Question

Assume that demand for a commodity is represented by the equation

P = 75 - 2Qd
Supply is represented by the equation
P = 4Qs - 15
where Qd and Qs are quantity demanded and quantity supplied, respectively, and P is price.
a. Using the equilibrium condition Qs = Qd, determine equilibrium price.
b. Now determine equilibrium quantity.

Answer 1

How are quantity demanded (QD) and price related?

Answer 2

(a) $45

(b) 15 units

Step-by-step explanation:

Given that,

Demand equation: P = 75 - 2Qd

Supply equation: P = 4Qs - 15

Qd and Qs are quantity demanded and quantity supplied,

(a) At equilibrium,

Qs = Qd = Q*

P = 75 - 2Q*

Q* = (75 - P) ÷ 2

P = 4Q* - 15

P = 4[(75 - P) ÷ 2] - 15

P = 150 - 2P - 15

3P = 135

P* = 45

Therefore, equilibrium price P* = 45

(b) Equilibrium quantity,

Q* = (75 - P) ÷ 2

= (75 - 45) ÷ 2

= 15