The national demand and price for a certain type of energy-efficient exhaust fan are related by P=480-7/4q, where p is the price (in dollars) and q is the demand (in thousands). The price and supply of the exhaust fans are related by p =5/4q, where p is the price (in dollars) and q is the supply (in thousands) of exhausts fans. Find the price for a demand of 140,000 exhaust fans. Find the demand of exhausts fans at a price of $102 Find the supply when the price is $225 Graph p=480-7/4q and p=5/4q on the same set of axes Find the equilibrium quantity Find the equilibrium price
Solution:
1- Find the price for a demand of 140,000 exhaust fans.
P=480-7/4q, where p is the price (in dollars) and q is the demand (in thousands). Then q=140 substitute:
p= 480-(7/4)140=$235
2-Find the demand of exhausts fans at a price of $102
P=480-7/4q , p=$102 substitute and solve for q
102=480-(7/4)q, -378=-(7/4)q, q=216 or 216,000 exhaust fans
3-Find the supply when the price is $225
The price and supply of the exhaust fans are related by p =5/4q
p=$225 substitute $225=(5/4)q, q=180 or 180,000 exhaust fans
4-Graph p=480-7/4q and p=5/4q on the same set of axes Find the equilibrium quantity Find the equilibrium price
in this step equate p to p and solve for q. Note that the two equations above represent straight lines with q being the x axis coordinate and p represent the y axis
p=480-7/4q and p=5/4q substitute 5/4q for P
5/4q=480-7/4q, 5/4q+7/4q=480, 12/4q=480, 3q=480,
q=160 is the equilibrium quantity of exhaust fans that is 160,000 fans
The equilibrium price would be:
Substitute in equation p=(5/4)q=(5/4)160=$200
or p=480-7/4q=480-(7/4)160=$200
please note that the supply and demand curves intersect each others at one point (p,q) or ( 160, 200) and the point of intersection represent the equilibrium quantities
