Question

A certain product has supply and demand functions given by p equals 40 q plus 300p=40q+300 and p equals 5300 minus 60 q commap=5300−60q, respectively.
a. if the price p is ​$11001100​, how many units q are supplied and how many are​ demanded?
b. what price gives market​ equilibrium, and how many units are demanded and supplied at this​ price?

Answer 1

Answer: a. Qs=20, Qd=70

b. P=$2300, Q=50

Explanation:

a. Supply function: $p=40q+300$

Demand function: $p=5300−60q$

When the price is $1100,

Supply=$P= 40q+300 1100=40q+300 800=40q 20=qs$

Therefore, quantity supplied is 20 units.

Demand=$P= 5300 - 60q 1100=5300-60q60q=5300-110060q=4200qd=70$

therefore, quantity demand is 70 units.

b. Equilibrium is given by demand = supply

$\frac{P-300}{40} =\frac{5300-P}{60} 6P-1800=21200-4P 10P=23000 P= 2300$

Substituting P into the supply equation we get,

$p=40q+300 2300=40q_300 2000=40q 50=q$

Therefore, equilibrium price is $2300 and quantity is 50 units.