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

Step-by-step 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 </p><p>1100=5300-60q</p><p>60q=5300-1100</p><p>60q=4200</p><p>qd=70`

therefore, quantity demand is 70 units.

b. Equilibrium is given by demand = supply

`(P-300)/(40) =(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.