The quantity demanded x each month of russo espresso makers is 250 when the unit price p is $138. the quantity demanded each month is 1000 when the unit price is $108. the suppliers will market 700 espresso makers when the unit price is $72. at a unit price of $102, 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.

units
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(a)

(b)

(c)

Step-by-step explanation:

(a) For the demand equation D(q) we have

P1: 138 Q1: 250

P2: 108 Q2: 1000

We can find m, which is the slope of the demand equation,

and then we find b, which is the point where the curve intersects the y axis.

We can do it by plugging one point and the slope into the line equation form:

With b: 148 and m: -1/25 we can write our demand equation D(q)

(b) to find the supply equation S(q) we have

P1: 102 Q1: 2200

P2: 102 Q2: 700

Similarly we find m, and b

And we can write our Supply equation S(q):

(c) Now we may find the equilibrium quantity q* and the equilibrium price p* by writing D(q)=S(q), which means the demand equals the supply in equilibrium:

We plug 1500 as q into any equation, in this case S(q) and we get:

Which is the equilibrium price p*.