = 150 un
P = $174/un