Answer to Question #290325 in Calculus for helenabebe

Question

. Given market demand Qd = 50 - P, and market supply P = Qs + 5

A) Find the market equilibrium price and quantity?

B) What would be the state of the market if market price was fixed at Birr 25 per unit?

C) Calculate and interpret price elasticity of demand at the equilibrium point.

Answer 1

A. Qd= 50 - P, P = Qs + 5 -> Qs = P - 5. 

The market equilibrium price and quantity are:

Qd = Qs,

50 - P = P - 5,

2P = 55,

P = $27.5.

Q = 27.5 - 5 = 22.5 units.

B. If market price was fixed at $25 per unit, then there will be a shortage (Qd > Qs).

C. Price elasticity of demand at the equilibrium point is:

$Ed = -1×\frac{27.5}{22.5} = -1.22,$

so the demand is elastic.