Question

The market equilibrium point for a product is reached when 7000 units are produced and sold at $25 per unit. The manufacturer will not produce any units at the price of $3, and the customers will not buy any at the price of $70. Find the supply and demand equations, assuming they are linear. The equations should express price p in terms of quantity q.

Answer 1

Supply equation is p=(22/7000)*q+3

The demand equation is p=-(45/7000)*q+70

Explanation:

Let supply equation be P=aq+b

Let demand equation be P=cq+d

P=price per unit while q=quantity manufactured and sold

According to the information given the producer will produce zero unit at the price of $3

In other words,when p=$1,q=0

3=a(0)+b

b=3

At equilibrium q=7000 units and p=$25

Therefore,25=7000a+3

25-3=7000a

22=7000a

a=22/7000

Supply equation is p=(22/7000)*q+3

According to data given consumers will demand zero unit at the price of $70

p=$70 when q =0

Supply equation is given as

p=2

P=cq+d

70=c(0)+d

d=70

at equilibrium q=7000,p=25

25=7000c+70

25-70=7000c

-45=7000c

c=-45/7000

Demand equation is given as :

p=-(45/7000)*q+70