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.

(a) $45

(b) 15 units

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